ccccx.tex

\section{CCCCR}
\label{sCCCCR}

\hypertarget{sCCCCRhy}{This}
module is used to produce the standard CCCC interface files
ISOTXS, BRKOXS, and DLAYXS from
\hyperlink{sGROUPRhy}{GROUPR} output.

This chapter describes the CCCCR module in NJOY2016.0.

\subsection{Introduction}
\label{ssCCCCR_intro}

The CCCC interface files (commonly pronounced ``four cees'') were
developed by the Committee for Computer Code Coordination for the
US Fast Breeder Reactor Program.\index{CCCC interface files}
\index{Fast Breeder Reactor Program}  When
the members of this committee started work in 1970,
they noted that because of the large variety of
computers and computer systems, computer codes developed at one
laboratory were often incompatible with computers at other
laboratories.  Major rewrites of codes or wasteful duplicate efforts
were common.  They hoped to create a system that would allow different
laboratories to create codes that could be moved to other sites more
easily.  Moreover, they hoped that the codes developed at different
laboratories could easily work together, thereby achieving larger and
more capable calculational systems than any one laboratory could hope to
develop by itself.

Much of the following discussion was developed long ago, and so some
of the code examples conform to FORTRAN-77.  We assume the reader can
easily convert this into modern Fortran.

They approached this problem in two ways.  First, they tried to establish
general programming standards that would make computer codes more
portable.  And second, they tried to establish standard interface files
for reactor physics codes that would make it easier for computer codes to
communicate with each other.  The results of this work appeared in fullest
form as the CCCC-III and CCCC-IV standards\cite{CCCC3,CCCC4}.
\index{CCCC format!CCCC-III}
\index{CCCC format!CCCC-IV}

The MINX\index{MINX} code\cite{MINX}, which was the predecessor of NJOY,
was able to produce libraries \cite{LIBIV}\index{LIB-IV} that used
the CCCC-III interface formats.  The LINX\index{LINX} and
BINX\index{BINX} library management codes\cite{LINXBINX} and the
CINX\index{CINX} group collapse code\cite{CINX} were also released
during this period.  Major codes that used data in CCCC-format
included SPHINX\cite{SPHINX}\index{SPHINX} from
Westinghouse\index{Westinghouse}, TDOWN\cite{TDOWN}\index{TDOWN}
from General Electric\index{General Electric},
DIF3D\cite{DIF3D}\index{DIF3D} from Argonne National Laboratory,
\index{Argonne National Laboratory!ANL} and ONEDANT\cite{ONEDANT}\index{ONEDANT}
from LANL\index{Los Alamos National Laboratory!LANL}.  It was indeed found that
codes could be moved more easily than before.  Analysts could use
ONEDANT and DIF3D on similar problems; they could even use one code to
generate utility files (for example, mixture and geometry files) that
would work with the other code!  When NJOY was developed, it first
produced version III formats and was later upgraded to the CCCC-IV
standard.

With the demise of the breeder reactor program, development of the CCCC
system has stopped.  However, many good programs are still available
that make use of CCCC files and programming standards.  The LANL
DANDE system\cite{DANDE} was an example of how the use of standard
interface files can be used to couple several reactor physics programs
together into an easy-to-use and powerful product.  In areas where the
CCCC standards were not very successful, such as gamma ray cross
sections and cross sections for the fusion energy range,
the MATXS format is available as an alternative.  This generalized
material cross section library format uses CCCC-type techniques.
The modern S$_{\rm N}$ code PARTISN\cite{PARTISN} makes very heavy
use of both standard and non-standard CCCC files  Thus, the CCCC
spirit is not dead.
\index{DANDE}
\index{MATXS format}

\subsection{CCCC Procedures and Programming Standards}
\label{ssCCCCR_Proc}

Although the CCCC programming standards went so far as to give advice on
program structure, documentation, and good coding practice, their main
purpose was to make it easier to move computer codes from one machine
to another.  The main problems in those days were the slightly different
implementations of input/output on CDC and IBM machines, the different
word size on CDC and IBM machines, and the relatively small size of the
main memory on the CDC 7600.  The last of these problems was attacked by
limiting the maximum memory requirements for CCCC-compliant codes.  This
problem has disappeared for modern computers.

The word-size problem has three components.  First, it is often
necessary to change the statements that allocate space for variables
and arrays [for example, ``\cword{DIMENSION A(10)}'' might have to be
changed to ``\cword{REAL*8 A(10)}'' when moving from a long-word
machine (CDC, Cray) to a short-word machine (IBM, VAX, Sun)].  Second,
the names of functions that work with double-precision variables
normally must be changed (for example, \cword{ALOG10} to \cword{DLOG10}).
And third, the word boundaries of double-precision variables must be
properly aligned in common blocks and equivalenced arrays.  The standard
CCCC method for handling name changes has been based on using standard
control cards.  As an example, a code for a long-word machine might
contain the following code fragment:

\newpage
\small
\begin{ccode}

CSW
C     REAL*8 HA(10)
CSW
CLW
      INTEGER HA(10)
CLW

\end{ccode}
\normalsize

The variable \cword{HA} is intended to hold 10 words of Hollerith
information using the standard CCCC 6-character word length.  Such a
variable must be declared as double precision on short-word machines,
which typically allow four Hollerith characters per word.  To change
this code to its short-word version, a special utility code reads
through each line removing the comment ``C'' from lines bracketed by
the ``SW'' comments and inserting a ``C'' in column 1 for all lines
bracketed by ``LW'' comments.  Early versions of NJOY used this
scheme; later versions used UPD\cite{UPD} conditional
\index{UPD}
statements instead.  For example, the source file contained

\small
\begin{ccode}

*IF SW
      REAL*8 HA(10)
*ELSE
      INTEGER HA(10)
*ENDIF

\end{ccode}
\normalsize

\noindent
and the compile file produced by UPD had only one of the two
alternatives activated, depending on whether \cword{SW} has been
set or not.  NJOY2016 uses built-in features of Fortran-90 to
handle this problem.  The \cword{locale} module defines a
special "kind" for the Hollerith data that is packed into
CCCC records.

The word-alignment problem requires that some care be used in
allocating arrays and common blocks.  For example,

\small
\begin{ccode}

REAL*8 HA
COMMON/BAD/IA(3),HA(10)

\end{ccode}
\normalsize

\noindent
should be avoided; it would be OK with \cword{IA(4)}.  Most CCCC records
contain mixtures of Hollerith, floating-point, and integer variables.
The desired data is normally extracted by making use of equivalenced
arrays.  For example, a code could contain the following declarations:

\small
\begin{ccode}

REAL*8 HA(10)
DIMENSION A(20),IA(20)
EQUIVALENCE (HA(1),A(1)),(IA(1),A(1))

\end{ccode}
\normalsize

\noindent
Assume that a record containing 2 Hollerith variables (which require
two single-precision variables each), 2 floating-point numbers (at
single precision), and 2 integers has been read into array \cword{A}.
How do you extract the first of the integers? The solution depends on
defining a CCCC-standard quantity called \cword{mult},
\index{mult@{\ty mult}}
which is 1 for long-word machines and 2 for short-word machines.  Now,
the desired value can be obtained with an expression of the form

\small
\begin{ccode}

I1=IA(2*MULT+3)

\end{ccode}
\normalsize

\noindent
The second Hollerith variable would be extracted using the simple
expression

\small
\begin{ccode}

H2=HA(2)

\end{ccode}
\normalsize

\noindent
Changing the value of \cword{mult} when transporting a code to a
different machine is easily handled using control-card brackets or UPD
conditionals as described above.

In NJOY2012 and later, common blocks are no longer used, but equivalencing
is still used to pack Hollerith (or character), integer, and real data
into the CCCC records.  While such coding techniques may bring tears to
the eyes of modern programmers, it remains a valid coding mechanism and
we continue to exploit this capability.

The remaining feature of the CCCC programming standards that is used
in codes like PARTISN is the concept of standardized input/output subroutines.
The CCCC interface files are sequential binary files (binary for
efficiency and sequential for simplicity).  The interface formats are
arranged so that the length of any record can be calculated using
parameters already read from previous records.  It is convenient to
insulate CCCC input/output from system variations by defining two
standard routines:
\index{REED@{\ty REED}}
\index{RITE@{\ty RITE}}

\begin{description}
\begin{singlespace}

\item[\cword{REED(NREF,IREC,ARRAY,NWDS,MODE)}] ~\par
  Read record \cword{IREC} from unit \cword{NREF} into
  \cword{ARRAY}.  The record has length \cword{NWDS}
  in single-precision words.  The \cword{MODE} parameter
  is used to control I/O buffering, and it is not used
  in NJOY. Records can be read out of sequence; the
  routine does any record skipping (forward or backward)
  needed to arrive at record number \cword{IREC}.
\item[\cword{RITE(NREF,IREC,ARRAY,NWDS,MODE)}] ~\par
  Write record \cword{IREC} onto unit \cword{NREF} using
  the data in \cword{ARRAY}.  The first \cword{NWDS}
  single-precision words will be written.  The \cword{MODE}
  parameter is ignored.  The records \cword{NREF} must be
  written in sequence.  The unit will be rewound if
  \cword{IREC=1}.

\end{singlespace}
\end{description}

\noindent
When transporting a code between different computer systems,
it is only necessary to have (or prepare) operational versions
of \cword{REED} and \cword{RITE} for the target machine.

In the conversion to Fortran-90 style, we tried to avoid all these
tricks.  The reading and writing of CCCC records was coded in
directly to avoid word-length problems (no more REED or RITE).  All
internal variable and data read from the GENDF file use 8-byte words.
It is only at the last stage when the data are stored into the CCCC
records that the 8-byte data are converted to 4-byte words.  Thus,
\cword{mult} is always equal to 2.  In general, the accuracy
obtained with 4-byte words is sufficient for multigroup data.

\subsection{The Standard Interface Files}
\label{ssCCCCR_Interface}

The CCCCR module produces data libraries that use three of the CCCC-IV
standard interface files, namely:
\index{ISOTXS}
\index{BRKOXS}
\index{DLAYXS}

\begin{description}
\begin{singlespace}

\item[ISOTXS] for nuclide (isotope)-ordered multigroup neutron
  cross sections including cross section versus energy functions
  for the principal cross sections, group-to-group scattering
  matrices, and fission neutron production and spectra tables;
\item[BRKOXS] for Bondarenko-type self-shielding factors versus
  energy group, temperature, and background cross section for
  the reactions with major resonance contributions; and
\item[DLAYXS] for delayed-neutron precursor yields, emission
  spectra, and decay constants for the major fissionable
  isotopes.

\end{singlespace}
\end{description}

\noindent
The format of each of these files, the definition of the types of data
included, and the uses and weaknesses of these three standard file
formats are discussed in the following three sections.

As mentioned in the preceding section, the normal form of the CCCC files
is binary and sequential.  CCCCR writes its output in this binary mode.
Of course, coded versions (ASCII for modern systems) are needed to move
library files between different machines, and the formats used for the
coded versions are given in the file descriptions below.  A separate
program, BINX\cite{LINXBINX}, is used to convert back and forth between
coded and binary modes.  BINX can also be used to prepare an
interpreted listing of a library.  CCCCR can prepare an entire
multimaterial library in one run if a multimaterial GENDF file is
available.  It can also be used to prepare an interface file containing
only one material.  These one-material files can be merged into
multimaterial libraries using the LINX code\cite{LINXBINX}.

\subsection{ISOTXS}
\label{ssCCCCR_ISOTXS}

The format for the ISOTXS\index{ISOTXS} material (isotope)-ordered
cross section file is given below.  This computer-text format is
standard for the CCCC interface files.  Of course, if these lines
were to be inserted into a modern Fortran (say .f90 or later)
code, the initial "C" will have to be changed to ``!".

\small
\begin{ccode}

C***********************************************************************
C                       REVISED 11/30/76                               -
C                                                                      -
CF          ISOTXS-IV                                                  -
CE          MICROSCOPIC GROUP NEUTRON CROSS SECTIONS                   -
C                                                                      -
CN                      THIS FILE PROVIDES A BASIC BROAD GROUP         -
CN                      LIBRARY, ORDERED BY ISOTOPE                    -
CN                      FORMATS GIVEN ARE FOR FILE EXCHANGE PURPOSES   -
CN                      ONLY.                                          -
C                                                                      -
C***********************************************************************

C-----------------------------------------------------------------------
CS          FILE STRUCTURE                                             -
CS                                                                     -
CS             RECORD TYPE                        PRESENT IF           -
CS             ===============================    ===============      -
CS             FILE IDENTIFICATION                ALWAYS               -
CS             FILE CONTROL                       ALWAYS               -
CS             FILE DATA                          ALWAYS               -
CS             FILE-WIDE CHI DATA                 ICHIST.GT.1          -
CS   **************(REPEAT FOR ALL ISOTOPES)                           -
CS   *         ISOTOPE CONTROL AND GROUP                               -
CS   *                        INDEPENDENT DATA    ALWAYS               -
CS   *         PRINCIPAL CROSS SECTIONS           ALWAYS               -
CS   *         ISOTOPE CHI DATA                   ICHI.GT.1            -
CS   *  **********(REPEAT TO NSCMAX SCATTERING BLOCKS)                 -
CS   *  *  *******(REPEAT FROM 1 TO NSBLOK)                            -
CS   *  *  *   SCATTERING SUB-BLOCK               LORD(N).GT.0         -
CS   *************                                                     -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE IDENTIFICATION                                        -
C                                                                      -
CL    HNAME,(HUSE(I),I=1,2),IVERS                                      -
C                                                                      -
CW    1+3*MULT=NUMBER OF WORDS                                         -
C                                                                      -
CB    FORMAT(11H 0V ISOTXS  ,1H*,2A6,1H*,I6)                           -
C                                                                      -
CD    HNAME       HOLLERITH FILE NAME - ISOTXS -                       -
CD    HUSE(I)     HOLLERITH USER IDENTIFICATION (A6)                   -
CD    IVERS       FILE VERSION NUMBER                                  -
CD    MULT        DOUBLE PRECISION PARAMETER                           -
CD                    1- A6 WORD IS SINGLE WORD                        -
CD                    2- A6 WORD IS DOUBLE PRECISION WORD              -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE CONTROL   (1D RECORD)                                 -
C                                                                      -
CL    NGROUP,NISO,MAXUP,MAXDN,MAXORD,ICHIST,NSCMAX,NSBLOK              -
C                                                                      -
CW    8=NUMBER OF WORDS                                                -
C                                                                      -
CB    FORMAT(4H 1D ,8I6)                                               -
C                                                                      -
CD    NGROUP        NUMBER OF ENERGY GROUPS IN FILE                    -
CD    NISO          NUMBER OF ISOTOPES IN FILE                         -
CD    MAXUP         MAXIMUM NUMBER OF UPSCATTER GROUPS                 -
CD    MAXDN         MAXIMUM NUMBER OF DOWNSCATTER GROUPS               -
CD    MAXORD        MAXIMUM SCATTERING ORDER (MAXIMUM VALUE OF         -
CD                     LEGENDRE EXPANSION INDEX USED IN FILE).         -
CD    ICHIST        FILE-WIDE FISSION SPECTRUM FLAG                    -
CD                     ICHIST.EQ.0,      NO FILE-WIDE SPECTRUM         -
CD                     ICHIST.EQ.1,      FILE-WIDE CHI VECTOR          -
CD                     ICHIST.GT.1,      FILE-WIDE CHI MATRIX          -
CD    NSCMAX        MAXIMUM NUMBER OF BLOCKS OF SCATTERING DATA        -
CD    NSBLOK        SUBBLOCKING CONTROL FOR SCATTER MATRICES. THE      -
CD                     SCATTERING DATA ARE SUBBLOCKED INTO NSBLOK      -
CD                     RECORDS (SUBBLOCKS) PER SCATTERING BLOCK.       -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE DATA   (2D RECORD)                                    -
C                                                                      -
CL    (HSETID(I),I=1,12),(HISONM(I),I=1,NISO),                         -
CL   1(CHI(J),J=1,NGROUP),(VEL(J),J=1,NGROUP),                         -
CL   2(EMAX(J),J=1,NGROUP),EMIN,(LOCA(I),I=1,NISO)                     -
C                                                                      -
CW    (NISO+12)*MULT+1+NISO                                            -
CW    +NGROUP*(2+ICHIST*(2/ICHIST+1)))=NUMBER OF WORDS                 -
C                                                                      -
CB    FORMAT(4H 2D ,1H*,11A6,1H*/     HSETID,HISONM                    -
CB   11H*,A6,1H*,9(1X,A6)/(10(1X,A6)))                                 -
CB    FORMAT(6E12.5)                  CHI (PRESENT IF ICHIST.EQ.1)     -
CD    FORMAT(6E12.5)                  VEL,EMAX,EMIN                    -
CD    FORMAT(12I6)                    LOCA                             -
C                                                                      -
CD    HSETID(I)     HOLLERITH IDENTIFICATION OF FILE (A6)              -
CD    HISONM(I)     HOLLERITH ISOTOPE LABEL FOR ISOTOPE I (A6)         -
CD    CHI(J)        FILE-WIDE FISSION SPECTRUM(PRESENT IF ICHIST.EQ.1) -
CD    VEL(J)        MEAN NEUTRON VELOCITY IN GROUP J (CM/SEC)          -
CD    EMAX(J)       MAXIMUM ENERGY BOUND OF GROUP J (EV)               -
CD    EMIN          MINIMUM ENERGY BOUND OF SET (EV)                   -
CD    LOCA(I)       NUMBER OF RECORDS TO BE SKIPPED TO READ DATA FOR   -
CD                     ISOTOPE I.  LOCA(1)=0                           -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE-WIDE CHI DATA   (3D RECORD)                           -
C                                                                      -
CC        PRESENT IF ICHIST.GT.1                                       -
C                                                                      -
CL    ((CHI(K,J),K=1,ICHIST),J=1,NGROUP),(ISSPEC(I),I=1,NGROUP)        -
C                                                                      -
CW    NGROUP*(ICHIST+1)=NUMBER OF WORDS                                -
C                                                                      -
CB    FORMAT(4H 3D ,5E12.5/(6E12.5))   CHI                             -
CB    FORMAT(12I6)                     ISSPEC                          -
C                                                                      -
CD    CHI(K,J)      FRACTION OF NEUTRONS EMITTED INTO GROUP J AS A     -
CD                     RESULT OF FISSION IN ANY GROUP,USING SPECTRUM K -
CD    ISSPEC(I)     ISSPEC(I)=K IMPLIES THAT SPECTRUM K IS USED        -
CD                     TO CALCULATE EMISSION SPECTRUM FROM FISSION     -
CD                     IN GROUP I                                      -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          ISOTOPE CONTROL AND GROUP INDEPENDENT DATA   (4D RECORD)   -
C                                                                      -
CL    HABSID,HIDENT,HMAT,AMASS,EFISS,ECAPT,TEMP,SIGPOT,ADENS,KBR,ICHI, -
CL   1IFIS,IALF,INP,IN2N,IND,INT,LTOT,LTRN,ISTRPD,                     -
CL   2(IDSCT(N),N=1,NSCMAX),(LORD(N),N=1,NSCMAX),                      -
CL   3((JBAND(J,N),J=1,NGROUP),N=1,NSCMAX),                            -
CL   4((IJJ(J,N),J=1,NGROUP),N=1,NSCMAX)                               -
C                                                                      -
CW    3*MULT+17+NSCMAX*(2*NGROUP+2)=NUMBER OF WORDS                    -
C                                                                      -
CB    FORMAT(4H 4D ,3(1X,A6)/6E12.5/                                   -
CB   1(12I6))                                                          -
C                                                                      -
CD    HABSID        HOLLERITH ABSOLUTE ISOTOPE LABEL - SAME FOR ALL    -
CD                            VERSIONS OF THE SAME ISOTOPE IN FILE (A6)-
CD    HIDENT        IDENTIFIER OF LIBRARY FROM WHICH BASIC DATA        -
CD                            CAME (E.G. ENDF/B) (A6)                  -
CD    HMAT          ISOTOPE IDENTIFICATION (E.G. ENDF/B MAT NO.) (A6)  -
CD    AMASS         GRAM ATOMIC WEIGHT                                 -
CD    EFISS         TOTAL THERMAL ENERGY YIELD/FISSION (W.SEC/FISS)    -
CD    ECAPT         TOTAL THERMAL ENERGY YIELD/CAPTURE (W.SEC/CAPT)    -
CD    TEMP          ISOTOPE TEMPERATURE (DEGREES KELVIN)               -
CD    SIGPOT        AVERAGE EFFECTIVE POTENTIAL SCATTERING IN          -
CD                            RESONANCE RANGE (BARNS/ATOM)             -
CD    ADENS         DENSITY OF ISOTOPE IN MIXTURE IN WHICH ISOTOPE     -
CD                            CROSS SECTIONS WERE GENERATED (A/BARN-CM)-
CD    KBR           ISOTOPE CLASSIFICATION                             -
CD                     0=UNDEFINED                                     -
CD                     1=FISSILE                                       -
CD                     2=FERTILE                                       -
CD                     3=OTHER ACTINIDE                                -
CD                     4=FISSION PRODUCT                               -
CD                     5=STRUCTURE                                     -
CD                     6=COOLANT                                       -
CD                     7=CONTROL                                       -
CD    ICHI          ISOTOPE FISSION SPECTRUM FLAG                      -
CD                      ICHI.EQ.0,     USE FILE-WIDE CHI               -
CD                      ICHI.EQ.1,     ISOTOPE CHI VECTOR              -
CD                      ICHI.GT.1,     ISOTOPE CHI MATRIX              -
CD    IFIS          (N,F) CROSS SECTION FLAG                           -
CD                     IFIS=0, NO FISSION DATA IN PRINCIPAL CROSS      -
CD                                       SECTION RECORD                -
CD                         =1, FISSION DATA PRESENT IN PRINCIPAL       -
CD                                       CROSS SECTION RECORD          -
CD    IALF          (N,ALPHA) CROSS SECTION FLAG                       -
CD                     SAME OPTIONS AS IFIS                            -
CD    INP           (N,P) CROSS SECTION FLAG                           -
CD                     SAME OPTIONS AS IFIS                            -
CD    IN2N          (N,2N) CROSS SECTION FLAG                          -
CD                     SAME OPTIONS AS IFIS                            -
CD    IND           (N,D) CROSS SECTION FLAG                           -
CD                     SAME OPTIONS AS IFIS                            -
CD    INT           (N,T) CROSS SECTION FLAG                           -
CD                     SAME OPTIONS AS IFIS                            -
CD    LTOT          NUMBER OF MOMENTS OF TOTAL CROSS SECTION PROVIDED  -
CD                     IN PRINCIPAL CROSS SECTIONS RECORD              -
CD    LTRN          NUMBER OF MOMENTS OF TRANSPORT CROSS SECTION       -
CD                     PROVIDED IN PRINCIPAL CROSS SECTION RECORD      -
CD    ISTRPD        NUMBER OF COORDINATE DIRECTIONS FOR WHICH          -
CD                     COORDINATE DEPENDENT TRANSPORT CROSS SECTIONS   -
CD                     ARE GIVEN, IS ISTRPD=0, NO COORDINATE DEPENDENT -
CD                     TRANSPORT CROSS SECTIONS ARE GIVEN.             -
CD    IDSCT(N)      SCATTERING MATRIX TYPE IDENTIFICATION FOR          -
CD                     SCATTERING BLOCK N, SIGNIFICANT ONLY IF         -
CD                     LORD(N).GT.0                                    -
CD                     IDSCT(N)=000 + NN, TOTAL SCATTERING, (SUM OF    -
CD                         ELASTIC, INELASTIC, AND N2N SCATTERING      -
CD                         MATRIX TERMS),                              -
CD                             =100 + NN, ELASTIC SCATTERING           -
CD                             =200 + NN, INELASTIC SCATTERING         -
CD                             =300 + NN, (N,2N) SCATTERING,----SEE    -
CD                              NOTE BELOW----                         -
CD                     WHERE NN IS THE LEGENDRE EXPANSION INDEX OF THE -
CD                     FIRST MATRIX IN BLOCK N                         -
CD    LORD(N)       NUMBER OF SCATTERING ORDERS IN BLOCK N.  IF        -
CD                     LORD(N)=0, THIS BLOCK IS NOT PRESENT FOR THIS   -
CD                     ISOTOPE.  IF NN IS THE VALUE TAKEN FROM         -
CD                     IDSCT(N), THEN THE MATRICES IN THIS BLOCK       -
CD                     HAVE LEGENDRE EXPANSION INDICES OF NN,NN+1,     -
CD                     NN+2,...,NN+LORD(N)-1                           -
CD    JBAND(J,N)    NUMBER OF GROUPS THAT SCATTER INTO GROUP J,        -
CD                     INCLUDING SELF-SCATTER, IN SCATTERING BLOCK N.  -
CD                     IF JBAND(J,N)=0, NO SCATTER DATA IS PRESENT IN  -
CD                     BLOCK N                                         -
CD    IJJ(J,N)      POSITION OF IN-GROUP SCATTERING CROSS SECTION IN   -
CD                     SCATTERING DATA FOR GROUP J, SCATTERING BLOCK   -
CD                     N, COUNTED FROM THE FIRST WORD OF GROUP J DATA. -
CD                     IF JBAND(J,N).NE.0 THEN IJJ(J,N) MUST SATISFY   -
CD                     THE RELATION 1.LE.IJJ(J,N).LE.JBAND(J,N)        -
C                                                                      -
CD                  NOTE- FOR N,2N SCATTER, THE MATRIX CONTAINS TERMS  -
CD                     SCAT(J TO G), WHICH ARE EMISSION (PRODUCTION)-  -
CD                     BASED, I.E., ARE DEFINED SUCH THAT MACROSCOPIC  -
CD                     SCAT(J TO G) TIMES THE FLUX IN GROUP J GIVES    -
CD                     THE RATE OF EMISSION (PRODUCTION) OF NEUTRONS   -
CD                     INTO GROUP G.                                   -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          PRINCIPAL CROSS SECTIONS   (5D RECORD)                     -
C                                                                      -
CL    ((STRPL(J,L),J=1,NGROUP),L=1,LTRN),                              -
CL   1((STOTPL(J,L),J=1,NGROUP),L=1,LTOT),(SNGAM(J),J=1,NGROUP).       -
CL   2(SFIS(J),J=1,NGROUP),(SNUTOT(J),J=1,NGROUP),                     -
CL   3(CHISO(J),J=1,NGROUP),(SNALF(J),J=1,NGROUP),                     -
CL   4(SNP(J),J=1,NGROUP),(SN2N(J),J=1,NGROUP),                        -
CL   5(SND(J),J=1,NGROUP),(SNT(J),J=1,NGROUP),                         -
CL   6((STRPD(J,I),J=1,NGROUP),I=1,ISTRPD)                             -
C                                                                      -
CW   (1+LTRN+LTOT+IALF+INP+IN2N+IND+ISTRPD+2*IFIS+                     -
CW   ICHI*(2/(ICHI+1)))*NGROUP=NUMBER OF WORDS                         -
C                                                                      -
CB   FORMAT(4H 5D ,5E12.5/(6E12.5)) LENGTH OF LIST AS ABOVE            -
C                                                                      -
CD    STRPL(J,L)   PL WEIGHTED TRANSPORT CROSS SECTION                 -
CD                    THE FIRST ELEMENT OF ARRAY STRPL IS THE          -
CD                    CURRENT (P1) WEIGHTED TRANSPORT CROSS SECTION    -
CD                    THE LEGENDRE EXPANSION COEFFICIENT FACTOR (2L+1) -
CD                    IS NOT INCLUDED IN STRPL(J,L).                   -
CD    STOTPL(J,L)  PL WEIGHTED TOTAL CROSS SECTION                     -
CD                    THE FIRST ELEMENT OF ARRAY STOTPL IS THE         -
CD                    FLUX (P0) WEIGHTED TOTAL CROSS SECTION           -
CD                    THE LEGENDRE EXPANSION COEFFICIENT FACTOR (2L+1) -
CD                    IS NOT INCLUDED IN STOTPL(J,L).                  -
CD    SNGAM(J)     (N,GAMMA)                                           -
CD    SFIS(J)      (N,F)        (PRESENT IF IFIS.GT.0)                 -
CD    SNUTOT(J)    TOTAL NEUTRON YIELD/FISSION (PRESENT IF IFIS.GT.0)  -
CD    CHISO(J)I    ISOTOPE CHI  (PRESENT IF ICHI.EQ.1)                 -
CD    SNALF(J)     (N,ALPHA)    (PRESENT IF IALF.GT.0)                 -
CD    SNP(J)       (N,P)        (PRESENT IF INP.GT.0)                  -
CD    SN2N(J)      (N,2N)       (PRESENT IF IN2N.GT.0)  ----SEE        -
CD                    NOTE----                                         -
CD    SND(J)       (N,D)        (PRESENT IF IND.GT.0)                  -
CD    SNT(J)       (N,T)        (PRESENT IF INT.GT.0)                  -
CD    STRPD(J,I)   COORDINATE DIRECTION I TRANSPORT CROSS SECTION      -
CD                              (PRESENT IF ISTRPD.GT.0)               -
C                                                                      -
CN                 NOTE - THE PRINCIPAL N,2N CROSS SECTION SN2N(J)     -
CN                    IS DEFINED AS THE N,2N REACTION CROSS SECTION,   -
CN                    I.E., SUCH THAT MACROSCOPIC SN2N(J) TIMES THE    -
CN                    FLUX IN GROUP J GIVES THE RATE AT WHICH N,2N     -
CN                    REACTIONS OCCUR IN GROUP J.  THUS, FOR N,2N      -
CN                    SCATTERING, SN2N(J) = 0.5*(SUM OF SCAT(J TO G)   -
CN                    SUMMED OVER ALL G).                              -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          ISOTOPE CHI DATA   (6D RECORD)                             -
C                                                                      -
CC          PRESENT IF ICHI.GT.1                                       -
C                                                                      -
CL    ((CHIISO(K,J),K=1,ICHI),J=1,NGROUP),(ISOPEC(I),I=1,NGROUP)       -
C                                                                      -
CW    NGROUP*(ICHI+1)=NUMBER OF WORDS                                  -
C                                                                      -
CB    FORMAT(4H 6D ,5E12.5/(6E12.5))   CHIISO                          -
CB    FORMAT(12I6)                     ISOPEC                          -
C                                                                      -
CD    CHIISO(K,J)   FRACTION OF NEUTRONS EMITTED INTO GROUP J AS       -
CD                     RESULT OF FISSION IN ANY GROUP,USING SPECTRUM K -
CD    ISOPEC(I)     ISOPEC(I)=K IMPLIES THAT SPECTRUM K IS USED        -
CD                     TO CALCULATE EMISSION SPECTRUM FROM FISSION     -
CD                     IN GROUP I                                      -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          SCATTERING SUB-BLOCK   (7D RECORD)                         -
C                                                                      -
CC          PRESENT IF LORD(N).GT.0                                    -
C                                                                      -
CL    ((SCAT(K,L),K=1,KMAX),L=1,LORDN)                                 -
C                                                                      -
CC    KMAX=SUM OVER J OF JBAND(J,N) WITHIN THE J-GROUP RANGE OF THIS   -
CC       SUB-BLOCK.  IF M IS THE INDEX OF THE SUB-BLOCK, THE J-GROUP   -
CC       RANGE CONTAINED WITHIN THIS SUB-BLOCK IS                      -
CC       JL=(M-1)*((NGROUP-1)/NSBLOK+1 TO JU=MIN0(NGROUP,JUP),         -
CC       WHERE JUP=M*((NGROUP-1)/NSBLOK+1).                            -
C                                                                      -
CC    LORDN=LORD(N)                                                    -
CC    N IS THE INDEX FOR THE LOOP OVER NSCMAX (SEE FILE STRUCTURE)     -
C                                                                      -
CW    KMAX*LORDN=NUMBER OF WORDS                                       -
C                                                                      -
CB    FORMAT(4H 7D ,5E12.5/(6E12.5))                                   -
C                                                                      -
CD    SCAT(K,L)     SCATTERING MATRIX OF SCATTERING ORDER L, FOR       -
CD                     REACTION TYPE IDENTIFIED BY IDSCT(N) FOR THIS   -
CD                     BLOCK, JBAND(J,N) VALUES FOR SCATTERING INTO    -
CD                     GROUP J ARE STORED AT LOCATIONS K=SUM FROM 1    -
CD                     TO (J-1) OF JBAND(J,N) PLUS 1 TO K-1+JBAND(J,N).-
CD                     THE SUM IS ZERO WHEN J=1, J-TO-J SCATTER IS     -
CD                     THE IJJ(J,N)-TH ENTRY IN THE RANGE JBAND(J,N),  -
CD                     VALUES ARE STORED IN THE ORDER (J+JUP),         -
CD                     (J+JUP-1),...,(J+1),J,(J-1),...,(J-JDN),        -
CD                     WHERE JUP=IJJ(J,N)-1 AND JDN=JBAND(J,N)-IJJ(J,N)-
C                                                                      -
C-----------------------------------------------------------------------

\end{ccode}
\normalsize
\vspace{1 pt}

Most of the variables in the ``File Identification and File Control''
record are taken from the user's input.  Note that \cword{MAXUP}
is always set to zero.  CCCCR does not process the NJOY thermal data
at the present time.  The \cword{ICHIST} parameter will always be
zero.  CCCCR does not produce a file-wide fission spectrum or matrix.
The old practice of using a single fission spectrum for all calculations
is inaccurate and obsolete.  Actually, the effective fission spectrum
depends on the mixture of isotopes and the flux.  Any file-wide spectrum
would have to be at least problem dependent, and it should also be
region dependent.  The parameters \cword{NSCMAX} and \cword{NSBLOK}
in the ``File Control'' record will be discussed in connection with
the scattering matrix format.

In the ``File Data'' record, the Hollerith set identification and the
isotope names are taken from the user's input.  As mentioned above,
the file-wide fission spectrum \cword{CHI} never appears.  The mean
neutron velocities by group (\cword{VEL}) are obtained from the inverse
velocities computed by \hyperlink{sGROUPRhy}{GROUPR}:

\begin{equation}
  \Big<\frac{1}{v}\Big>_g=\frac{\displaystyle\int_g \,\frac{1}{v}\,\phi(E)\,dE}
        {\displaystyle\int_g \phi(E)\,dE} \,\,,
\end{equation}
\vspace{1 pt}

\noindent
where $g$ is the group index, $\phi(E)$ is the
\hyperlink{sGROUPRhy}{GROUPR} weighting spectrum,
and $v$ is the neutron velocity, which is computed from the neutron mass
and energy using $v{=}\sqrt{2E/m}$.  The units of these quantities are s/m;
they are converted to cm/s for ISOTXS by inverting and multiplying by 100.
The group structure [see \cword{EMAX(J)} and \cword{EMIN}] is obtained
directly from \cword{mf}=1, \cword{mt}=451 on the GENDF tape.  Note
that \hyperlink{sGROUPRhy}{GROUPR} energy groups
are given in order of increasing energy and ISOTXS energy groups are given
in order of decreasing energy.  CCCCR handles the conversion.

The ``File-Wide Chi Data'' record never appears; see the discussion
above for the reasons.

In the ``Isotope Control and Group Independent Data'' record, the first
ten parameters are  taken from the user's input.  The gram atomic weight
for the material (\cword{AMASS}) can be computed from the ENDF AWR
parameter available on the GENDF file using the gram atomic weight of
the neutron as a multiplier.  The energy-release parameters \cword{EFISS}
and \cword{ECAPT} must also be computed by the user.  The \cword{ECAPT}
values are normally based on the ENDF Q values given in File 3, but,
in some cases, it is also necessary to add additional decay energy
coming from short-lived activation steps.  For example, the \cword{ECAPT}
value for $^{238}$U should include the energy for the $^{239}$U
$\beta$-decay step, and perhaps even the energy from the $^{239}$Np
$\beta$ decay.  The values for \cword{EFISS} should be based on the total
non-neutrino energy release, which can be obtained from
\cword{mf}=3, \cword{mt}=18 or
\cword{mf}=1, \cword{mt}=458 on the ENDF tape.  The \cword{TEMP}
parameter is normally set
to 300K.  The value of \cword{SIGPOT} can be computed from the
scattering-radius parameter AP in File 2 of the ENDF tape using
$\sigma_p{=}4\pi a^2$.  The parameter \cword{ADENS} is usually set
to zero to imply infinite dilution.  \cword{KBR} can be chosen based
on the normal use of the material by the community for which the library
is being produced.

The \cword{ICHI} parameter is related to the \cword{ichix} parameter in
the user's input.  As discussed above, the option \cword{ICHI=0} is
never used by CCCCR.  Beyond that, the NJOY user has the option of producing
a fission $\chi$ vector using the default GROUPR flux (which is available
on the GENDF tape) or a user-supplied weighting flux \cword{SPEC}.  This
enables the user to produce an ISOTXS library appropriate to a class of
problems with a flux similar to \cword{SPEC}.  In general, the
incident-energy dependence of the fission spectrum is weak, so the
choice of this weighting spectrum is not critical.  Noticeable differences
might be expected between a thermal spectrum on the one hand and a
fast-reactor or fusion-blanket spectrum on the other.  The $\chi$ vector
is defined as follows:

\begin{equation}
   \chi_{g'}=\frac{\displaystyle\sum_g \sigma_{f g\rightarrow g'}\,\phi_g}
       {\displaystyle\sum_{g'} \sum_g \sigma_{f g\rightarrow g'}\,\phi_g}\,\, ,
\end{equation}

\noindent
where $\sigma_f$ is the fission group-to-group matrix from
\hyperlink{sGROUPRhy}{GROUPR},
$\phi_g$ is either the model flux or \cword{SPEC}, and the denominator
assures that $\chi_{g'}$ will be normalized.  Actually, the calculation
is more complicated than that because of the necessity to include
delayed-neutron production.  A ``steady-state'' value for the fission
spectrum can be obtained as follows:

\begin{equation}
   \chi^{SS}_{g'}=\frac{\displaystyle\sum_g\sigma_{f g\rightarrow g'}
     \,\phi_g + \chi^D_{g'}\sum_g\bar{\nu}^D_g\sigma_{fg}\,\phi_g}
     {\displaystyle\sum_{g'}\sum_g\sigma_{f g\rightarrow g'}\,\phi_g
     +\sum_g\bar{\nu}^D_g\sigma_{fg}\,\phi_g} \,\,,
\end{equation}

\noindent
where $\bar{\nu}^D_g$ is the delayed-neutron yield obtained from
\cword{mf}=3, \cword{mt}=455 on the GENDF tape, $\chi^D_g$ is the
total delayed-neutron
spectrum obtained by summing over the time groups in
\cword{mf}=5, \cword{mt}=455,
and $\sigma_{fg}$ is the fission cross section for group $g$ obtained
from \cword{mf}=3, \cword{mt}=18.

This is still not the end of the complications of fission.  If the
partial fission reactions MT=19, 20, 21, and 38 are present, the fission
matrix term in the above equations is obtained by adding the contributions
from all the partial reactions found.  In these cases, a matrix for
MT=18 will normally  not be present on the GENDF tape.  If it is, it will
be ignored.  Beginning with NJOY 91.0, a new and more efficient
representation is used for the fission matrix computed in
\hyperlink{sGROUPRhy}{GROUPR}.  It is well known that the shape
of the fission spectrum is independent of energy up to energies of
several hundred keV.  \hyperlink{sGROUPRhy}{GROUPR} takes advantage
of this by computing this low-energy spectrum only once.  It then
computes a fission neutron production cross section for all the groups
up to the energy at which significant energy dependence starts.  At
higher energies, the full group-to-group fission matrix is computed as
in earlier versions of NJOY.  Therefore, it is now necessary to compute
the values of $\sigma_{fg\rightarrow g'}$ as used in the above equations
using

\begin{equation}
   \sigma_{fg\rightarrow g'}=\chi^{LE}_{g'}(\bar{\nu}\sigma_f)^{LE}_g
     +\sigma^{HE}_{fg\rightarrow g'} \,\,,
\end{equation}

\noindent
where LE stands for low energy, HE stands for high energy; the
low-energy production cross sections written as $\nu\sigma_f$ will be
found on the GENDF tape using the special flag \cword{IG2LO=0}, and the
low-energy $\chi$ will be found on the GENDF tape with \cword{IG=0}.

In order to obtain still better accuracy, CCCCR can produce
a fission $\chi$ matrix instead of the vector.  Using the above
notation, the full $\chi$ matrix becomes

\begin{equation}
   \chi^{SS}_{g\rightarrow g'}=\frac{\chi^{LE}_{g'}(\bar{\nu}\sigma_f)^{LE}_g
     +\sigma^{HE}_{fg\rightarrow g'}+\chi^D_{g'}\bar{\nu}^D_g\sigma_{fg}}
      {{\rm NORM}} \,\,,
\end{equation}

\noindent
where NORM is just the value that normalizes the $\chi$ matrix; that is,
the sum of the numerator over all $g'$.  Note that the ``Isotope Chi
Data'' record allows for a rectangular fission matrix similar to the
one produced by \hyperlink{sGROUPRhy}{GROUPR}.  It is obtained
by using the input \cword{SPEC} array to define the range of groups
that will be averaged into each
of the final \cword{ICHIX} spectra.  For example, to collapse a
ten-group $\chi$ matrix into a five-group matrix, \cword{SPEC} might
contain the ten values 1, 2, 3, 4, 5, 5, 5, 5, 5, 5. More formally,

\begin{equation}
   \chi^{SS}_{k\rightarrow g'}=\frac{\displaystyle\sum_{s(g)=k}\big(
       \chi^{LE}_{g'}(\bar{\nu}\sigma_f)^{LE}_g
     +\sigma^{HE}_{fg\rightarrow g'}+\chi^D_{g'}\bar{\nu}^D_g
        \sigma_{fg}\big)\,\phi_g}
      {{\rm NORM}} \,\,,
\end{equation}

\noindent
where $\phi_g$ is the default weighting function from the GENDF tape,
$s(g)$ is the \cword{SPEC} array provided by the user, and the summation
is over all groups $g$ satisfying the condition that $s(g){=}k$.  Future
versions of CCCCR could construct the \cword{SPEC} array automatically
using the information in the new GENDF format.

Continuing with the description of the ``Isotope Control and Group
Independent Data'' record, the next 9 parameters are flags that tell
what reactions will be described in the ``Principal Cross Sections''
record.  They will be described below.  Similarly, the parameters
\cword{IDSCT}, \cword{LORDN}, \cword{JBAND}, and \cword{IJJ}
will be described later in connection with the ``Scattering Sub-Block''
records.

The ISOTXS format allows for a fixed set of principal cross sections that
was chosen based on the needs of fission reactor calculations.  This
is one of its main defects; the list does not allow for other reactions
that become important above 6--10 MeV, and it does not allow for other
quantities of interest, such as gas production, KERMA factors, and
radiation damage production cross sections.  Most of the reactions are
simply copied from \cword{mf}=3 on the GENDF tape with the group order
inverted --- this is true for \cword{SNGAM}, the (n,$\gamma$) cross
section, which is taken from \cword{mt}=102; for \cword{SFIS}, the (n,f) cross
section, which is taken from \cword{mt}=18; for \cword{SNALF}, the (n,$\alpha$)
cross section, which is taken from \cword{mt}=107; for \cword{SNP}, the (n,p)
cross section, which is taken from \cword{mt}=103; for \cword{SND}, the (n,d)
cross section, which is taken from \cword{mt}=104; and for \cword{SNT}, the
(n,t) cross section, which is taken from \cword{mt}=105.  The (n,2n) cross
section, \cword{SN2N}, is normally taken from \cword{mt}=16.  However, earlier
versions of ENDF represented the sequential (n,2n) reaction in $^9$Be
using \cword{mt}=6, 7, 8, and 9.  If present, these partial (n,2n) reactions
are added into \cword{SN2N}.  The flags \cword{IFIS}, \cword{IALF},
\cword{INP}, \cword{IN2N}, \cword{IND}, and \cword{INT} in the
``Isotope Control and Group Independent Data'' record are set to
indicate which of these reactions have been found for this material.

In going from version III of the CCCC specifications to version IV,
there was some controversy over the appropriate definition for the
(n,2n) cross section and matrix.  It was decided that the quantity
in \cword{SN2N} would be the (n,2n) reaction cross section; that
is, it would define the probability that an (n,2n) reaction takes
place.  The (n,2n) matrix would be defined such that the sum over
all secondary groups would produce the (n,2n) production cross section,
which is two times larger than the reaction cross section.

The \cword{CHISO} vector, which contains the fission spectrum vector
(if any), was discussed above.  A complete calculation of the fission
source also requires the fission yield, \cword{SNUTOT}, which can be used
together with the fission cross section to calculated the fission neutron
production cross section, $\bar{\nu}\sigma_f$.  The fission yield can be
calculated from the \hyperlink{sGROUPRhy}{GROUPR} fission matrix using

\begin{equation}
   \bar{\nu}_g=\frac{\displaystyle\sum_{g'}\sigma_{fg\rightarrow g'}}
      {\sigma_{fg}} \,\,.
\end{equation}
\vspace{0.5 pt}

\noindent
Adding delayed neutron contributions and accounting for the partition of
the fission matrix into low-energy and high-energy parts (see the
discussion of $\chi$ above) gives the equation actually used by CCCCR:

\begin{equation}
   \bar{\nu}^{SS}_g=\frac{\displaystyle\sum_{g'}\sigma^{HE}_{fg\rightarrow g'}
     +(\bar{\nu}\sigma_f)^{LE}_g + \bar{\nu}^D_g\sigma_{fg}}
      {\sigma_{fg}} \,\,.
\end{equation}
\vspace{0.5 pt}

The total cross section produced by \hyperlink{sGROUPRhy}{GROUPR}
contains two components:
the flux-weighted or P$_0$ total cross section, and the current-weighted
or P$_1$ total cross section.  The P$_0$ part is stored into
\cword{STOTPL}, and the \cword{LTOT} flag is set to 1.  \cword{STRPL}
contains the transport cross section used by diffusion codes; this is,

\begin{equation}
   \sigma_{tr,g}= \sigma_{t1,g}-\sum_{g'}\sigma_{e1,g\rightarrow g'} \,\,,
\end{equation}
\vspace{0.5 pt}

\noindent
where $\sigma_{t1,g}$ is the P$_1$ total cross section and
$\sigma_{e1,g\rightarrow g'}$ is the P$_1$ component of the elastic
scattering matrix, which is obtained from \cword{mf}=6,
\cword{mt}=2 on the GENDF tape from
\hyperlink{sGROUPRhy}{GROUPR}.  The flag \cword{LTRN} is set to
1; that is, no higher-order transport corrections are
provided.  Direction-dependent transport cross sections are not
computed by CCCCR; therefore, \cword{ISTRPD} is always zero, and
the \cword{STRPD} vectors are missing.

As discussed above, the ``Isotope Chi Data'' record may be present
if the user set \cword{ICHIX>1} and supplied a \cword{SPEC} vector to
define how the full $\chi$ matrix is to be collapsed into a
rectangular $\chi$ matrix.

The treatment of scattering matrices in the ISOTXS format is complex
and has lots of possible variations.  Only the variations supported
by CCCCR will be described here.  First of all, the scattering data are
divided into blocks and subblocks.  A block is either one of the
designated scattering reactions [that is, total, elastic, inelastic,
or (n,2n)] and contains all the group-to-group elements and Legendre
orders for that reaction (\cword{IFOPT=1}), or it is one particular
Legendre order for one of the designated reactions and contains all
the group-to-group elements for that order and reaction (\cword{IFOPT=2}).
Its actual content is determined by \cword{IDSCT} and \cword{LORDN}.
If \cword{IFOPT=1} has been selected, \cword{IDSCT(1)=100} and
\cword{LORDN(1)=4} would designate a block for the elastic scattering
matrix of order P$_3$ that contains all 4 Legendre orders and all
group-to-group elements.  If \cword{IFOPT=2} has been selected,
\cword{IDSCT(1)=100} with \cword{LORDN(1)=1} would designate a block
containing all group-to-group elements for the P$_0$ elastic matrix,
\cword{IDSCT(2)=101} with \cword{LORDN(2)=1} would designate
a block containing the P$_1$ elastic matrix, and so on.  In CCCCR,
\cword{LORDN} is always equal to 1 for \cword{IFOPT=2}.

The ISOTXS format attempts to pack scattering matrices efficiently.
First, all the scattering matrices treated here are triangular
because only downscatter is present.  And second, because of the
limited range of elastic downscatter, only a limited range of groups
above the inscatter group will contribute to the scattering into
a given secondary-energy group.  Therefore, ISOTXS removes zero
cross sections by defining bands of incident energy groups that
contribute to each final energy group.  The bands are defined by
\cword{JBAND}, the number of initial energy groups in the band,
and \cword{IJJ}, an index to identify the position of the ingroup
element in the band.  The following table illustrates banding for
a hypothetical elastic scattering reaction:

\begin{center}
\begin{tabular}{cccc}
Band & Element & JBAND & IJJ \\ \hline
1    & 1$\rightarrow$1 & 1 & 1 \\
2    & 2$\rightarrow$2 & 2 & 1 \\
     & 1$\rightarrow$2 &   &   \\
3    & 3$\rightarrow$3 & 2 & 1 \\
     & 2$\rightarrow$3 &   &   \\
4    & 4$\rightarrow$4 & 2 & 1 \\
     & 3$\rightarrow$4 &   &   \\ \hline
\end{tabular}
\end{center}

Note that \cword{IJJ} is always 1 in the absence of upscatter.  This
scheme is efficient for elastic scattering, but it is not efficient
for threshold reactions because the ingroup element must always be
included in the band.  This means that lots of zeros must be given
for final energy groups below the threshold group.  An improved
and simplified scheme is used in the MATXS format.

For \cword{IFOPT=2}, the elements in the table above would be stored
in the sequence shown, top to bottom.  Each Legendre order would
have its own block arranged in the same order.  For \cword{IFOPT=1},
the Legendre order data are intermixed with the group-to-group
data.  In each band, the elements for all initial groups for
P$_0$ are given, then all initial groups for P$_1$, and so on
through \cword{LORDN} Legendre orders.

Scattering matrices can be very large.  For example, an 80-group
elastic matrix can have as many as $80\times 79/2=3160$ elements
per Legendre order.  That would be 12 640 words for a P$_3$ block
using \cword{IFOPT=1}, or four blocks of 3160 words each for
\cword{IFOPT=2}.  The latter is practical; the former is not
\footnote{At least it was not practical many years ago.  However
we see no benefit in revising the existing algorithm, and so
keep this description}.  The
corresponding numbers for 200 groups would be 79 600 and 19 900.
Both of these numbers are clearly impractical as record sizes.  This
is where subblocking comes in.  If each block is divided up so that
there is one subblock for each energy group, the maximum record size
is reduced substantially.  For \cword{IFOPT=1}, the maximum record
size is equal to the number of groups times the number of Legendre
orders, or 800 for the 200-group P$_3$ case.  For \cword{IFOPT=2},
the maximum record size is just equal to the number of groups.
Although the ISOTXS formats allows subblocks to contain several
groups, CCCCR does not.  The possible values of \cword{NSBLOK} are
limited to 1 and \cword{NGROUP}.  In summary, the CCCCR user has
four matrix blocking options:
\begin{enumerate}
\begin{singlespace}
\item  {\it IFOPT=1 and NSBLOK=1}. This produces a single block and a
  single subblock for each reaction.  It is probably the best
  choice for small group structures (up to about 30 groups).
  The maximum record size is $n_\ell\times n_g(n_g{-}1)/2$.

\item {\it IFOPT=1 and NSBLOK=NGROUP}. This produces a block for
  each reaction, and each block contains $n_g$ subblocks.  The
  maximum record size is $n_\ell\times n_g$.  This is a good
  choice for larger group structures because it keeps the
  record size up as compared with option 4 below.

\item {\it IFOPT=2 and NSBLOK=1}. This produces $n_\ell$ blocks
  and subblocks for each reaction.  The maximum record size is
  $n_g(n_g{-}1)/2$.  It has only a modest advantage in the maximum
  number of groups over option 1. Unless the application that uses
  the library finds it convenient to read one Legendre order at a time,
  the user might just as well choose option 2 if option 1 produces
  records that are too large.
\item {\it IFOPT=2 and NSBLOK=NGROUP}.  This produces $n_\ell$ blocks for
  each reaction, each with $n_g$ subblocks.  The maximum record size
  is $n_g$.  The number of groups would have to be on the order
  of 1000 before this option would be preferred to option 2.
\end{singlespace}
\end{enumerate}

If CCCCR does not have enough memory to process option 1 or 3, the
code automatically sets \cword{NSBLOK} to \cword{NGROUP}, thereby
activating option 2 or 4, respectively.

Note that the ISOTXS format specifies that the total scattering matrix
is the sum of the elastic, inelastic, and (n,2n) matrices [see the
definition of \cword{IDSCT(N)}].  This implies that the inelastic
matrix must contain the normal (n,n$'$) reactions from \cword{mt}=51-91,
and also any other neutron-producing reactions that might be
present.  Examples are (n,n$'\alpha$), (n,n$'$p), and (n,3n).

\subsection{BRKOXS}
\label{ssCCCCR_BRKOXS}

The format for the BRKOXS\index{BRKOXS} Bondarenko-type self-shielding
factor file is given below in the standard format.

\small
\begin{ccode}

C***********************************************************************
C                       REVISED 11/30/76                               -
C                                                                      -
CF          BRKOXS-IV                                                  -
CE          MICROSCOPIC GROUP DELAYED NEUTRON PRECURSOR DATA           -
C                                                                      -
CN                      THIS FILE PROVIDES DATA NECESSARY FOR          -
CN                      BONDARENKO TREATMENT IN ADDITION TO            -
CN                      THOSE DATA IN FILE ISOTXS                      -
CN                      FORMATS GIVEN ARE FOR FILE EXCHANGE PURPOSES   -
CN                      ONLY.                                          -
C                                                                      -
C***********************************************************************

C-----------------------------------------------------------------------
CS          FILE STRUCTURE                                             -
CS                                                                     -
CS             RECORD TYPE                        PRESENT IF           -
CS             ===============================    ===============      -
CS             FILE IDENTIFICATION                ALWAYS               -
CS             FILE CONTROL                       ALWAYS               -
CS             FILE DATA                          ALWAYS               -
CS   **************(REPEAT FROM 1 TO NISOSH)                           -
CS   *         SELF-SHIELDING FACTORS             ALWAYS               -
CS   *         CROSS SECTIONS                     ALWAYS               -
CS   **************                                                    -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE IDENTIFICATION                                        -
C                                                                      -
CL    HNAME,(HUSE(I),I=1,2),IVERS                                      -
C                                                                      -
CW    1+3*MULT=NUMBER OF WORDS                                         -
C                                                                      -
CB    FORMAT(11H 0V BRKOXS  ,1H*,2A6,1H*,I6)                           -
C                                                                      -
CD    HNAME       HOLLERITH FILE NAME - BRKOXS -                       -
CD    HUSE(I)     HOLLERITH USER IDENTIFICATION (A6)                   -
CD    IVERS       FILE VERSION NUMBER                                  -
CD    MULT        DOUBLE PRECISION PARAMETER                           -
CD                    1- A6 WORD IS SINGLE WORD                        -
CD                    2- A6 WORD IS DOUBLE PRECISION WORD              -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE CONTROL   (1D RECORD)                                 -
C                                                                      -
CL    NGROUP,NISOSH,NSIGPT,NTEMPT,NREACT,IBLK                          -
C                                                                      -
CW    6 = NUMBER OF WORDS                                              -
C                                                                      -
CB    FORMAT(4H 1D ,6I6)                                               -
C                                                                      -
CD    NGROUP        NUMBER OF ENERGY GROUPS IN SET                     -
CD    NISOSH        NUMBER OF ISOTOPES WITH SELF-SHIELDING FACTORS     -
CD    NSIGPT        TOTAL NUMBER OF VALUES OF VARIABLE X (SEE FILE DATA-
CD                     RECORD) WHICH ARE GIVEN.  NSIGPT IS EQUAL TO    -
CD                     THE SUM FROM 1 TO NISOSH OF NTABP(I)            -
CD    NTEMPT        TOTAL NUMBER OF VALUES OF VARIABLE TB (SEE FILE    -
CD                     DATA RECORD) WHICH ARE GIVEN.  NTEMPT IS EQUAL  -
CD                     TO THE SUM FROM 1 TO NISOSH OF NTABT(I)         -
CD    NREACT        NUMBER OF REACTION TYPES FOR WHICH SELF-SHIELDING  -
CD                     FACTORS ARE GIVEN (IN PREVIOUS VERSIONS OF THIS -
CD                     FILES NREACT HAS BEEN IMPLICITLY SET TO 5).     -
CD    IBLK          BLOCKING OPTION FLAG FOR SELF-SHIELDING FACTORS,   -
CD                     IBLK=0, FACTORS NOT BLOCKED BY REACTION TYPE,   -
CD                     IBLK=1, FACTORS ARE BLOCKED BY REACTION TYPE.   -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE DATA   (2D RECORD)                                    -
C                                                                      -
CL    (HISONM(I),I=NISOSH),(X(K),K=1,NSIGPT),(TB(K),K=1,NTEMPT),       -
CL   1(EMAX(J),J=1,NGROUP),EMIN,(JBFL(I),I=1,NISOSH),                  -
CL   2(JBFH(I),I=NISOSH),(NTABP(I),I=1,NISOSH),(NTABT(I),I=1,NISOSH)   -
C                                                                      -
CW    (4+MULT)*NISOSH+NSIGPT+NTEMPT+NGROUP+1=NUMBER OF WORDS           -
C                                                                      -
CB    FORMAT(4H 2D ,9(1X,A6)/          HISONM                          -
CB   1(10(1X,A6)))                                                     -
CB    FORMAT(6E12.5)                   X,TB,EMAX,EMIN                  -
CB    FORMAT(12I6)                     JBFL,JBFH,NTABP,NTABT           -
C                                                                      -
CD    HISONM(I)     HOLLERITH ISOTOPE LABEL FOR ISOTOPE I (A6).  THESE -
CD                     LABELS MUST BE A SUBSET OF THOSE IN FILE ISOTXS -
CD                     OR GRUPXS, IN THE CORRESPONDING ARRAY.          -
CD    X(K)          ARRAY OF LN(SIGP0)/LN(10) VALUES FOR ALL ISOTOPES, -
CD                     WHERE SIGP0 IS THE TOTAL CROSS SECTION OF THE   -
CD                     OTHER ISOTOPES IN THE MIXTURE IN BARNS PER ATOM -
CD                     OF THIS ISOTOPE.  FOR ISOTOPE I, THE NTABP(I)   -
CD                     VALUES OF X FOR WHICH SELF-SHIELDING FACTORS    -
CD                     ARE GIVEN ARE STORED STARTING AT LOCATION L=1+  -
CD                     SUM FROM 1 TO I-1 OF NTABP(K).                  -
CD    TB(K)         ARRAY OF TEMPERATURES (DEGREES C) FOR ALL ISOTOPES.-
CD                     FOR ISOTOPE I, THE NTBT(I) VALUES OF TB FOR     -
CD                     WHICH SELF-SHIELDING FACTORS ARE GIVEN ARE      -
CD                     STORED AT LOCATION L=1+SUM FROM 1 TO I-1 OF     -
CD                     NTABT(K).                                       -
CD    EMAX(J)       MAXIMUM ENERGY BOUND OF GROUP J (EV)               -
CD    EMIN          MINIMUM ENERGY BOUND OF SET (EV)                   -
CD    JBFL(I)       LOWEST NUMBERED OF HIGHEST ENERGY GROUP FOR WHICH  -
CD                     SELF-SHIELDING FACTORS ARE GIVEN                -
CD    JBFH(I)       HIGHEST NUMBERED OR LOWEST ENERGY GROUP FOR WHICH  -
CD                     SELF-SHIELDING FACTORS ARE GIVEN                -
CD    NTABP(I)      NUMBER OF SIGP0 VALUES FOR WHICH SELF-SHIELDING    -
CD                     FACTORS ARE GIVEN FOR ISOTOPE I.                -
CD    NTABT(I)      NUMBER OF TEMPERATURE VALUES FOR WHICH SELF-       -
CD                     SHIELDING FACTORS ARE GIVEN FOR ISOTOPE I.      -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          SELF-SHIELDING FACTORS   (3D RECORD)                       -
C                                                                      -
CL    ((((FFACT(N,K,J,M),N=1,NBINT),K=1,NBTEM),J=JBFLI,JBFHI),M=ML,MU) -
CL                  ------ SEE DESCRIPTION BELOW ------                -
C                                                                      -
CC    NBINT=NTABP(I)                                                   -
CC    NBTEM=NTABT(I)                                                   -
CC    JBFLI=JBFL(I)                                                    -
CC    JBFHI=JBFH(I)                                                    -
CC    FOR ML, MU SEE STRUCTURE BELOW                                   -
C                                                                      -
CW    NBINT*NBTEM*(JBFHI-JBFLI+1)*(MU-ML+1) = NUMBER OF WORDS          -
C                                                                      -
CB    FORMAT(4H 3D ,5E12.5/(6E12.5))                                   -
C                                                                      -
CC    DO 1 L=1,NBLOK                                                   -
CC  1 READ(N) *LIST AS ABOVE*                                          -
C                                                                      -
CC          IF IBLK=0, NBLOK=1, ML=1, MU=NREACT                        -
CC          IF IBLK=1, NBLOK=NREACT, ML=MU=L, WHERE L IS THE BLOCK     -
C                                                                      -
CD    FFACT(N,K,J,M)    SELF-SHIELDING FACTOR EVALUATED AT X(N) AND    -
CD                         TB(K) FOR ENERGY GROUP J, THE M INDEX IS    -
CD                         A DUMMY INDEX TO DENOTE THE REACTION TYPE,  -
CD                         THE FIRST FIVE REACTION TYPES ARE, IN       -
CD                         ORDER, TOTAL, CAPTURE, FISSION, TRANSPORT,  -
CD                         AND ELASTIC.                                -
C                                                                      -
CB          NOTE THAT IS IBLK=1, EACH REACTION TYPE WILL CONSTITUTE    -
CB             A SEPARATE DATA BLOCK.                                  -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          CROSS SECTIONS   (4D RECORD)                               -
C                                                                      -
CL    (XSPO(J),J=1,NGROUP),(XSIN(J),J=1,NGROUP),(XSE(J),J=1,NGROUP),   -
CL   1(XSMU(J),J=1,NGROUP),(XSED(J),J=1,NGROUP),(XSX(J),J=1,NGROUP)    -
C                                                                      -
CW    6*NGROUP=NUMBER OF WORDS                                         -
C                                                                      -
CB    FORMAT(4H 4D ,5E12.5/(6E12.5))                                   -
C                                                                      -
CD    XSPO(J)       POTENTIAL SCATTERING CROSS SECTION (BARNS)         -
CD    XSIN(J)       INELASTIC CROSS SECTION (BARNS)                    -
CD    XSE(J)        ELASTIC CROSS SECTION (BARNS)                      -
CD    XSMU(J)       AVERAGE COSINE OF ELASTIC SCATTERING ANGLE         -
CD    XSED(J)       ELASTIC DOWN-SCATTERING TO ADJACENT GROUP          -
CD    XSXI(J)       AVERAGE ELASTIC SCATTERING LETHARGY INCREMENT      -
C                                                                      -
C-----------------------------------------------------------------------

\end{ccode}
\normalsize

The BRKOXS file is used to supply self-shielding factors for use
with the Bondarenko method\cite{Bondarenko} for calculating effective
macroscopic cross sections for the components of nuclear systems.
As discussed in detail in the
\hyperlink{sGROUPRhy}{GROUPR} chapter of this manual, this
system is based on using a model flux for isotope $i$ of the form

\begin{equation}
   \phi^i_\ell(E,T)=\frac{C(E)}{[\sigma^i_0+\sigma^i_t(E,T)]^{\ell+1}}\,\,,
\end{equation}

\noindent
where $C(E)$ is a smooth weighting flux, $\sigma^i_t(E,T)$ is the
total cross section for material $i$ at temperature $T$, $\ell$
is the Legendre order, and $\sigma^i_0$ is a parameter that can
be used to account for the presence of other materials and the
possibility of escape from the absorbing region
(heterogeneity).  \hyperlink{sGROUPRhy}{GROUPR} uses
this model flux to calculate effective multigroup
cross sections for the resonance-region reactions (total, elastic,
fission, capture) for user specified values of $\sigma_0$ and $T$.

When $\sigma_0$ is large with respect to the highest peaks in
$\sigma_t$, the flux is essentially proportional to $C(E)$.  This
is called infinite dilution, and the corresponding cross
sections are appropriate for an absorber in a dilute mixture or
for a very thin sample of the absorber.  As $\sigma_0$ decreases,
the flux $\phi(E)$ develops dips where $\sigma_t$ has peaks.  These
dips cancel out part of the effect of the corresponding peaks in
the resonance cross sections, thereby reducing, or self-shielding,
the reaction rate.  It is convenient to represent this effect
as a self-shielding factor; that is,

\begin{equation}
   \sigma_{xg}(T,\sigma_0)=f_{xg}(T,\sigma_0)\times
     \sigma_{xg}(300^{\circ}K,\infty)\,\,.
\end{equation}

\noindent
In the CCCC system, the f-factors are stored in the BRKOXS file
and the infinitely dilute cross sections are stored in the ISOTXS file.
A code that prepares effective cross sections, such as
SPHINX\cite{SPHINX} or 1DX\cite{1DX}, determines the appropriate
$T$ and $\sigma_0$ values for each region and group in a reactor
problem, using equivalence theory together with the user's
specifications for composition and geometry.  It then reads
in the cross sections and f-factors from the ISOTXS
and BRKOXS files, interpolates in the $T$ and $\sigma_0$ tables
to obtain the desired f-factors, and multiplies to obtain the
effective cross sections.

In the BRKOXS file specification given above, the components of the
``File Identification'' record are the same as for ISOTXS.
The parameters in the ``File Control'' record are used to
calculate the sizes and locations of data in the records
to follow.  The ``File Data'' record contains all the
isotope names, all the $\sigma_0$ values for every isotope, all
the $T$ values for every isotope, the group structure, and several
arrays used for unpacking the other data.  The Hollerith material
names in \cword{HISONM} are the same as those used in ISOTXS, and
they are obtained from the user's input.  The $\sigma_0$ values are
packed into \cword{X(K)} using \cword{NTABP(I)}.  Note that the
base-10 logarithm of $\sigma_0$ is stored.  Therefore, a typical
library might contain the following:

\begin{center}
\begin{tabular}{ccl}
   material \cword{I} & \cword{NTABP(I)} & \cword{X(K)} \\ \hline
      1  & 3  &  3.0 2.0 1.0 \\
      2  & 7  &  4.0 3.0 2.0 1.477 1. 0. -1. \\
      3  & 5  &  4.0 3.0 2.0 1.0 0.0 \\
     $\cdots$ & $\cdots$ & $\cdots$  \\ \hline
\end{tabular}
\end{center}

\noindent
Similarly, the $T$ values are stored in \cword{TB(K)} using
\cword{NTABT(I)}.  The absolute temperatures used by
\hyperlink{sGROUPRhy}{GROUPR} must
be changed to $^\circ$C before being stored.
The energy bounds for the group structure found
on the GENDF tape are stored in \cword{EMAX(J)} and \cword{EMIN}.
As discussed in connection with the ISOTXS format, group boundaries
are stored in order of decreasing energy in the BRKOXS file.

The self-shielding factor approach is designed to account for
resonance self-shielding.  It is not necessarily
appropriate for low energies if only broad resonance features
are apparent, or for high energies where only small residual
fluctuations in the cross section are seen.  For
this reason, the BRKOXS format provides the \cword{JBFL(I)}
and \cword{JBFH(I)} arrays in the ``File Data'' record.  They
are used to limit the range of the numbers given
in the ``Self-Shielding Factors'' record.  The reactions that
are active in the resonance energy range usually include
only the total, elastic, fission, and capture channels.  The
total cross section is usually computed for the two Legendre
orders $\ell{=}0$ and $\ell{=}1$.  This second value is often
called the current-weighted total cross section, and it is
needed to compute the self-shielded diffusion
coefficient.  \hyperlink{sGROUPRhy}{GROUPR} also computes
a self-shielded elastic scattering matrix.
It can be used to provide two quantities for the BRKOXS file.
First, the diffusion coefficient requires the calculation of
a transport cross section for diffusion.  The relationships are
as follows:

\begin{equation}
   D_g=\frac{1}{3\sigma_{tr,g}}\,\,,
\end{equation}

\noindent
and

\begin{equation}
   \sigma_{tr,g}=\sigma_{t1,g}- \sum_{g'}
      \sigma_{e1,g\rightarrow g'}\,\,.
\end{equation}

\noindent
Therefore, the current-weighted P$_1$ elastic cross section
contributes to the transport self-shielding factor.  The
second use for the self-shielded elastic scattering matrix
is to compute a self-shielding factor for elastic removal.  For
heavy isotopes, the energy lost in elastic scattering is small,
and all the removal is normally to one group.  The format requires
that at least the five standard reactions be given in a specified
order.  NJOY is able to add one more as follows:

\begin{singlespace}
\begin{enumerate}
\item total (P$_0$ weighted),
\item capture (P$_0$),
\item fission (P$_0$),
\item transport (P$_1$),
\item elastic (P$_0$), and
\item elastic removal (P$_0$)
\end{enumerate}
\end{singlespace}

The normal pattern for the BRKOXS file expects that there will be
one record of self-shielding factors for each material.  Such a record
could get quite large.  For example, with 6 reactions, 6 temperatures,
6 $\sigma_0$ values, and 100 resonance groups, a ``Self-Shielding Factors''
record could have over 20 000 words.  This number can be made more
manageable by setting the \cword{IBLK} flag in the ``File Control''
record to 1.  Then there will be a separate record of self-shielding
factors for each reaction; this would reduce the record size for the
example to a more reasonable 3600 words.

The actual self-shielding factors are computed from the cross
sections given on the GENDF tape and stored into the
\cword{FFACT(N,K,J,M)} array of the ``Self-Shielding Factors''
record with group order converted to the standard decreasing-energy
convention.  Following the FORTRAN convention, \cword{N} is the fastest
varying index in this array, \cword{K} is the next fastest varying
index, and so on.  The identities of these indices are

\begin{description}
\begin{singlespace}

\item[\cword{    N}] $\sigma_0$,
\item[\cword{    K}] temperature $T$,
\item[\cword{    J}] group, and
\item[\cword{    M}] reaction

\end{singlespace}
\end{description}

The ``Cross Sections'' record contains some additional cross sections
and special parameters that are often used in self-shielding codes
and are not included in the ISOTXS file.  The \cword{XSPO} cross
section is taken to be constant and equal to the CCCCR input parameter
\cword{XSPO}, which is computed as $4\pi a^2$.  The \cword{XSIN}
cross section is obtained by summing over the final group index for every
group-to-group matrix in File 6 except elastic, (n,2n), and fission.
Therefore, it may contain effects of multiplicities greater than
1 if reactions like (n,3n) or (n,2n$\alpha$) are active for the
material.  It may be slightly larger in high-energy groups
than the cross section that
would be obtained using the same sum over reactions in
File 3.  The \cword{XSE} cross section is obtained from \cword{mf}=6,
\cword{mt}=2 on the GENDF tape by summing over final groups.  The
parameters for continuous slowing down theory, \cword{XSMU} and
\cword{XSXI}, are obtained from \cword{mt}=251
and \cword{mt}=252, respectively.  The methods used for calculating these
quantities are described in the
\hyperlink{sGROUPRhy}{GROUPR} section of this report.
Finally, the elastic downscattering cross section is obtained from
the elastic matrix on the GENDF tape (\cword{mf}=6, \cword{mt}=2).


\subsection{DLAYXS}
\label{ssCCCCR_DLAYXS}

The format for the DLAYXS\index{DLAYXS} delayed-neutron data file is given
below in the standard format.

\small
\begin{ccode}

C***********************************************************************
C                       REVISED 11/30/76                               -
C                                                                      -
CF          DLAYXS-IV                                                  -
CE          MICROSCOPIC GROUP DELAYED NEUTRON PRECURSOR DATA           -
C                                                                      -
CN                      THIS FILE PROVIDES PRECURSOR YIELDS,           -
CN                      EMISSION SPECTRA, AND DECAY CONSTANTS          -
CN                      ORDERED BY ISOTOPE.  ISOTOPES ARE IDENTIFIED   -
CN                      BY ABSOLUTE ISOTOPE LABELS FOR RELATION TO     -
CN                      ISOTOPES IN EITHER FILE ISOTXS OR GRUPXS.      -
CN                      FORMATS GIVEN ARE FOR FILE EXCHANGE PURPOSES   -
CN                      ONLY.                                          -
C                                                                      -
C***********************************************************************

C-----------------------------------------------------------------------
CS          FILE STRUCTURE                                             -
CS                                                                     -
CS             RECORD TYPE                        PRESENT IF           -
CS             ===============================    ===============      -
CS             FILE IDENTIFICATION                ALWAYS               -
CS             FILE CONTROL                       ALWAYS               -
CS             FILE DATA, DECAY CONSTANTS, AND                         -
CS                EMISSION SPECTRA                ALWAYS               -
CS   *************(REPEAT TO NISOD)                                    -
CS   *         DELAYED NEUTRON PRECURSOR                               -
CS   *            YIELD DATA                      ALWAYS               -
CS   *************                                                     -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE IDENTIFICATION                                        -
C                                                                      -
CL    HNAME,(HUSE(I),I=1,2),IVERS                                      -
C                                                                      -
CW    1+3*MULT=NUMBER OF WORDS                                         -
C                                                                      -
CB    FORMAT(11H 0V DLAYXS  ,1H*,2A6,1H*,I6)                           -
C                                                                      -
CD    HNAME       HOLLERITH FILE NAME - DLAYXS -                       -
CD    HUSE(I)     HOLLERITH USER IDENTIFICATION (A6)                   -
CD    IVERS       FILE VERSION NUMBER                                  -
CD    MULT        DOUBLE PRECISION PARAMETER                           -
CD                    1- A6 WORD IS SINGLE WORD                        -
CD                    2- A6 WORD IS DOUBLE PRECISION WORD              -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE CONTROL   (1D RECORD)                                 -
C                                                                      -
CL    NGROUP,NISOD,NFAM,IDUM                                           -
C                                                                      -
CW    4=NUMBER OF WORDS                                                -
C                                                                      -
CB    FORMAT(4H 1D ,4I6)                                               -
C                                                                      -
CD    NGROUP        NUMBER OF NEUTRON ENERGY GROUPS IN SET             -
CD    NISOD         NUMBER OF ISOTOPES IN DELAYED NEUTRON SET          -
CD    NFAM          NUMBER OF DELAYED NEUTRON FAMILIES IN SET          -
CD    IDUM          DUMMY TO MAKE UP FOUR-WORD RECORD                  -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          FILE DATA, DECAY CONSTANTS, AND EMISSION SPECTRA           -
C                             (2D RECORD)                              -
C                                                                      -
CL    (HABSID(I),I=1,NISOD),(FLAM(N),N=1,FAM),((CHID(J,N),J=1,NGROUP), -
CL    N=1,NFAM),(EMAX(J),J=1,NGROUP),EMIN,(NKFAM(I),I=1,NISOD),        -
CL    (LOCA(I),I=1,NISOD)                                              -
C                                                                      -
CW    (2+MULT)*NISOD+(NGROUP+1)*(NFAM+1)=NUMBER OF WORDS               -
C                                                                      -
CB    FORMAT(4H 2D ,9(1X,A6))          HABSID                          -
CB   1(10(1X,A6)))                                                     -
CB    FORMAT(6E12.5)                   FLAM,CHID,EMAX,EMIN             -
CB    FORMAT(12I6)                     NKFAM,LOCA                      -
C                                                                      -
CD    HABSID(I)     HOLLERITH ABSOLUTE ISOTOPE LABEL FOR ISOTOPE I (A6)-
CD    FLAM(N)       DELAYED NEUTRON PRECURSOR DECAY CONSTANT           -
CD                     FOR FAMILY N                                    -
CD    CHID(J,N)     FRACTION OF DELAYED NEUTRONS EMITTED INTO NEUTRON  -
CD                     ENERGY GROUP J FROM PRECURSOR FAMILY N          -
CD    EMAX(J)       MAXIMUM ENERGY BOUND OF GROUP J (EV)               -
CD    EMIN          MINIMUM ENERGY BOUND OF SET (EV)                   -
CD    NKFAM(I)      NUMBER OF FAMILIES TO WHICH FISSION IN ISOTOPE I   -
CD                     CONTRIBUTES DELAYED NEUTRON PRECURSORS          -
CD    LOCA(I)       NUMBER OF RECORDS TO BE SKIPPED TO READ DATA FOR   -
CD                     ISOTOPE I, LOCA(1)=0                            -
C                                                                      -
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
CR          DELAYED NEUTRON PRECURSOR YIELD DATA   (3D RECORD)         -
C                                                                      -
CL    (SNUDEL(J,K),J=1,NGROUP),K=1,NKFAMI),(NUMFAM(K),K=1,NKFAMI)      -
C                                                                      -
CC    NKFAMI=NKFAM(I)                                                  -
C                                                                      -
CW    (NGROUP+1)*NKFAMI=NUMBER OF WORDS                                -
C                                                                      -
CB    FORMAT(4H 3D ,5E12.5/(6E12.5))  SNUDEL                           -
CB    FORMAT(12I6)                    NUMFAM                           -
C                                                                      -
CD    SNUDEL(J,K)   NUMBER OF DELAYED NEUTRON PRECURSORS PRODUCED IN   -
CD                     FAMILY NUMBER NUMFAM(K) PER FISSION IN          -
CD                     GROUP J                                         -
CD    NUMFAM(K)     FAMILY NUMBER OF THE K-TH YIELD VECTOR IN          -
CD                     ARRAY SNUDEL(J,K)                               -
C                                                                      -
C-----------------------------------------------------------------------

\end{ccode}
\normalsize

This file is used to communicate delayed-neutron data to reactor kinetics
codes.  The ENDF files give a total delayed-neutron yield $\bar{\nu}_d$
in the section labeled \cword{mf}=1,
\cword{mt}=455.  \hyperlink{sGROUPRhy}{GROUPR} averages this
yield for each neutron group $g$ using

\begin{equation}
   \bar{\nu}^D_g=\frac{\displaystyle\int_g \nu_d(E)\sigma_f(E)\phi(E)\,dE}
      {\displaystyle\int_g\sigma_f(E)\phi(E)\,dE} \,\,.
\end{equation}

\noindent
This same section of the ENDF tape contains the decay constants for the
delayed-neutron time groups.  These numbers are passed on to the
\hyperlink{sGROUPRhy}{GROUPR} routine that averages the
delayed-neutron spectra, and they end up in the \cword{mf}=5
record on the GENDF tape.  The ENDF evaluations give the
delayed-neutron spectra for the time groups in \cword{mf}=5,
\cword{mt}=455.  These spectra are not separately
normalized.  Rather, the sum over all
time groups is normalized, but the integral of any one of the spectra
gives the ``delayed fraction'' for that time
group.  \hyperlink{sGROUPRhy}{GROUPR} simply
averages these spectra using the specified neutron group structure.
The resulting group spectra (and the decay constants from File 1) are
written onto the GENDF tape.

Returning to the DLAYXS format description, the parameters in the
``File Identification'' record are obtained from the user's input,
just as for ISOTXS and BRKOXS.  The parameter \cword{NGROUP} is also
a user input quantity.  \cword{NISOD} is determined after the entire
GENDF tape has been searched for isotopes that are on the user's list
of \cword{NISO} materials and that have delayed-neutron data.
The \cword{NFAM} parameter needs some additional explanation.
A ``family'' for the DLAYXS file is actually an index that selects
one particular spectrum from the \cword{CHID} array.  It could
correspond to an actual delayed-neutron precursor isotope left after
a fission event.  In such a case, there would be many ``families''
corresponding to the many possible fission fragment isotopes.
The \cword{SNUDEL} yields would be analogous to fission product
yields.  The ENDF evaluations take a more macroscopic approach.
Spectra are chosen to include all the emissions from a group of
delayed-neutron precursors for a particular fissioning nucleus with
similar decay constants.  In this representation, the DLAYXS ``family''
corresponds to a particular decay constant and spectrum for a
particular target isotope.  Therefore, the number of families is
simply six or eight times the number of isotopes, {\it e.g.},
\cword{NFAM=6*NISOD}.

In the ``File Data, Decay Constants, and Emission Spectra'' record,
the Hollerith isotope names \cword{HABSID} are obtained from the names
in the user's input.  The \cword{FLAM} values come directly from the
decay constant values originally extracted from File 1 of the ENDF tape.
The family index for isotope \cword{ISO} and time group \cword{I} is
simply computed as \cword{6*(ISO-1)}+\cword{I} or \cword{8*(ISO-1)}+\cword{I}.
The \cword{CHID} array is loaded from the \cword{mf}=5, \cword{mt}=455 section
on the GENDF tape using the family index and the group index.  As usual, the
order of groups has to be changed from the GROUPR convention with
increasing-energy order to the CCCC convention with decreasing-energy
order.  The group structure itself is obtained from the GENDF header
record and stored into \cword{EMAX} and \cword{EMIN} in the
conventional order.  The value of \cword{NKFAM} is simply 6 or 8
for every isotope.  The \cword{LOCA} values are also easy to compute;
they are just \cword{ISO} minus 1.

The delayed-neutron yields versus incident neutron energy group and
family index are given in the ``Delayed Neutron Precursor Yield Data''
record.  As mentioned above, the total yield is given in \cword{mf}=3 of the
GENDF tape, and the delayed fractions can be computed by summing the
spectrum for each time group over the energy group index.  The array
\cword{SNUDEL} in this DLAYXS record contains the product of these
values.  Note that there is one of these yield records for each
delayed-neutron isotope, and each record contains six or eight families.
The \cword{NKFAM} vector is used to establish the correspondence
between these families and the entire list of families used in the
file data record.  As an example, \cword{NUMFAM(1)} would contain
1, 2, 3, 4, 5, 6; \cword{NUMFAM(2)} would contain 7, 8, 9, 10, 11,
12, and so on.

\subsection{Coding Details}
\label{ssCCCCR_code}

Subroutine \cword{ccccr}\index{ccccr@{\ty ccccr}}
is the only public call for
module \cword{ccccm}\index{modules!ccccm@{\ty ccccm}}.
The module has a number of global variables and
arrays defined.  One key set of variables and arrays provides the
area for accumulating the CCCC data.  It provides a set of
equivalenced arrays so that integers, reals, and Hollerith strings
can all be stored in the same binary records.  It sets up both
integers and reals to be 4-byte quantities.  Hollerith words
(with up to 8 characters each) are 8-byte quantities.  The CCCC
\cword{mult} value is set to 2.  See \cword{a(50000)},
\cword{ia(50000)}, and \cword{ha(25000)}.  The parameter
\cword{isiza=50000} defines the size of these equivalenced arrays
in 4-byte units.

The main subroutine of CCCCR starts by allocating an array \cword{maxe}
for reading in data from the input ENDF-format files.  Note that this
array uses 8-byte words.  The values read in will be converted to the
4-byte words used in the CCCC \cword{a,ia,ha} set as necessary.  Note
the variable \cword{next}.  It will keep track of the next available
location in the \cword{a,ia,ha} area.

Next, the unit numbers for input and output are read.  The signs given
for CCCC units are ignored; they are opened as binary files.  The
subroutine continues by reading input cards 2 through 5.  At this
point, CCCCR branches to different subroutines for each of the three
interface file types that have been requested (see
\cword{cisotx}\index{cisotx@{\ty cisotx}},
\cword{cbrkxs}\index{cbrkxs@{\ty cbrkxs}}, and
\cword{cdlyxs}\index{cdlyxs@{\ty cdlyxs}}).  Each of these routines is
paired with a print routine that is called if the \cword{iprint} flag has
been set to 1 (see \cword{pisotx}\index{pisotx@{\ty pisotx}},
\cword{pbrkxs}\index{pbrkxs@{\ty pbrkxs}}, and
\cword{pdlyxs}\index{pdlyxs@{\ty pdlyxs}}).
When the last of these routines returns, CCCCR closes its active
I/O units, writes a report, and terminates.

\paragraph{ISOTXS File Preparation.}
The \cword{cisotx}\index{cisotx@{\ty cisotx}} routine starts by calling
\cword{ruinis}\index{ruinis@{\ty ruinis}} to read in
the portion of the user's input specific to the ISOTXS file.  It then
calls \cword{isxdat}\index{isxdat@{\ty isxdat}} to read through the
input GENDF file and extract the ISOTXS data.

Subroutine \cword{ISXDAT}\index{isxdat@{\ty isxdat}} starts by
setting up pointers in the \cword{a,ia,ha} area for the different
types of data to be read in.  These pointers are identified in the
comments at the start of the subroutine.  The routine then reads
the GENDF header record for the first material and extracts
the group boundary energies.  If the group structure found does
not match the one requested in the user's input, an error message
is issued.  Otherwise, the order of the groups is changed from
the \hyperlink{sGROUPRhy}{GROUPR}/ENDF convention
of increasing energy to the
CCCC convention of decreasing energy (which is the normal ordering for
application programs) as the 8-byte GENDF data are copied into the
4-byte words of the \cword{a} array.  The routine then begins a loop
over all the materials (isotopes) requested (see \cword{do 300 i=1,niso}).
It searches through the input GENDF tape for the first material with
the requested MAT number (that is, the first temperature for the MAT)
and copies it to a scratch file.  Note that materials are written in the
order requested by the user's input material list, not in the
order that they are found on the GENDF tape.

This scratch tape is scanned for the ISOTXS principal cross section data
in \cword{prinxs}\index{prinxs@{\ty prinxs}}.  This process is fairly
simple for most of the ENDF File 3 cross sections.  Each MT number
in File 3 is compared to the list of desired principal cross sections
in \cword{nstx}; if a match is found, the corresponding element
of \cword{iflag} is set, and the cross section table is copied
into memory using a pointer from the \cword{iptr} array.
The (n,2n) reaction is a special case.  In addition to \cword{mt}=16, the
routine watches for the partial (n,2n) representation used in the
ENDF/B-IV and -V evaluations for $^9$Be (namely, \cword{mt}=6, 7, 8, and 9),
and adds them into the appropriate memory locations.  Fission is
obtained from \cword{mt}=18, but if the partial fission reactions are present
(\cword{mt}=19, 20, 21, 38), the flag \cword{mt=19} is set.  Average neutron
velocities are obtained from the special
\hyperlink{sGROUPRhy}{GROUPR}-produced section labeled
by \cword{mt}=259.  These are inverse velocities in s/m, and \cword{prinxs}
inverts them and multiplies by 100 to get velocities in cm/s.  In
addition to the normal flux-weighted total cross section, the routine
also stores the current-weighted, or P$_1$, cross section for use in
calculating the transport cross section (see below).  Finally, File 3
may also contain \cword{mt}=455, the delayed-neutron $\bar{\nu}$ parameter.
The GENDF record for this parameter also contains $\sigma_f$ and the
flux for each group.  The delayed-neutron production rate
$\bar{\nu}_d\sigma_f$ is stored for use in calculating the total
$\bar{\nu}$ parameter, and $\bar{\nu}_d\sigma_f\phi$ is added into
the \cword{dnorm} array for later use in normalizing the total fission
spectrum, $\chi$.  Note that there are two options for the flux used
in this normalization: it can be the default library flux found on each
record of the GENDF file, or it can be a flux spectrum \cword{spec}
provided by the user.

While reading through the scratch tape, \cword{prinxs} also watches for
the elastic scattering matrix (\cword{mf}=6, \cword{mt}=2).  The total
P$_1$ elastic
cross section is calculated by summing over all secondary neutron groups,
and the result is subtracted from the current-weighted total cross section
to obtain the transport cross section.

The processing of the fission matrix (\cword{mf}=6, \cword{mt}=18) and
the delayed-fission
spectra (\cword{mf}=5, \cword{mt}=455) depend on the \cword{ichix} option.  The
$\bar{\nu}$ parameter \cword{SNUTOT} is always calculated for fissionable
isotopes.  \cword{CHISO} is only calculated if the vector representation
was requested; in addition, it can be calculated using the flux from GENDF
or using the input flux in \cword{SPECT}.  Starting with NJOY 91.0, the
fission matrix is represented by a real group-to-group matrix at high
energies, and by a single spectrum  (with \cword{IG=0}) and an associated
production cross section (with \cword{IG2LO=0}) at low energies.  This
representation can lead to great savings for libraries with many
low-energy groups.  The contributions to \cword{SNUTOT} from the
low-energy range are easily obtained by adding in the production
cross section.  At high energies, the sum of the group-to-group matrix
over all secondary-energy groups is added in.  After \cword{mf}=3,
\cword{mt}=455 and \cword{mf}=6, \cword{mt}=18 have been processed,
it is only necessary to divide the total
production rate in memory by the fission cross section to obtain the
required total $\bar{\nu}$ values.

The prompt part of the fission $\chi$ vector or matrix is obtained from
\cword{mf}=6, \cword{mt}=18, or if the \cword{MT=19} flag was set while
reading File 3,
from \cword{mt}=19, 20, 21, and 38.  The code starts at statement number 207,
and it is fairly complicated because it has to cope with the following
options:

\begin{singlespace}
\begin{enumerate}
\item $\chi$ vector versus $\chi$ matrix,

\item default weighting for the vector versus input weighting,

\item square matrix versus collapsed rectangular matrix, and

\item constant and matrix parts of \cword{mf}=6 GENDF record.
\end{enumerate}
\end{singlespace}

\noindent
Note that separate normalization sums are accumulated in
\cword{cnorm(ispec)} for the chi vector or for each column of the
matrix while the $\chi$ elements are being stored.  The delayed
contributions to the fission $\chi$ vector or matrix are taken from
\cword{mf}=5, \cword{mt}=455 (see statement number 230).  The
time group spectra are added and multiplied by the delayed neutron
production rate \cword{dnorm} (which can be incident energy dependent
through the \cword{ispec} index if a matrix is being constructed).
The delayed contributions to the normalization sum for the $\chi$ vector
or for each column of the $\chi$ matrix are added into \cword{cnorm}
during this step.  After all the components of the fission spectrum
have been read from the GENDF file, the $\chi$ vector or the
columns of the $\chi$ matrix are normalized using this quantity.

When all sections of the scratch tape have been processed,
\cword{prinxs} goes through the principal cross section block,
removing any parts that have zero cross sections.  The resulting
block is written to scratch file \cword{nscrt2}.  Finally, it writes
the chi matrix data, if any, to the same scratch file and returns
to \cword{isxdat}.

Subroutine \cword{isomtx}\index{isomtx@{\ty isomtx}} is then called
to read through the scratch tape and process the group-to-group
matrices into CCCC format.  In order to allow large matrices
to be processed on machines with limited memory, one
or more passes can be made through the scratch tape (see
\cword{do 400 nj=1,npass}).  The number of passes used depends upon the
amount of space available in scratch array \cword{b} and on the
subblocking option requested by the user.  The four options supported
by CCCCR were discussed in connection with the ISOTXS format description.
Only one pass is required for the first option.  In the other cases, the
length of one subblock is divided into the length of the scratch array
to determine the number of subblocks that can be accumulated on one
pass (\cword{nrec}) and the number of passes required (\cword{npass}).

Four matrix reactions are extracted from the scratch tape (see
\cword{do 500 i=1,4}).  The total matrix is obtained by adding all
matrices found on the GENDF tape except the fission matrices.  The
elastic matrix is obtained from \cword{mt}=2 only.  The (n,2n) matrix is
normally obtained from MT=16, but the sum of \cword{mt}=6, 7, 8, 9, 46, 47, 48,
and 49 will be used for the old $^9$Be representation, if found.  The
inelastic matrix is the sum of everything else; that is, it includes
the normal inelastic reactions \cword{mt}=51-91, and it also includes other
neutron-producing reactions like (n,3n), (n,n$'$p), and (n,n$'\alpha$).
Each GENDF section found is passed to \cword{shuffl}, which rearranges
the input data into the CCCC order in scratch array \cword{b}, and
then to \cword{wrtmtx}, which repacks the data into banded form
and writes the results to \cword{nscrt2}.

Subroutine \cword{shuffl}\index{shuffl@{\ty shuffl}} reads each
of the group-to-group cross sections for a given reaction (MT)
and calculates a location for each cross section in the
scratch array (\cword{noloc}).   Different formulas are used
for the location of the two allowed values of \cword{IFOPT}.
For \cword{IFOPT=1}, the data are stored with incident group index
\cword{jg1} changing fastest, then Legendre index \cword{il}, and with
final group index \cword{jg2} changing slowest.  Note that the indexing
scheme only stores the triangle of the matrix corresponding to ingroup
scattering and downscatter (that is, \cword{jg2}$\ge$\cword{jg1}).  In
addition, the first group in a subblocking range \cword{ng2z} is used.
This means that values of \cword{jg2} less than \cword{ng2z} will result
in storage locations less than \cword{irsize}, and they will not be
stored (see statement 200).  Groups with \cword{jg2} above the subblock
might be stored in memory, or they might end up above the upper limit
of the memory area and be suppressed by statement number 200.  Similarly,
the data for \cword{IFOPT=2} are stored with \cword{jg1} as the fastest
varying index, then \cword{jg2}, and finally with \cword{il} as the
slowest varying index.  Here also, the storage pointer \cword{noloc}
is calculated so that only elements with \cword{jg2}$\ge$\cword{jg1} are
stored, and elements that are outside of a given subblock are removed
if they fall outside the bounds of the memory array.

Subroutine \cword{wrtmtx}\index{wrtmtx@{\ty wrtmtx}} searches
through the memory area loaded in \cword{shuffl} to find the
bands of group-to-group elements that will be written on the
final ISOTXS file.  The calculation of locations in the memory
array depends on the blocking and subblocking options selected.
In general, the routine calculates locations \cword{NOLOCA} and tests the
cross section found there against the value \cword{eps=1.E-10}.  The
highest index that violates this test for a given final energy group
determines the bandwidth for that group.  (Remember that the
inscattering group is always kept, even if it has zero cross section.)
Once the band limits have been found, the subroutine loops back through
the memory area and squeezes out the locations that are not included in
the bands.  At this point, all the elements of the ``Scattering Sub-Block''
are in their final locations, and the record is written out to
scratch tape \cword{nscrt2}.

When \cword{isomtx} returns to \cword{isxdat}, the ``Isotope
Control and Group Independent Data'' record is completed by filling
in the values of \cword{IDSCT} and \cword{IJJ}, and the record is
written to scratch tape \cword{nscrt3}.  The \cword{LOCA} values for
the ``File Date'' record are also calculated at this point.  They
remain in memory at \cword{l19}.  Once the ``\cword{do 300}'' loop
over the requested isotopes has finished, the \cword{isxdat} routine
returns.

Back in \cword{cisotx}, all the data needed for the ISOTXS file are now
in memory or on one of the CCCC-style scratch files \cword{nscrt2} or
\cword{nscrt3}.  The routine simply steps through the ISOTXS records
and either constructs them or copies them from a scratch file.  When
the file has been written, the routine returns to \cword{ccccr}, which
checks the print flag, and calls \cword{pisotx}, if requested.

Subroutine \cword{pisotx}\index{pisotx@{\ty pisotx}} is a fairly
simple routine.  It reads through the ISOTXS file produced by CCCCR
and prepares an interpreted listing of the data.

\paragraph{BRKOXS File Preparation.}
Subroutine \cword{cbrkxs}\index{cbrkxs@{\ty cbrkxs}} is used to
prepare the BRKOXS file, if requested.  Following the same pattern
as \cword{cisotx}, it calls \cword{ruinbr}\index{ruinbr@{\ty ruinbr}}
to read the user's input, then it calls \cword{brkdat} to extract
the desired data from the GENDF file, and finally it writes
the output BRKOXS file using data stored in memory and on a scratch
tape by \cword{brkdat}.

The storage locations used by \cword{brkdat}\index{brkdat@{\ty brkdat}}
are outlined in the comment cards at the beginning of the subroutine.
The subroutine now opens the input GENDF file and reads in the header
record.  After checking for possibly incompatible group structures, it
reverses the order of the group bounds and loads them into the \cword{emax}
and \cword{emin} arrays.  The data block starting at \cword{l19} is
sized to hold 13 infinitely dilute cross section vectors that will
either be needed during the processing (vectors 1 through 7) or
will be written into the ``Cross Sections'' record.  These
13 quantities are

\begin{singlespace}
\begin{enumerate}

\item P$_0$ total cross section,
\item capture cross section,
\item fission cross section,
\item P$_1$ total - P$_1$ elastic,
\item elastic cross section,
\item P$_1$ total cross section,
\item P$_1$ flux,
\item \cword{XSPO},
\item inelastic cross section,
\item elastic cross section,
\item average elastic scattering cosine $\bar{\mu}$,
\item elastic downscatter to adjacent group, and
\item average elastic lethargy increment $\xi$.

\end{enumerate}
\end{singlespace}

\noindent
Pointer \cword{l20} defines the balance of the available memory.

The next step is to determine whether it is necessary to subblock
the self-shielding factor record.  The amount of space available
in the memory area is compared with the maximum amount of memory
required for the f-factors.  If there is not enough space,
\cword{nsblk} is increased to \cword{nreact}; otherwise, it is
left at 1.  The value of \cword{nsblk} is stored into the \cword{IBLK}
field of the BRKOXS ``File Control'' record.

The isotope loop is complicated because CCCCR allows the materials
on the GENDF tape to be in any order, but it arranges things so that the
materials on the BRKOXS files are in the order that the materials are
named in the user's input.  The main loop is controlled by
\cword{do 370 i=1,niso}.  For each pass, the input GENDF tape is rewound
and searched for isotope \cword{I} (see \cword{do 170 j=1,niso}).  Once
a desired material has been found, the $\sigma_0$ list in the header
record is examined.  Either the first abs(\cword{nzi}) values are
extracted (for \cword{nzi} negative), or the particular values that
occur on the input \cword{asig} list are extracted (for \cword{nzi}
positive).  In either case, \cword{nzj} is the number of $\sigma_0$
values found, \cword{isig} contains the pointers to the values selected,
and \cword{csig} contains the actual values of $\sigma_0$.

GENDF tapes contain one or more temperatures for each material recorded
as consecutive MATs.  Starting at statement number 190,
\cword{brkdat}\index{brkdat@{\ty brkdat}} reads through all the
materials with the current MAT number selecting the desired
temperatures and copying them to a scratch file \cword{nscrt1}.
The procedure used to select temperatures is similar to the one used to
select $\sigma_0$ values.  If \cword{nti} is negative, the first
abs(\cword{nti}) temperatures are extracted.  If \cword{nti} is positive,
only temperatures on the list in \cword{atem} are extracted. In either
case, \cword{ntj} is the number of temperatures found for this material,
\cword{item} contains indices to those temperatures, and \cword{ctem}
contains the actual temperature values.

In the loop beginning at \cword{do 340 nsb=1,nsblk}, a pass through the
scratch tape is made for each subblock (1 or \cword{nreact}).  Each
section of the GENDF format is located, and either \cword{xsproc}
(for \cword{mf}=3) or \cword{mxproc} (for \cword{mf}=6) is called to
process the data in the section.

Subroutine \cword{xsproc}\index{xsproc@{\ty xsproc}} is called
once for each reaction in File 3 of the GENDF tape.  It reads in
all the data, checks which reaction is present, and stores the data
in one of the 13 cross section locations (see \cword{l19}), or
in one of the f-factor locations (see \cword{l20}).  If the
denominator for the f-factor calculation is zero, the division
is skipped, and a warning message is issued.

Subroutine \cword{mxproc}\index{mxproc@{\ty mxproc}} is  called
once for each reaction in File 6 of the GENDF tape.  It loops
through statement number 120 to read all of the incident groups,
and then it uses different sections of coding to  fill in
or fix up the rest of the 13 elements in the infinitely dilute
cross section block at \cword{l19}.  These quantities include the
elastic and inelastic cross sections, the transport cross section, and
the removal cross section.  This routine also computes the elastic
removal self-shielding factors from \cword{mf}=6, \cword{mt}=2, and stores
the results in the f-factor area at \cword{l20}.

Back in \cword{brkdat}, the self-shielded transport cross sections are
converted into f-factors.  A check is then made to see if the transport
values were properly computed.  This requires that a self-shielded
elastic matrix was available for all the higher temperatures.  A
warning message is issued if the required data were not present.  The
last 6 of the 13 vectors stored starting at \cword{l19} are the data
needed for the ``Cross Sections'' record; that block is written to
scratch file \cword{nscrt2}.  Next, the accumulated f-factor data at
\cword{l20} are written to \cword{nscrt2}, and the \cword{NTABP} and
\cword{NTABT} arrays are stored at \cword{l14} and \cword{l15},
respectively.

The last step inside the isotope loop is to call
\cword{thnwrt}\index{thnwrt@{\ty thnwrt}} to thin
out the f-factor data and write the results onto scratch file
\cword{nscrt3}.  It starts by reading the cross section data from
\cword{nscrt2} into memory. Then it reads the f-factor data into memory
and repacks it to take account of the group range for interesting
self-shielding factors, namely, \cword{JBFL} to \cword{JBFH}.  When this
is finished, it writes the f-factor array out to \cword{nscrt3}, and
then it writes the unchanged cross section block out to \cword{nscrt3}.
Note that these two records are now in the correct order to be copied
to the BRKOXS file.

Subroutine \cword{thnwrt} now returns control to \cword{brkdat}.
When the ``\cword{do 370}'' loop has finished, the routine cleans
up the ``File Data'' information in memory and returns to the
main BRKOXS routine.  At this point, all the information required
to construct the output file is present in memory or on scratch
tape \cword{nscrt3}.  The routine steps through the records of the
BRKOXS format constructing them or copying them from the CCCC-style
scratch file.  It then returns to \cword{ccccr}, which checks to
see whether \cword{pbrkxs} should be called.

Subroutine \cword{pbrkxs}\index{pbrkxs@{\ty pbrkxs}} is a
fairly simple routine.  It reads through the BRKOXS file produced
by \cword{ccccr} and prepares an interpreted listing of the data.

\paragraph{DLAYXS File Preparation.}
Subroutine \cword{cdlyxs}\index{cdlyxs@{\ty cdlyxs}} is used
to prepare a DLAYXS file, if requested.  It starts by calling
\cword{dldata}\index{dldata@{\ty dldata}} to extract the
delayed-neutron data from the input GENDF file.  Since all the
data are stored into memory, \cword{cdlyxs}\index{cdlyxs@{\ty cdlyxs}}
continues by simply writing out the required ``File Identification",
``File Control", ``File Data, Decay Constants, and Emission Spectra",
and ``Delayed Neutron Precursor Yield Data" records.  If no
delayed-neutron data are found, \cword{cdlyxs} issues a fatal
error message.  The coding can handle either the traditional
6 time groups of ENDF/B or the 8 time groups used in some other
evaluation systems.  For convenience, the following discussion will
just use the 6 time groups.

Subroutine \cword{dldata}\index{dldata@{\ty dldata}} starts by
reserving space for the dynamic arrays used to store the
delayed-neutron data; the purpose for each of these arrays is
summarized in the comment block at the beginning of the subroutine.
ENDF delayed-neutron files are based on the traditional 6 time groups;
therefore, CCCCR makes each time group for each isotope correspond
to one DLAYXS ``delayed-neutron family'' (see \cword{NFAM=6*NISOD}).
Next, \cword{dldata} starts reading through the materials on the GENDF
tape and looking at each material requested in the user's input
(the material loop goes through statement 110).  For the first
material, it reads the header record, checks that the group
structure is compatible with the user's input value \cword{ngroup},
and stores the structure in \cword{EMAX} and \cword{EMIN} in the
conventional decreasing-energy order.  For all materials,
it watches for sections with \cword{mf}=3, \cword{mt}=455 or
\cword{mf}=5, \cword{mt}=455.

When \cword{mf}=3/\cword{mt}=455 is found (see statement 310),
\cword{dldata}\index{dldata@{\ty dldata}} stores the total delayed-neutron
yield from \hyperlink{sGROUPRhy}{GROUPR} in the
\cword{snudel} array (pointer \cword{l8})
using an offset computed from the time group index (which varies
from 1 to 6), the group index, and the isotope index.  (The
group index goes through statement 130).  For the present,
the same value is stored for every time group.

When \cword{mf}=5/\cword{mt}=455 is found (see statement
410), the rest of the data
for this isotope are stored into memory.  The \cword{HABSID} field
is obtained from the isotope name in the user's input.  The
\cword{LOCA} field is easy to calculate from the isotope index.
The decay constants for each of the time groups are copied into
\cword{FLAM} from the GENDF record.  The number of families
for this isotope is simply 6; this number is loaded into the
location corresponding to \cword{NKFAM}.  Finally, the actual
delayed-neutron spectra for each time group are loaded into
the \cword{CHID} area using energy group and family number as
indexes. At this point, the spectrum for each time group is
summed over group index to determine the delayed fraction for that
time group [see \cword{FRACT(I)}].  Then this fraction is used
to change the total delayed-neutron yield for each time group
in the \cword{SNUDEL} area into the fractional delayed-neutron
yield for that time group (family).

When all the isotopes containing delayed-neutron data have been
processed, \cword{dldata} returns to \cword{cdlyxs}.  When
\cword{cdlyxs} returns to the main subroutine of CCCCR after
writing the DLAYXS file, the print routine
\cword{pdlyxs}\index{pdlyxs@{\ty pdlyxs}} may be called.  This
is a fairly simple routine that reads through a file
in DLAYXS format and prepares an interpreted listing.


\subsection{User Input}
\label{ssCCCCR_inp}

The user input instructions copied from the comment cards at the
beginning of the CCCCR source code are given below.  It is always
a good idea to check the comments cards in the current version of
the code in case there have been any changes.
\index{CCCCR!CCCCR input}
\index{input!CCCCR}

\small
\begin{ccode}

   !---input specifications (free format)---------------------------
   !
   !-ccccr-
   ! card 1 units
   !    nin      input unit for data from groupr
   !    nisot    output unit for isotxs (0 if isotxs not wanted)
   !    nbrks    output unit for brkoxs (0 if brkoxs not wanted)
   !    ndlay    output unit for dlayxs (0 if dlayxs not wanted)
   ! card 2 identification
   !    lprint    print flag (0/1=not print/printed)
   !    ivers     file version number (default=0)
   !    huse      user identification (12 characters)
   !              delimited by *, ended by /.
   !              (default=blank)
   ! card 3
   !    hsetid    hollerith identification of set (12 characters)
   !              delimited by *, ended by /.
   !              (default=blank)
   ! card 4 file control
   !    ngroup    number of neutron energy groups
   !    nggrup    number of gamma energy groups
   !    niso      number of isotopes desire
   !    maxord    maximum legendre order
   !    ifopt     matrix blocking option (1/2=blocking by
   !                               reaction/legendre order)
   ! card 5 isotope parameters (one card per isotope)
   !       (first four words are hollerith, up to six characters
   !       each, delimited by *)
   !    hisnm     hollerith isotope label
   !    habsid    hollerith absolute isotope label
   !    hident    identifier of data source library (endf)
   !    hmat      isotope identification
   !    imat      numerical isotope identifier (endf mat number)
   !    xspo      average potential scattering cross sect. (brkoxs)
   !-cisotx- (only if nisot.gt.0)
   ! card 1 file control
   !    nsblok    subblocking option for scattering matrix
   !              (1 or ngrup sub-blocks allowed)
   !    maxup     maximum number of upscatter groups (always zero)
   !    maxdn     maximum number of downscatter groups
   !    ichix     fission chi representation
   !                   -1   vector (using groupr flux)
   !                    0   none
   !                   +1   vector (using input flux)
   !                .gt.1   matrix
   ! card 2 chi vector control (ichix=1 only)
   !    spec      ngroup flux values used to collapse the groupr
   !              fission matrix into a chi vector
   ! card 3 chi matrix control (ichix.gt.1 only)
   !    spec      ngroup values of spec(i)=k define the range of
   !              groups i to be averaged to obtain spectrum k.
   !              index k ranges from 1 to ichi.
   !              the model flux is used to weight each group i.
   ! card 4 isotope control (one card per isotope)
   !    kbr       isotope classification
   !    amass     gram atomic weight
   !    efiss     total thermal energy/fission
   !    ecapt     total thermal energy/capture
   !    temp      isotope temperature
   !    sigpot     average effective potential scattering
   !    adens     density of isotope in mixture
   !
   !-cbrkxs- (only if nbrks.gt.0)
   ! card 1 (2i6) file data
   !    nti       number of temperatures desired
   !              (-n means accept first n temperatures)
   !    nzi       number of sigpo values desire
   !              (-n means accept first n dilution factors)
   ! card 2 (not needed if nti.lt.0)
   !    atem(nti) values of desired temperatures
   ! card 3 (not needed if nzi.lt.0)
   !    asig(nzi) values of desired sigpo
   !
   !-cdlayx-- no input required
   !--------------------------------------------------------------------
\end{ccode}
\normalsize

These instructions are divided into four parts.  First, there is a
general section that applies to all three interface files following
\cword{-ccccr-}.  Second, there is a section of special parameters
for ISOTXS following \cword{-cisotx-}. Third, there is a section of
special parameters for BRKOXS following \cword{-cbrkxs-}.  And fourth,
there is a comment following \cword{-cdlaxs-} noting that no special
input is required for the DLAYXS file.

In the \cword{-ccccr-} section, Card 1 is used to read in the unit
numbers for input and output.  \cword{nin} must be a GENDF tape
prepared using \hyperlink{sGROUPRhy}{GROUPR}, and it
can have either binary (\cword{nin<0})
or ASCII (\cword{nin>0}) mode.  The units for the output ISOTXS,
BRKOXS, and DLAYXS files are all binary, but either sign can be
used on the unit numbers.  If any unit number is given as zero,
the corresponding CCCC interface file will not be generated.
On Card 2, the \cword{lprint=1} is used to request a full
printout of all the CCCC files generated.  The file version number
\cword{ivers} can be used to distinguish between different libraries
generated using NJOY.  The user identification field \cword{huse}
can contain any desired 12-character string.  An example of Card 2
might be

\small
\begin{ccode}

  0  7  'T2 LANL NJOY'/

\end{ccode}
\normalsize

\noindent
Card 3 contains a description of the library using up to 72
characters (12 standard CCCC words of 6 characters each).  For
example,

\small
\begin{ccode}

  'LIB-IV 50-GROUP LMFBR LIBRARY FROM ENDF/B-IV (1976)'/

\end{ccode}
\normalsize

On Card 4, the values given for \cword{ngroup} must agree with the
number of groups on the input GENDF tape or a fatal error message
will be issued.  \cword{nggrup} is not used.  \cword{niso} is
the total number of materials or isotopes to be searched for on
the GENDF tape.  The value of \cword{maxord} should be less than or
equal to the maximum Legendre order used in the
\hyperlink{sGROUPRhy}{GROUPR} run.  The
use of the matrix blocking parameter \cword{ifopt} was discussed
in detail in connection with the description of the ISOTXS format
above.  A value of 1 has been normally used for Los Alamos libraries.

A line using the Card 5 format is given for each of the \cword{niso}
isotopes or materials to be processed.  The Hollerith isotope label
and the Hollerith absolute isotope label have normally been set
to the conventional isotope name at Los Alamos; for example,
\cword{u235} or \cword{cnat}.  The library name in \cword{habsid}
can vary quite  a lot now that many other libraries are available in
ENDF format.  The values of \cword{hmat} and \cword{imat} will
normally be derived from the MAT number characteristic of all
libraries in ENDF format.  Unfortunately, \cword{xspo}, the
average potential scattering cross section, must be entered by
hand.  It can be obtained from \cword{mf}=2, \cword{mt}=151 on
the ENDF file for
the material by determining the scattering radius $a$ from the
\cword{AP} field and computing $\sigma_p{=}4\pi a^2$.  The
following fragment of an ENDF/B evaluation shows the vicinity
of \cword{AP}:

\small
\begin{ccode}

  ...
 9.223500+4 2.330248+2          0          0          1          09228 2151
 9.223500+4 1.000000+0          0          1          2          09228 2151
 1.000000-5 2.250000+3          1          3          0          19228 2151
 3.500000+0 9.602000-1          0          0          1          39228 2151
 2.330200+2 9.602000-1          0          0      19158       31939228 2151
-2.038300+3 3.000000+0 1.970300-2 3.379200-2-4.665200-2-1.008800-19228 2151
  ...

\end{ccode}
\normalsize

\noindent
The scattering radius is the second number on the fourth card in the
section \cword{mf}=2, \cword{mt}=151.  Using it as $a$ gives
$4\pi(0.96020)^2=11.582$ barns
for the value of \cword{xspo}.  An example of Card 5 follows:

\small
\begin{ccode}

  U235 U235 ENDF6 '9228' 9228 11.582

\end{ccode}
\normalsize

\noindent
Note that the Hollerith string ``9228'' had to be delimited
by quotes because it does not begin with a letter.  The delimiters
are optional for the other Hollerith variables.

The next block of input cards is specific to ISOTXS and only appears
if ISOTXS processing was requested with a nonzero value for \cword{nisot}.
The first parameter on Card 1 is \cword{nsblok}, which was
discussed in connection with matrix blocking and subblocking.
\cword{nsblok} and \cword{ifopt} work together to control how
a large scattering matrix is broken up into smaller records on
the ISOTXS interface file.  The important factor is the maximum
size of the binary records.  They should be small enough to fit into
a reasonable amount of memory in any application codes that use
ISOTXS files, but they should be large enough to keep the
number of I/O operations to a minimum.  The maximum record size
for each option is repeated below for the convenience of the
reader:

\begin{singlespace}
\begin{enumerate}

\item {\cword{ifopt=1} and \cword{nsblok=1}}: $n_\ell\times n_g(n_g{-}1)/2$,
\item {\cword{ifopt=1} and \cword{nsblok=ngroup}}: $n_\ell\times n_g$,
\item {\cword{ifopt=2} and \cword{nsblok=1}}: $n_g(n_g{-}1)/2$.,
\item {\cword{ifopt=2} and \cword{nsblok=ngroup}}:  $n_g$,

\end{enumerate}
\end{singlespace}

\noindent
where $n_\ell$ is the number of Legendre orders and $n_g$ is the
number of groups.  If the user specifies \cword{nsblok=1} and the
resulting output record is too large for the available memory,
\cword{nsblok} will be changed to \cword{ngroup} automatically.

Card 1 of the ISOTXS section continues with \cword{maxup}.  This
parameter is always zero for CCCCR; thermal upscatter matrices are
not processed.  The normal value of \cword{maxdn} is \cword{ngroup},
but it can be made smaller to reduce the size of the matrices.
The cross section for any removed downscatter groups will be
lumped into the last group in order to preserve the production
cross section. The \cword{ichix} is used to control the generation
of fission $\chi$ vectors and matrices.  The representations allowed
were discussed above in connection with the description of the
ISOTXS format (see Section~\ref{ssCCCCR_ISOTXS}).  The most commonly used
option has been \cword{ichix=-1} because most application codes cannot
handle fission $\chi$ matrices.  The
\hyperlink{sGROUPRhy}{GROUPR} flux is normally
chosen to be characteristic of the class of problems a given
library is intended to treat; therefore, it is rarely necessary
to supply an input weighting spectrum (see \cword{ichix}=+1 and
\cword{spec}).  The following scenario illustrates a case where
this option might be useful.  Assume that an 80-group library
is made using the \hyperlink{sGROUPRhy}{GROUPR}
fast reactor weight function
(\cword{iwt=8}), which contains a shape in the fission range
typical of both fast reactors and fusion blankets plus a fusion
peak at 14 MeV.  This GENDF library could be used to generate
two different ISOTXS libraries, one using the default flux and
useful for fusion problems, and one using a spectrum \cword{spec}
from which the fusion peak has been removed.  The latter would
be better for fast reactor analysis because the $\chi$ vectors
would not contain the component of high-energy fission from the
14 MeV range.  Card 2 is used to input the user's choice for
\cword{spec}.

CCCCR can also produce fission $\chi$ matrices for codes that can
use them.  These matrices can be rectangular to take advantage of
the fact that the $\chi_{g\rightarrow g'}$ function is basically
independent of $g$ at low energies (large values of $g$).  Taking
the \hyperlink{sGROUPRhy}{GROUPR} 30-group structure as an
example, if the energy at
which significant incident-energy dependence begins is taken to
be about 100 keV, then groups 16 through 30 will have identical
$\chi$ vectors.  The value of \cword{ichix} should be set to 16,
and the \cword{spec} vector of Card 3 should be set to

\small
\begin{ccode}

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
  16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16/

\end{ccode}
\normalsize

\noindent
The resulting $\chi$ matrix will be rectangular with $16\times 30$
elements.

Card 4 completes the input specific to ISOTXS.  The value of \cword{kbr}
can be set to reflect the normal use of this material in the applications
that this library is intended to treat.  The \cword{amass} parameter
has units of gram atomic weight.  It can be calculated from the normal
ENDF AWR parameter (the atomic weight ratio to the neutron) by
multiplying by the gram atomic weight of the neutron.  \cword{temp}
was historically 300K for NJOY CCCC libraries.  The same value can be used
for \cword{sigpot} and \cword{xspo} (see above).  The \cword{adens}
parameter has no meaning for CCCCR; it can be set to zero to imply
infinite dilution.

The choice of values for \cword{efiss} and \cword{ecapt} is more
complicated.  As discussed in Section~\ref{ssCCCCR_ISOTXS}, \cword{efiss}
is basically
the total non-neutrino energy released by a fission reaction.  It
is available in eV as the pseudo Q value in \cword{mf}=3, \cword{mt}=18
(the energy release from fission is given in more detail in \cword{mf}=1,
\cword{mt}=458).  The following fragment of the ENDF/B-VI evaluation for
$^{235}$U shows how to find the Q value:

\footnotesize
%\small
\begin{ccode}
  ...
                                                                  9228 3  0 4413
 9.223500+4 2.330250+2          0          0          0          09228 3 18 4414
 1.937200+8 1.937200+8          0          0          1        3339228 3 18 4415
        333          2                                            9228 3 18 4416
 1.000000-5 0.000000+0 7.712960+1 0.000000+0 2.250000+3 0.000000+09228 3 18 4417
 2.250000+3 5.362770+0 2.300000+3 5.396710+0 2.500000+3 5.957280+09228 3 18 4418
  ...

\end{ccode}
\normalsize

\noindent
The Q value is the second number on the second card of the section
\cword{mf}=3, \cword{mt}=18.  Converting to CCCC units gives

\noindent
\begin{center}

193.72${\times}10^6$ eV $\times$ 1.602${\times}10^{-19}$ watt-s/eV
     = .31034${\times}10^{-10}$ watt-s/fission

\end{center}
\noindent
The value for \cword{ecapt} is determined from the Q value for
\cword{mf}=3, \cword{mt}=102,
the radiative capture reaction.  However, if the isotope remaining after
capture has a relatively short half-life, the energy of the decays leading
to the final stable daughter should be added onto the capture Q value.
(The meaning of ``stable'' may vary from application to application).
As an example, consider aluminum.  The $^{28}$Al capture product
decays with a half-life of 2.24 minutes producing 9.31 MeV of
$\beta^-$ energy and a 1.779 MeV photon.  Therefore, the actual
value of \cword{ecapt} should be calculated as follows:

\begin{center}
\begin{tabular}{rl}
  7.724 MeV & \cword{mt}=102 prompt Q value \\
  9.310 MeV & $\beta^-$  energy \\
  1.779 MeV & delayed-$\gamma$ energy \\ \cline{1-1}
 18.813 MeV &  \\
 $\times 1.602\times 10^{-13}$ & \\ \cline{1-1}
 $.3014\times 10^{-11}$ & in watt-s/capture
\end{tabular}
\end{center}

The next section of the input file is specific to BRKOXS.  Card 1
enables the user to just accept all or part of the temperatures
and sigma-zero values on the input GENDF tape.  If the
value of \cword{nti} is negative, the first abs(\cword{nti})
$T$ values for each material will be used.  If fewer
values are available, only those will be used.  If \cword{nti}
is positive, input Card 2 will be read for a list of $T$ values,
and only data with temperatures on that list
will be extracted from the GENDF tape.  The parameter \cword{nzi}
and the list of $\sigma_0$ values on Card 3 work in the same way.

No additional input is required for DLAYXS files.

\subsection{Error Messages}
\label{ssCCCCR_msg}

\begin{description}
\begin{singlespace}

\item[\cword{error in isxdat***incompatible group structures}] ~\par
  The number of groups on the input GENDF tape must match the
  number of groups specified in the CCCCR input.  Check whether
  the correct input file was mounted.

\item[\cword{error in isomtx***input record too large}] ~\par
  There is not enough space in the scratch array \cword{b} to
  read in the input records from the GENDF tape.  The only
  solution is to increase the size of the main CCCC equivalanced
  array set.  See \cword{a,ia,ha} with \cword{isiza=50000}
  at the beginning of the \cword{ccccm} module.

\item[\cword{error in isomtx***output record too large}] ~\par
  There is not enough space in the scratch array \cword{b} for
  the output subblock record, even with \cword{nsblok} changed
  to \cword{ngroup}.  The only solution is to increase the size of
  the main CCCC equivalanced array set.  See \cword{a,ia,ha} with
  \cword{isiza=50000} at the beginning of the \cword{ccccm} module.

\item[\cword{error in shuffl***sigze of endf input array exceeded}] ~\par
  See the global parameter \cword{maxe=8000} at the start of the module.

\item[\cword{error in pisotx***input record too large}] ~\par
  One of the binary records on the ISOTXS file is too large
  for the memory available to \cword{prinxs}.  This should not
  occur because there was enough memory to create the record
  in the first place.

\item[\cword{error in brkdat***incompatible group structures}] ~\par
  The number of groups on the input GENDF tape must match the
  number of groups specified in the CCCCR input.  Check whether
  the correct input file was mounted.

\item[\cword{error in brkdat***max size of endf record exceeded.}] ~\par
  See the global parameter \cword{maxe=8000} at the start of the module.

\item[\cword{message from brkdat---all available mats have been processed}]
  ~\par
  This message is issued when all the materials on the GENDF file
  have been processed, but one or more of the materials requested
  in the user's input were not found.  Check the input material
  list, and check which materials were written onto the input
  GENDF file.

\item[\cword{message from brkdat---no temperatures for mat=nnnn}] ~\par
  This means that none of the requested temperatures were found for
  this MAT.  This makes it impossible to include the material in the BRKOXS
  file.  The warning message is issued, and all references to this
  material are thinned out of the BRKOXS records.

\item[\cword{message from brkdat---need elastic matrices at higher temps}] ~\par
  The self-shielded transport cross section requires self-shielded
  P$_1$ elastic scattering matrices for accurate results.  This means
  that \cword{mf}=6, \cword{mt}=2 should be available on the GENDF tape for all
  temperatures.  If this scattering matrix is missing for the higher
  temperatures, this warning message is issued.

\item[\cword{error in xsproc***max size of endf record exceeded.}] ~\par
  See the global parameter \cword{maxe=8000} at the start of the module.

\item[\cword{message from xsproc---infinite f-factor mt jg jz temp}] ~\par
  The calculation of an f-factor requires division by the infinitely
  dilute cross section.  This message means that the divisor was
  zero for reaction \cword{mt}, group \cword{jg}, background cross
  section \cword{jz}, and temperature \cword{temp}.  The division is skipped,
  and the numerator is used unchanged.

\item[\cword{error in mxproc***max size of endf record exceeded.}] ~\par
  See the global parameter \cword{maxe=8000} at the start of the module.

\item[\cword{error in pbrkxs***input record too large}] ~\par
  One of the binary records on the BRKOXS file is too large
  for the memory available to \cword{pbrkxs}.  This should not
  occur because there was enough memory to create the record
  in the first place.

\item[\cword{message from cdlyxs---no delayed neutron data found}] ~\par
  There was no delayed-neutron data found by \cword{DLDATA}.  Make
  sure that \cword{mf}=3, \cword{mt}=455 and \cword{mf}=5, \cword{mt}=455
  were requested during the \hyperlink{sGROUPRhy}{GROUPR}
  run and that the delayed-neutron isotopes were included in the
  material list given in the CCCCR input.

\item[\cword{error in dldata***max size of endf record exceeded.}] ~\par
  See the global parameter \cword{maxe=8000} at the start of the module.

\item[\cword{error in dldata***incompatible group structures}] ~\par
  The number of groups on the input GENDF tape must match the
  number of groups specified in the CCCCR input.  Check whether
  the correct input file was mounted.

\item[\cword{error in pdlyxs***input record too large}] ~\par
  One of the binary records on the DLAYXS file is too large
  for the memory available to \cword{pdlyxs}.  This should not
  occur because there was enough memory to create the record
  in the first place.

\end{singlespace}
\end{description}

\cleardoublepage