PSR-0105 MINX.

1. NAME OR DESIGNATION OF PROGRAM:  MINX.
A Multigroup Interpretation of Nuclear X-Sections from ENDF/B.

3. DESCRIPTION OF PROBLEM OR FUNCTION

MINX calculates fine-group averaged infinitely diluted cross sections and self-shielding factors from ENDF/B-IV data. Its primary purpose is to generate a pseudo-composition-independent multigroup library which is input to  the SPHINX space-energy collapse program (2) (PSR-0129) through standard CCCC-III (8) interfaces. MINX incorporates and improves upon the resonance capabilities of existing codes such as ETOX (5) (NESC0388) and ENDRUN (9) and the high-order group-to-group transfer matrices of SUPERTOG (10) (PSR-0013) and ETOG (11). Fine group energy boundaries, Legendre expansion order, gross spectral shape component (in the Bondarenko flux model), temperatures and dilutions can all be used specifically.

4. METHOD OF SOLUTION

Infinitely dilute, unbroadened point cross sections are obtained from resolved resonance parameters using a modified version of the RESEND program (3) (NESC0465). The SIGMA1 (4) (IAEA0854) kernel-broadening method is used to Doppler broaden and thin the tabulated linearized pointwise cross sections at 0 K (outside of the unresolved energy region). Effective temperature- dependent self-shielded pointwise cross sections are derived from the formulation in the ETOX code. The primary modification to the ETOX algorithm is associated with the numerical quadrature scheme used to establish the mean values of the fluctuation intervals. The  selection of energy mesh points, at which the effective cross sections are calculated, has been modified to include the energy points given in the ENDF/B file or, if the energy-independent formalism was employed, points at half-lethargy intervals. Infinitely dilute group cross sections and self-shielding factors are generated using the Bondarenko flux weighting model with the gross spectral shape under user control. The integral over energy for each group is divided into a set of panels defined by the union  of the grid points describing the total cross section, the reaction  cross section of interest and the gross spectral shape. The integration scheme actually employed in MINX is adaptive Simpson's procedure for which the initial estimate is based on the unionized grid described above. The computation of elastic and discrete group- to-group matrices is based upon a semi-analytic scheme which treats  the rapidly fluctuating cross-section behaviour analytically. Where  this laboratory-system-based scheme becomes difficult to implement (e.g., light nuclei, inelastic thresholds), an alternative numerical integration in the center-of mass system is employed. Multigroup transfer matrices for processes in which the outgoing neutron energy and angular distribution is uncoupled are computed by direct numerical integration.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The principal restriction is the computing time available for a given desired accuracy, number of groups, and Legendre order. The paging technique and variable dimensioning make efficient use of available core storage; very large problems have been run with MINX (e.g. a complete 171-group P3 neutron library at ORNL and an extensive 240-group P4 library at LASL).

6. TYPICAL RUNNING TIME

This is difficult to define because it is a sensitive function of the (a) accuracy required, (b) number of resonances, (c) number of groups, (d) Legendre expansion order, (e)  number of temperature and dilutions, etc. Sample times for CDC 7600  are indicated below. For a problem with 50 groups, Legendre expansion P3, generally four temperatures involving 0 K, five dilution factors, tolerances: resonance reconstruction 0.5 % (1 % for U-238), linearization 0.2 %, Doppler thinning 0.2 %, adaptive integration 0.1 %, we find:

Isotope         ENDF/B-IV           MINX Timing
                 MAT No.              (sec)
-------         ---------           -----------
Na-33             1156                   667
Fe                1192                  1075
O-16              1276                   590
U-238             1262                  6454
Pu-239            1264                  3505

7. UNUSUAL FEATURES OF THE PROGRAM

MINX generates and uses (in the resolved energy region) a linearly interpolable, infinitely dilute temperature-dependent pointwise cross-section library in ENDF/B-IV format. This feature permits efficient computation of group cross sections with accurate Doppler broadening of single-level and multi- level cross sections. The multigroup constants generated therefrom are thus known to be compatible with the pointwise cross sections retrieved by contuous-energy Monte Carlo codes. New, accurate algorithms for the computation of Legendre moments of group-to-group transfer matrices have been developed and implemented. These calculations are based on an expansion of the differential scattering cross section in the laboratory system and use a semi- analytic procedure which treats the rapidly fluctuating cross- section behaviour analytically. Where Legendre expansion in the lab  system becomes difficult (e.g. for light nuclei or near inelastic thresholds) an alternative numerical integration in the centre-of- mass is employed. The procedures employed in MINX for constructing,  interpolating and integrating cross sections are intended to provide and quantify user control of computational errors (assuming that the data base and weighting function are known explicitly). A paging technique which manipulates huge amounts of cross-section information one block at a time (block size variable), is used throughout MINX, in addition to variable dimensioning to reduce storage requirements and to use available storage efficiently. Finally, the code and the multigroup data sets derived therefrom are intended to satisfy nuclear design standards currently being implemented under auspicies of the American National Standards Institute.

8. RELATED AND AUXILIARY PROGRAMS

Three utility codes are provided to manipulate the CCCC data files:
LINX: will combine two multi-isotope CCCC files (ISOTXS or BRKOXS
      only) (6) (PSR-0129)
BINX: will convert CCCC data (ISOTXS, BRKOXS, or DLAYXS) from binary       to BCD mode or vice-versa and selectively print the contents
      of the files (6) (PSR-0129).
CINX: will exactly collapse fine group data (ISOTXS, BRKOXS, or
      DLAYXS) to a subset coarse group structure, and will also
      change the format of the data to 1DX/PERT-V form, if desired
      (7) (PSR-0117).

These codes were written to be as IBM-compatible as possible. The changes required are identified on the listings with "C IBM comment" cards.

10. REFERENCES

(1) C.R. Weisbin, P.D. Soran, R.E. MacFarlane, D.R. Harris,
    R.J. LaBauve, J.S. Hendricks, J.E. White, R.B. Kidman:
    MINX: A Multigroup Interpretation of Nuclear X-sections from
    ENDF/B.
    LA-6486-MS (September 1976)
(2) W.J. Davis, M.B. Yarbrough, A.B. Bortz:
    SPHINX: A One Dimensional Diffusion and Transport Nuclear Cross
    Section Processing Code.
    WARD-XS-3045-17 (August 1977)
(3) O. Ozer:
    RESEND: A Program to Preprocess ENDF/B Materials with Resonance
    Files into a Pointwise Form.
    BNL-17134 (1972)
(4) D.E. Cullen:
    SIGMA (Version 74-1): A Program to Exactly Doppler Broaden
    Tabulated Cross Sections in the ENDF/B Format.
    UCID-16426 (1974)
(5) R.E. Schenter, J.L. Baker, R.B. Kidman:
    ETOX: A Code to Calculate Group Constants for Nuclear Reactor
    Calculations.
    BNWL-1002 (1969)
(6) R.E. MacFarlane, R.B. Kidman:
    LINX and BINX: CCCC Utility Codes for the MINX Multigroup Pro-
    cessing Code.
    LA-6219-MS (February 1976)
(7) R.B. Kidman, R.E. MacFarlane:
    CINX: Collapsed Interpretation of Nuclear X-Sections.
    LA-6287-MX (April 1976)
(8) B.M. Carmichael:
    Standard Interface Files and Procedures for Reactor Physics
    Codes, Version III.
    LA-5486-MS (February 1974)
(9) B.A. Hutchins, C.L. Cowan, M.D. Kelley, J.E. Turner:
ENDRUN II - A Computer Code to Generate a Generalized Multigroup     Data File for ENDF/B.
    General Electric Co report GEAP-13703 (March 1971)
(10) R.Q. Wright, N.M. Greene, J.L. Lucius, C.W. Craven:
     SUPERTOG: A Program to Generate fine Group Constants and PN
     Scattering Matrices from ENDF/B.
     ORNL-TM-2679 (1969).
(11) D.E. Kusner, R.A. Daniels:
     ETOG-1, A FORTRAN IV Program to Process Data from the ENDF/B
     File to MUFT GAM and ANISN Formats.
     Westinghouse Corporation Report WCAP-3845-1 (December 1969)

11. MACHINE REQUIREMENTS

Core and external storage such as magnetic tape or disk devices depend on the characteristics of the problem. The 50-group library would require about 330k bytes of core storage  on the IBM 360 series computer or 49000 words of LCM on the CDC-7600.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

IBM OS 360 with the FORTRAN H compiler or LASL CROS with the CDC RUN compiler.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The program consists of 227 subroutines on about 15000 source cards. With a three-level overlay structure consisting of 11 segments, about 330k bytes are required on the IBM machines and 49000 decimal  words on CDC-7600.

15. NAME AND ESTABLISHMENT OF AUTHOR

P.D. Soran, R.E. MacFarlane, D.R. Harris, R.J. LaBauve,
J.S. Hendricks, R.B. Kidman
Los Alamos Scientific Laboratory
Los Alamos, New Mexico 87545, U.S.A.

C.R. Weisbin, J.E. White
Oak Ridge National Laboratory
Oak Ridge, Tennessee, U.S.A.

File name	File description	Records
PSR0105_01.001	INFORMATION	10
PSR0105_01.002	ENDF/B LIBRARY DATA (BCD , TAPE 408)	18381
PSR0105_01.003	SOURCE PROGRAM (F4,EBCDIC)	14751
PSR0105_01.004	SAMPLE PROBLEM INPUT DATA	9
PSR0105_01.005	SAMPLE PROBLEM PRINTED OUTPUT	3723

File name	File description	Records
PSR0105_02.002	INFORMATION	6
PSR0105_02.003	SOURCE PROGRAM - FORTRAN-4 EBCDIC	14675
PSR0105_02.004	SOURCE PROGRAM - BAL EBCDIC	183
PSR0105_02.005	ENDF/B-4 LIBRARY TAPE 408 (REV.2)	18381
PSR0105_02.006	JCL CARDS	24
PSR0105_02.007	OVERLAY CARDS	50
PSR0105_02.008	SAMPLE PROBLEM INPUT DATA	9
PSR0105_02.009	SAMPLE PROBLEM PRINTOUT	3721