GGC: Multigroup Cross Section Code System for Use in Diffusion and Transport Codes.

PSR-12A is GGC-3; PSR-12B is is GGC-4.

GGC-4 is packaged in the Argonne Code Center, Abstract 298.

**2. CONTRIBUTOR**

Gulf General Atomic, San Diego, California.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; IBM 360/65 or UNIVAC 1108.

**4. NATURE OF PROBLEM SOLVED**

The GGC System is a package of codes designed for the production of multigroup cross section sets. The program solves the multigroup spectrum equations with spatial dependence represented by a single positive input buckling. Broad group cross sections are prepared for diffusion and transport codes by averaging with the calculated spectra over input-designated energy limits.

The fast section of GGC as an option adjusts fine group absorption and fission cross sections by performing resonance integral calculations; calculates the energy dependent fast spectrum using an input buckling and a P1, B1, B2, or B3 approximation; as an option, calculates either 2 or 6 spatial moments of the spectrum due to a plane source; and performs, for as many input designated broad group structures as desired, spectrum weighted averages of microscopic and macroscopic cross sections and transfer arrays.

The thermal section determines a thermal spectrum by reading it as input, or by calculating a Maxwellian spectrum for a given temperature, or by an iterative solution of the P0, B0, P1, or B1 thermalization equations for an input buckling; as an option, calculates time moments of the time and energy dependent diffusion equations using the input buckling to represent leakage; produces spectrum weighted broad group averaged cross sections and transfer arrays.

The combining section takes the broad group averaged cross sections from the fast and thermal portions and forms multigroup cross section tables. It is also possible to use the combining section to produce mixtures not used in the spectrum calculations or to combine the results of different fast and thermal calculations.

GGC-4 includes new options for a spectrum calculation for systems with a negative or zero buckling; a calculation of effective resonance integrals; and a procedure for calculating a consistent set of transport cross sections.

**5. METHOD OF SOLUTION**

The code systems are based on the work of Joanou, Dudek, Smith, and Vieweg (GAM II, GA-4265,
1965; GATHER II, GA-4132, 1963, and GGC-II, GA-4436). The code system is divided into Fast (**G**AM),
Thermal (**G**ATHER), and **C**ombining sections, described above.

In the fast section either the P1 or the B1, B2, or B3 approximation is made to the transport equation using the positive, energy-independent buckling. In each approximation, Legendre moments of the angular flux are computed by direct numerical integration of the slowing down equations. In the resonance calculations, Doppler broadened absorption and scattering cross sections are used. The resonance treatment allows up to two admixed moderators in an absorber lump imbedded in a surrounding moderator. The absorber in the lump is treated by using either the narrow resonance approximation, the narrow resonance infinite mass approximation, or a solution of the slowing down integral equations to determine the collision density through the resonance. The admixed moderators are treated by using either an asymptotic form of, or an integral equation solution for, the collision density. In the resonance calculation either standard geometry collision probabilities are used or tables are entered. Dancoff corrections can also be made. In the region of unresolved resonances, resonance absorption is calculated by using Porter-Thomas distributions, but only S-wave neutrons are considered.

In the thermal section either the B0, B1, P0, or P1 approximation to the transport equation is made, and in all options Legendre moments of the angular flux are computed. A trapezoidal energy integration mesh is used, and the resulting equations are solved iteratively by using a source-normalized, over-relaxed, Gaussian technique. Averages over broad groups are performed by simple numerical integration.

The results obtained in the fast and thermal sections are stored on tapes which may contain results for a number of problems, each of which includes fine group cross section data for a number of nuclides. If the problem number is specified on the tapes, and a desired list of nuclides is given, the combining code will punch microscopic cross sections for the requested list of nuclides. The program also treats mixtures. Given the atomic densities of the nuclides in the mixture, the code will punch macroscopic cross sections. An option in GGC makes it possible to shorten the punching process for large two-dimensional transfer arrays by specifying a maximum number of desired upscattering and downscattering terms.

Several auxiliary codes are included in the package to prepare, handle, and update the basic cross section tapes which are used as input to GGC.

**6. RESTRICTIONS OR LIMITATIONS**

Maxima of: 99 fast groups, 101 thermal fine groups, 99 fast broad groups, 50 thermal broad groups, 50 broad groups in the combining section, 100 resonances per nuclide, 2 moderators mixed with a resonance absorber, 305 entries in the escape probability table for cylindrical geometries, 505 entries in the escape probability table for slab geometries, and a single and positive value for the buckling must be supplied.

**7. TYPICAL RUNNING TIME**

No study has been made by RSIC of typical running times for GGC.

**8. COMPUTER HARDWARE REQUIREMENTS**

GGC is operable on the UNIVAC 1108, IBM 360, and CDC 6600 computers.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran IV compiler is required.

**10. REFERENCES**

J. Adir and K. D. Lathrop, *Theory of Methods Used in the GGC-3 Multigroup Cross Section Code*,
GA-7156 (July 1967).

J. Adir, S. S. Clark, R. Froehlich, and L. L. Todt, *User's and Programmer's Manual for the GGC-3
Multigroup Cross Section Code, Parts 1 and 2*, GA-7157 (July 1967).

M. K. Drake, C. V. Smith, and L. J. Todt, *Description of Auxiliary Codes Used in the Preparation of
Data for the GGC-3 Code*, GA-7158 (August 1967).

J. Adir and K. D. Lathrop, *Theory of Methods Used in the GGC-4 Multigroup Cross Section Code*,
GA-9021 (October 1968).

**11. CONTENTS OF CODE PACKAGE**

**12. DATE OF ABSTRACT**

November 1972; updated October 1983.

**KEYWORDS: ** MULTIGROUP CROSS SECTION PROCESSING; NEUTRON CROSS SECTION
PROCESSING