**1. NAME AND TITLE**

ASFIT-VARI: Gamma-Ray Transport Code System for One-Dimensional Finite Systems.

This variable-dimension F77 version replaced ASFIT-DS2.

**2. CONTRIBUTORS**

Indira Gandhi Centre for Atomic Research, Kalpakkam, India.

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77; IBM 3033 and Data General MV/Family (A), IBM PC (B).

**4. NATURE OF PROBLEM SOLVED**

ASFIT-VARI solves problems of gamma-ray transport in slab geometry. The method is applicable to energy-dependent, multiregion radiation transport with arbitrary degree of anisotropy. Buildup factors and energy-angular distributions at the spatial mesh points are calculated and printed. The source is monoenergetic and either normally or isotropically incident at the surface or isotropic in a region. All secondary sources can be included: annihilation, bremsstrahlung, and fluorescence. Coherent scattering cannot be treated in this version. The code can be run in a multigroup mode which can treat neutron and coupled neutron-gamma-ray problems.

**5. METHOD OF SOLUTION**

A semi-analytical technique is used. The transport equation is written in the form of coupled integral equations separating the spatial and energy-angular transmission. Legendre polynomial approximation in the direction cosine, and discrete ordinate representation in energy and spatial domain are used for radiation source and flux. The space and energy-angle transmission kernels are evaluated analytically and the integral equations are then solved by a fast-converging iterative technique. For a plane parallel beam of radiation incident on a slab, the virgin and the first collision flux are not amenable to polynomial expansion due to the singularities. For this case, up to the second collision, the source is computed analytically and then recourse is taken to polynomial approximation.

Quadratic interpolation of the sources between space nodes is used for spatial integration

The only cross section input required are pair production and total cross sections for each region. Compton cross sections are computed internally.

**6. RESTRICTIONS OR LIMITATIONS**

Slab geometry, P_{10} expansion of flux, 4 regions, 99 space nodes, 96 angular nodes in Gaussian flux
integration. The multigroup mode was not tested at RSIC.

**7. TYPICAL RUNNING TIME**

The P_{1} sample problem (10 mfp lead, 0.1 MeV source) took 4.44 CPU seconds of execution time
on an IBM 3033. The execution times for the 6 sample problems varied from 5 to 38 minutes on an
IBM PC/XT. A PC/AT required about half as much time.

**8. COMPUTER HARDWARE REQUIREMENTS**

The code was developed on a Honeywell Bull computer. It requires 432 K bytes region size and uses standard I-O and one additional storage device. It has been tested on both IBM 3033 and DG MV4000 computers. The PC version requires a math coprocessor to run the executable file. A high density or hard disk is required.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran 77 compiler is required. The code may be compiled and executed in the standard operating system. The Jan. 1991 PC version was compiled by the Microsoft Version 5.0 compiler.

**10. REFERENCES**

D. V. Gopinath and K. V. Subbaiah, "Informal Notes, ASFIT-VARI" (April 1989).

D. V. Gopinath and K. Santhanam, "Radiation Transport in One-Dimensional Finite Systems--Part
I: Development in the Anisotropic Source--Flux Iteration Technique," *Nucl. Sci. Eng.*, 43, 186-196
(1971).

D. V. Gopinath and K. Santhanam, "Radiation Transport in One-Dimensional Finite Systems--Part
II: Gamma-Ray Transport Studies with ASFIT," *Nucl. Sci. Eng.*, 43, 197-211 (1971).

D. V. Gopinath, K. Santhanam, and D. P. Burte, "Some Modifications in the Anisotropic Source-Flux Iteration Technique," *Nucl. Sci. Eng.*, 52(4), 494-498 (1973).

K. V. Subbaiah, A. Natarajan, and D. V. Gopinath, "Effect of Fluorescence, Bremsstrahlung, and
Annihilation Radiation on the Spectra and Energy Deposition of Gamma Rays in Bulk Media," *Nucl.
Sci. Eng.*, 81, 172-195 (1982).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one DS/HD DOS diskette which contains the source codes and sample problem input and output.

**12. DATE OF ABSTRACT**

April 1989, updated January 1991.

**KEYWORDS:** ONE-DIMENSION; GAMMA-RAY; SLAB; INTEGRAL BOLTZMANN
EQUATION