**1. NAME AND TITLE**

SPHINX: A One-Dimensional Diffusion and Transport Nuclear Cross Section Processing
Code System.

**2. CONTRIBUTORS**

Westinghouse Advanced Reactors Division, Madison, Pennsylvania.

Computer Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV, Assembler Language; CDC-7600, IBM 360/370.

**4. NATURE OF PROBLEM SOLVED**

SPHINX provides a standardized calculational scheme for generating multigroup cross sections.
It interpolates to the correct composition-dependent self-shielding factors, provides elastic matrix
removal corrections if requested, and space-energy collapses or cell homogenizes the resultant cross
sections to a desired group structure for subsequent spatial calculations.

**5. METHOD OF SOLUTION**

SPHINX incorporates both one-dimensional diffusion and transport theory. SPHINX is standardized in that it uses a set of standard interface files as input and output and can be linked with other codes which use the same. The basic input to SPHINX consists of cross sections and self-shielding factors in standard interface format. The code uses one-dimensional diffusion theory or one-dimensional transport theory to space-energy collapse the cross sections to the desired group structure. Cell homogenization of the composition and temperature-corrected cross sections using transport fluxes are also available in SPHINX.

The self-shielding factor interpolation is a Lagrangian-interpolation scheme with safeguards to
prevent unreasonable interpolation. The heterogeneity effects are based on the approximate methods
of Sauer, Bell, Levine, and Wigner. PSR-96/1DX is the source for the elastic transfer corrections (as
suggested by Bondarenko, et al.), the space energy collapse, and the diffusion theory one-dimensional
space calculation. Cell homogenization of user specified cross sections is accomplished by using
fluxes from one-dimensional space calculation. The transport theory one-dimensional space calculation
is that of CCC-254/ANISN-ORNL.

**6. RESTRICTIONS OR LIMITATIONS**

Available core storage affects the size of the problem which can be executed. However, SPHINX
is variably dimensioned to allow a wide range of problems to be run.

**7. TYPICAL RUNNING TIME**

The running time is dependent upon the problem size and upon the data transfer speeds of a
particular system.

**8. COMPUTER HARDWARE REQUIREMENTS**

SPHINX is operable on the CDC-7600 computer (A) or the IBM 360/370 computers (B). 50,000
words of core storage and a reasonable amount of disk and/or tape backing storage are required.

**9. COMPUTER SOFTWARE REQUIREMENTS**

Fortran IV and Assembler Language compilers are required.

**10. REFERENCES**

**a. Included in the documentation: **

W. J. Davis, M. B. Yarbrough, and A. B. Bortz, "SPHINX, A One Dimensional Diffusion and Transport Nuclear Cross Section Processing Code," WARD-XS-3045-17 (August 1977).

R. Q. Wright, "SPHINX: Resonance and One Dimensional Diffusion Theory Nuclear Cross
Section Processing Code (IBM Version)," Draft (March 1978).

**b. Background information:**

G. I. Bell, "A Simple Treatment for Effective Resonance Absorption Cross Sections in Dense
Lattices," *Nucl. Sci. Eng*. 5 (1959) 138-139.

I. I. Bondarenko, ed., "Group Constants for Nuclear Reactor Calculations," New York: Consultants Bureau. 1964.

W. W. Engle, Jr., "A Users Manual for ANISN: A One Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering," K-1693 (1967, updated June 1973).

R. W. Hardie and W. W. Little, Jr., "1DX: A One-Dimensional Diffusion Code for Generating Effective Nuclear Cross Sections," BNWL-954 (March 1969).

M. M. Levine, "Resonance Integral Calculations for U^{238} Lattices," *Nucl. Sci. Eng.* 16 (1963)
271-279.

A. Sauer, "Approximate Escape Probabilities," *Nucl. Sci. Eng.* 16 (1963) 329-335.

E. P. Wigner, E. Creutz, H. Jupnik, and T. Snyder, "Resonance Absorption of Neutrons by
Spheres," *J. Appl. Phys.* 26 (1955) 260-270.

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents (10.a) and one (1.2MB) DOS diskette which contains the
source code and sample problem input.

**12. DATE OF ABSTRACT**

March 1984.

**KEYWORDS**: ANISN FORMAT; MULTIGROUP CROSS SECTION PROCESSING;
NEUTRON CROSS SECTION PROCESSING; SENSITIVITY ANALYSIS;
UNCERTAINTY ANALYSIS