**1. NAME AND TITLE**

GAMMON: Gamma-Ray Moments Method Codes--GRMM and SPENCER.

GRMM is a version frozen since 1966, SPENCER since 1968. They are retained by RSIC mainly to preserve the state of the art.

**2. CONTRIBUTORS**

Center for Radiation Research, National Bureau of Standards, Washington, D.C. (GRMM).

Atomics International, Canoga Park, California (SPENCER).

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; IBM 360, CDC 1604.

**4. NATURE OF PROBLEM SOLVED**

The code GRMM calculates the moments of the flux from a plane isotropic monoenergetic source in an infinite homogeneous medium.

SPENCER was designed to approximately reconstitute a function from a finite number of its moments.

**5. METHOD OF SOLUTION**

The directional dependence of quantities in the Boltzmann equation can be removed by making a spherical harmonic--or, in sufficiently symmetric cases, a Legendre polynomial expansion, of all the terms of the equation. The GRMM code restricts its notice to those symmetric cases where the Legendre expansion suffices. This expansion reduces the Boltzmann equation to an infinite set of coupled equations for the Legendre coefficients, which are functions of energy and distance (only one spatial variable is allowed).

In GRMM, calculation of the moments appears to be reasonably straightforward and in many ways similar to previous schemes.

A moments calculation is not complete without a means of reconstruction of functions from the moments. The companion program, SPENCER, performs this function.

**6. RESTRICTIONS OR LIMITATIONS**

None noted.

**7. TYPICAL RUNNING TIME**

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

**8. COMPUTER HARDWARE REQUIREMENTS**

The GAMMOM codes are operable on the IBM 360/75 equipment with standard I-O devices.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The FORTRAN IV Operating System of the IBM 360/75 may be used with the packaged codes.

**10. REFERENCES**

W. R. Kimel, Editor-in-Chief, *Radiation Shielding*, TR 40 (1966); L. V. Spencer, "Gamma
Ray Shielding Theory," Chapter I, p. 132-145.

Bruce D. O'Reilly and Richard C. Lewis, "SPENCER, A Fortran Program to Approximately Reconstitute a One-Dimensional Function from a Finite Number of Its Moments," NAA-SR-Memo-11653 (November 1965).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one (1.2MB) DOS diskette which contains the source codes (GRMM and SPENCER) plus input and output for a sample problem for each.

**12. DATE OF ABSTRACT**

February 1972; revised February 1983.

**KEYWORDS:** GAMMA-RAY; MOMENTS METHOD; ONE-DIMENSION; INFINITE MEDIUM