**1. NAME AND TITLE**

MOMGEM-MOMDIS: Moments Method Reconstruction of Scattered Gamma-Ray Distributions.

**AUXILIARY ROUTINES**

MOMGEN: Moments Generator.

MOMDIS: Differential Angular-energy Number Flux Distribution Calculator.

**2. CONTRIBUTORS**

U. S. Naval Radiological Defense Laboratory, San Francisco, California.

National Bureau of Standards provided the total scattering moments which are used as input to
MOMGEN.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; IBM 7090.

**4. NATURE OF PROBLEM SOLVED**

MOMGEN-MOMDIS represent a theoretical procedure to determine the distribution of
radiation which has been scattered by a barrier. The calculation is made for gamma rays which are
scattered in an infinite homogeneous medium from a plane perpendicular monoenergetic beam of
gamma-rays. Specifically, the differential angular-energy distributions of gamma-ray fluxes
scattered from media of various thicknesses are calculated.

**5. METHOD OF SOLUTION**

There are two phases in the moments method procedure. Phase one consists of generating moments (for the distributions) and phase two consists of constructing the distributions.

In phase one (MOMGEN), three sets of moments are computed. They are moments for total, first and second order scattering. The moments used in the next phase, referred to as third and higher order scattering moments, are obtained by adding moments for first and second scattering and subtracting their sum from total scattering moments.

In phase two (MOMDIS), a biorthogonal polynomial expansion is used to ``fit'' the moments.
The resulting distribution is for third and higher order scattering. Distributions for first and second
order scattering are determined from analytical expressions. Finally, a composite spectrum is
formed by adding the three distributions.

**6. RESTRICTIONS OR LIMITATIONS**

The calculation is limited to photons scattered in a forward direction. Distributions for no
more than 6 thicknesses, 10 angles of scatter, and 105 wavelengths may be calculated in each run.

**7. TYPICAL RUNNING TIME**

The combined running time for MOMGEN and MOMDIS is approximately 25 minutes per one hundred wavelengths on the IBM 70-4.

Estimated running time of the sample problem on the IBM 7090, in hours: MOMGEN, 0.09;
MOMDIS, 0.03.

**8. COMPUTER HARDWARE REQUIREMENTS**

The codes are designed for a 32 K core storage memory, two magnetic tape drives and a
printer. They are operable on the IBM 704 and the IBM 7090 computers.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The codes were designed for the IBM 704 FORTRAN II Monitor System. They were run by RSIC on the IBM FORTRAN IV IBJOB Monitor within the IBSYS Operating System. Tape assignments were made for I-O, systems, and one scratch tape.

A library of data for use in MOMGEN is packaged.

**10. REFERENCES**

**a. Included in package:**

C. V. Smith, "A Moments Method Computer Code for Reconstructing Scattered Gamma Ray
Distributions," USNRDL-TR-67-9 (January 1967).

**b. Background information:**

H. Goldstein, J. E. Wilkins, Jr., "Calculations of the Penetration of Gamma Rays," NYO-3075
(1954).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document (10.a) and one (1.2MB) DOS diskette which contains the
source codes, a library of data and input and otuput for a sample problem.

**12. DATE OF ABSTRACT**

January 1968; updated July 1981.

**KEYWORDS: ** MOMENTS METHOD; GAMMA-RAY