**1. NAME AND TITLE**

OOSII: Calculation of Isotropic Scattering by Particles for One-Dimensional and Three-Dimensional Transport in Slabs by Invariant Imbedding, Orders-of-Scattering Method, Including Check Calculations by Integral Transport Theory and Monte Carlo.

**2. CONTRIBUTOR**

Air Force Cambridge Research Laboratories, Hanscom Air Force Base, Massachusetts.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV, COMPASS; CDC 6600.

**4. NATURE OF PROBLEM SOLVED**

OOSII solves the class of particle transport problems for which a variation of the invariant imbedding method seems most appropriate. This situation can arise when the average energy of a particle can be reasonably well correlated with the number of collisions it has undergone in the course of transport through a scattering medium. For these cases, a method for calculating emergent nth scattered particle currents from scattering media has been developed which combines an orders-of-scattering formulation with the familiar invariant imbedding method.

**5. METHOD OF SOLUTION**

A novel, simplified approach to particle transport in slabs is given. The number of particles transmitted and reflected by a slab of finite thickness is obtained as a function of the number of collisions the particles receive. This "orders-of-scattering" solution is facilitated by an invariant imbedding approach which leads to a set of integral recursion relations between transmitted and reflected particle currents. Solutions are given for both one-dimensional and three-dimensional transport in slabs for an arbitrary anisotropic scattering law.

For comparison, the one-dimensional Boltzmann equation for isotropic scattering is formulated and the orders-of-scattering solution found numerically. A Monte Carlo calculation for orders-of-scattering is also described. These methods provide a valuable numerical check on the invariant imbedding solution, but they also demonstrate the greater computing efficiency of the new method. Finally, numerical solutions for three different cases of anisotropic scattering are given, including application to the case of electron-phonon scattering in solids.

**6. RESTRICTIONS OR LIMITATIONS**

None noted.

**7. TYPICAL RUNNING TIME**

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

**8. COMPUTER HARDWARE REQUIREMENTS**

The code was designed to run on the CDC computer.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A FORTRAN IV compiler is required.

**10. REFERENCE**

J. C. Garth and S. Woolf, "An Invariant Imbedding, Orders-of-Scattering Approach to Particle Transport in a Slab," AFCRL-TR-76-0023 (January 1976).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one (1.2MB) DOS diskette which contains the source codes and sample problem input.

**12. DATE OF ABSTRACT**

January 1982.

**KEYWORDS: ** SLAB; MONTE CARLO; INVARIANT IMBEDDING; NEUTRON; ONE-DIMENSION; INTEGRAL BOLTZMANN EQUATION; ONE-VELOCITY;
ELECTRON