**1. NAME AND TITLE**

SLDN: Code System for Shielding Calculations by the Method of Invariant Imbedding.

**AUXILIARY ROUTINES**

LTA: Calculates multigroup constants of neutrons for shielding calculations.

LTB: Calculates elastic scattering kernel of neutrons for shielding.

SL: Calculates reflection and transmission functions of radiations for homogeneous slabs.

ML: Calculates penetrations of radiations through multilayer slabs.

DF: Calculates multigroup one-dimensional diffusion for shielding of neutrons.

**2. CONTRIBUTOR**

Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki, Japan.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; GE 635/685, ACOS 77/700, FACOM M-200.

**4. NATURE OF PROBLEM SOLVED**

SLDN calculates the reflection and penetration of neutrons through multilayer slabs with the
multigroup constants generated from ENDF/B. One-dimensional multilayer slabs with a plane
source are treated. Albedo on a homogeneous slab with semi-infinite thickness can be calculated.

**5. METHOD OF SOLUTION**

LTA and LTB compute group averaged constants from ENDF/B with a specified weighting
spectrum. To avoid double numerical integration on the calculation of elastic scattering kernel, the
analytical formation is adapted instead of a numerical integration. SL calculates the reflection and
transmission functions of homogeneous slabs by the method of invariant imbedding under the
Gaussian quadrature approximation on angular variable and multigroup approximation on energy
variable. ML computes the penetration of neutrons through multilayer with the reflection and
transmission functions using the combination rule for the functions.

**6. RESTRICTIONS OR LIMITATIONS**

LTA, LTB:

Number of angular divisions 7

Number of energy groups 30

Number of fast energy groups (for transport calculation) 13

Number of Legendre moments 14

Number of energy points (for raw data) 1200

Weighting spectrum 1/E.fission spectrum

SL, ML, DF:

Number of angular divisions 7

Number of energy groups/fast energy groups 30/13

Number of isotopes/material 10

Number of slabs/(multilayer) 30

**7. TYPICAL RUNNING TIME**

The running time for a multilayer (iron-water), 1.5 m thickness, 3 angular divisions, 13 fast
groups, 30 total groups, 14 Legendre moments: LTA and LTB, 1-5 minutes per isotope; SL, 1
minute per slab; ML, 2 minutes; DF, 0.5 minutes.

**8. COMPUTER HARDWARE REQUIREMENTS**

SLDN is operable on the GE 635/685, ACOS 77/700, or FACOM M-200 computers. At least
196 K storage is required.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A FORTRAN IV compiler is required.

**10. REFERENCES**

I. Komatsu, Y. Yamashita, A. Shimizu, "SLDN-ML-2: A Code for the Calculations of Penetrations of Radiations for Multi-Layer Slabs," J201 71-11 (June 1971).

I. Komatsu, Y. Yamashita, A. Shimizu, "A Code System for Shielding Calculation by the Method of Invariant ImbeddingSLDN," J201 71-07 (June 1971).

I. Komatsu, Y. Yamashita, A. Shimizu, "SLDN-LTA-2: A Code for Calculating Multigroup Constants of Neutrons for Shielding Calculations," J201 71-08 (June 1971).

M. Nakai, Y. Sato, I. Komatsu, A. Shimizu, "Evaluation of the Multigroup Cross Sections for the Shielding Calculation," J201 72-06 (March 1972).

Y. Yamashita, I. Komatsu, A. Shimizu, "SLDN-DF-2: Multigroup One-Dimensional Diffusion Code for Shielding Calculations of Neutrons," J201 71-12 (June 1971).

Y. Yamashita, I. Komatsu, A. Shimizu, "SLDN-LTB-2: A Code for Calculating Elastic Scattering Kernel of Neutrons and Gamma Rays for Shielding Calculations," J201-71-09 (June 1971).

I. Komatsu, A. Shimizu, "SLDN-SL-2: A Code for the Calculation of the Reflection and
Transmission Functions of Radiations for Homogeneous Slabs," J201 71-10 (June 1971).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one (1.2MB) DOS diskette which contains the
source codes and sample data.

**12. DATE OF ABSTRACT**

October 1975; revised September 1982, March 1983.

**KEYWORDS: ** INVARIANT IMBEDDING; MULTIGROUP; NEUTRON; GAMMA-RAY;
ONE-DIMENSION