Semiempirical Formula for Energy-Space Distributions of Streamed Neutrons and Gamma-Rays in Cylindrical Ducts

Abstract

A semiempirical formula which describes energy-space distributions of streamed neutrons and γ-rays in cylindrical ducts, is derived. In the proposed formula, the spatial distribution of radiation fluxes is approximated by three multiscattered components for neutrons, namely direct, doubly scattered, and eight-time scattered components, and by two components for γ-rays, namely direct and single-scattered components. Then power of an albedo matrix is multiplied to the spatial distribution of each component of the fluxes to express energy spectra of the multiscattered radiation.

The spatial distribution of each multiscattered component is numerically computed by a recurrent relation of radiation current on the duct wall before and after a collision. Then an empirical formula is fitted to the obtained flux distributions.

For a bent duct, the obtained formula is applied repeatedly to each leg of the duct by using an additional relation which gives inflow of the radiation from the preceding leg into the following leg.

The albedo matrix is calculated by ANISN for neutrons, while it is made up for γ-rays by rearranging albedo data of a literature. The formula well reproduces experimental data of thermal neutrons, ²⁵²Cf fission neutrons in straight, single and double bent concrete ducts, and in straight polyethlene ducts. Dose rates of γ-rays estimated by the formula also are in good agreement with experimental data obtained with ¹³⁷ CS, ⁶⁰CO and ²⁴Na in two- and three-legged concrete ducts.

KEYWORDS:

• radiation streaming
• empirical formula
• duct streaming
• neutrons
• gamma radiation
• albedo
• radiation shielding
• concrete
• polyethylene
• shielding materials
• spatial distribution