Errors in the calculation of radiation fields in media

Bolyatko, V. V.; Vyrskii, M. Yu.; Ilyushkin, A. I.; Mashkovich, V. P.; Sakharov, V. K.; Stroganov, A. A.

doi:10.1007/bf01121134

Cited by 2 publications

(1 citation statement)

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“…Predominantly, the correlation between neutron self-shield factors and the set of parameters involved in the calculation of its value had been studied by several scientists [17][18][19][20][21][22][23][24][25][26][27], who gave dimensionless variables to identify and encompass the physical and geometric varieties of the sample geometries in order to attain a universal formula for self-shielding. The Montè-Carlo approach effectively calculates self-shielding, but it takes time and an experienced user to achieve acceptable accuracy and efficiency [28], see A. Empirical expressions, such as those given by researchers in [19][20][21][22][23] based on [17] have been derived for a few specific geometries and a limited number of elements.…”

Section: Introductionmentioning

confidence: 99%

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Elmaghraby,

Mahmoud,

Salama

et al. 2024

Phys. Scr.

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In the current study, an ab initio derivation of the neutron self-shielding factor to solve the complex neutron transport problem of the decrease of the neutron ﬂux as it penetrates into a material placed in an isotropic neutron ﬁeld. The theory of steady-state neutron transport was employed, starting from Stuart’s formula, to derive simple analytical formulae based on the integral cross-section parameters. The formulae could be adopted by the user according to various variables, such as the neutron ﬂux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interaction probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simpliﬁed version of neutron transport formulation. The derived analytic formulae agreed greatly with the experimental observations for diﬀerent elements and geometries.

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