Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical formulae for neutron self-shielding properties of media in
  an isotropic neutron field   The complexity of the neutron transport phenomenon throws its shadows on
every physical system wherever neutron is produced or used. In the current
study, an \emph{ab initio} derivation of the neutron self-shielding factor, the
problem of the decrease of the neutron flux as it penetrates into a material
placed in an isotropic neutron field, has been attempted by employing the
theory of steady-state neutron transport, starting from Stuart's formula.
Simple formulae were derived based on the integral cross-section parameters,
which can 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 a weight representing the ratio between the total and scattering
macroscopic cross-sections of the medium. The general convex volume geometries
are reduced to a set of chord lengths, while the neutron interactions
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. Accordingly, the
obtained general formulae were successful in giving the experimental values of
the neutron self-shielding factor for different elements and different
geometries. The results were validated by comparing them to the experimental
data as well as a variety of data extracted from the literature

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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph