  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 ab initio derivation of the neutron self-shielding factor to solve
the problem of the decrease of the neutron flux as it penetrates into a
material placed in an isotropic neutron field. We have employed the theory of
steady-state neutron transport, starting from Stuart's formula. Simple formulae
were derived based on the integral cross-section parameters that 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 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 values of the
experimental neutron self-shielding factor for different elements and different
geometries.
