Uncollided flux in a void

What is being verified

For an isotropic point source of strength \(S\) (particles/s) in a pure void, the uncollided scalar flux at distance \(r\) is, by geometric spreading alone:

\[ \Phi(r) = \frac{S}{4\pi r^2} \]

With no attenuating medium the exponential attenuation factor is exactly 1, so the point-kernel result must reduce to this analytic form to floating-point precision, independent of particle type, source energy, or cross-section library.

What the script does

verification_and_validation/uncollided_flux_in_void.py sweeps:

• Distances from 1 cm to 5000 cm (8 values, log-spaced)
• Four sources: 14.06 MeV neutron, 2.45 MeV neutron, 1 MeV photon, 662 keV photon

For each combination it calls calculate_flux through a single Layer of void (no material) and compares .uncollided_flux against \(S / (4\pi r^2)\). It also asserts that .transmission_fraction == 1.0 exactly.

Tolerance

Relative error must be \(\leq 10^{-12}\). In practice all 32 cases return 0.00e+00 relative error (the division is bitwise identical to the analytic formula because both reduce to the same floating-point operations).

Result

All 32 cases pass. This is a trivial but load-bearing check. If it ever fails it means the geometric factor has drifted (e.g. a stray density factor, the wrong \(4\pi\) constant, or incorrect handling of zero-thickness materials).