Investigation: deterministic stochastic_slab (Option A) — reduces to NR

[jon-proximafusion]

Independent investigation (off develop) of whether OpenMC's stochastic_slab representative weighting can be reproduced deterministically (no Monte Carlo). Conclusion: it reduces to NR — see the comment below. Recorded for the record; not proposed for merge as a separate method.

🤖 Generated with Claude Code

[jon-proximafusion]

Finding: a deterministic stochastic_slab reduces to NR

Goal (Option A): reproduce OpenMC's stochastic_slab representative weighting
deterministically (reflective box of mixed materials + volumetric source).

Result: it collapses to narrow-resonance (NR), not to slab

Weighting each material X by phi_X(E) = q_mix(E)/Sigma_t,X(E) — the material-mix
slowing-down source x X's own self-shielding — gives, vs material_wise (CCFE-709):

material	dslab	slab	NR
tungsten	1.77	2.56	1.96
Fe-56	3.28	1.39	3.26
steel	0.60	0.48	0.57
Li4SiO4	0.07	0.42	0.06

dslab ≈ NR everywhere.

Why

1. The mix slowing-down source q_mix(E) is ≈ 1/E (asymptotic slowing-down density is
   ~constant per lethargy for any moderating mix), so phi_X = q_mix/Sigma_t,X = NR.
2. Slab's actual edge over NR is NOT the spectrum — it is the sigma0-DILUTION of its
   finite (1 cm) mixed cells (equivalence-theory self-shielding: neutrons inflow from
   neighbouring non-resonant cells reduce resonance self-shielding). That is tied to
   slab's arbitrary cell size — partly a numerical artifact.

Conclusion

You cannot beat NR on deep resonant metals in an order-free / geometry-free way — the
improvement (cross-talk + finite-region escape self-shielding) is inherently
geometry-dependent. The physically-correct version is the real-geometry deterministic
transport (PR #114), which beats slab (Fe-56 0.32%) where this approach cannot.

Recommendation: do not pursue this branch as a separate method; it is the NR
transport-free collapse (PR #113). Focus on #114 (real-geometry transport).