Physics Reference

NEREIDS implements exact SAMMY physics for neutron resonance imaging. This chapter is a navigation guide to the rustdoc API documentation, not a standalone physics textbook.

All implementations reference specific sections of the SAMMY manual and SAMMY Fortran source files. See the rustdoc for each module for detailed equations and citations.

Cross-Section Formalisms

Formalism	ENDF LRF	Module	SAMMY Reference
Reich-Moore	LRF=3	`reich_moore`	Manual Sec. II, `rml/`
Breit-Wigner (single- and multi-level)	LRF=1,2	`slbw`	Manual Sec. II, `mlb/`

Not evaluated: R-Matrix Limited (LRF=7) and Unresolved Resonance Region (LRU=2) ranges are parsed-and-skipped — consumed for file alignment but contributing zero cross-section. A file containing only such ranges is rejected at load time; mixed evaluations load with a warning naming the skipped spans.

The penetrability and channel modules provide the underlying nuclear physics: hard-sphere phase shifts, penetrability factors, wave numbers, and statistical spin weights.

Broadening Models

Doppler Broadening

Free Gas Model (FGM) convolution accounting for thermal motion of target nuclei.

Module: doppler
SAMMY reference: fgm/ module (Dopfgm), manual Sec. III.B.1
Key function: doppler_broaden() — exact Free Gas Model convolution integral in velocity space (manual Eq. III B1.7, w²-weighted integrand); no psi/chi (Voigt) approximation is used

Resolution Broadening

Instrument resolution broadening from flight-path uncertainty, timing jitter, and moderator pulse width.

Module: resolution
SAMMY reference: convolution/ module, manual Sec. III.C
Supports: Gaussian convolution, Gaussian + exponential tail, tabulated resolution functions

Transmission Model

Beer-Lambert transmission: T(E) = exp(-sum_i n_i sigma_i(E))

Where n_i is the areal density (atoms/barn) and sigma_i(E) is the broadened total cross-section for isotope i.

Module: transmission
SAMMY reference: cro/, xxx/ modules, manual Sec. II; transmission experiments Sec. III.E.1
Handles multi-isotope samples with shared Doppler temperature (one global temperature parameter, optionally fitted jointly with densities)

Fitting Engines

Levenberg-Marquardt

Standard nonlinear least-squares minimization for Gaussian-distributed data.

Module: lm
SAMMY reference: fit/ module, manual Sec. IV
Parameters: areal densities with optional bounds, optional temperature fitting

Poisson KL Divergence

Maximum-likelihood fitting for low-count data where Gaussian statistics break down.

Module: joint_poisson – counts-domain joint-Poisson fit (conditional binomial deviance); the production path for counts data
Module: poisson – low-level single-arm Poisson likelihood (projected Levenberg–Marquardt in the Fisher metric); research diagnostics and the Fisher-information helper only — not a production fit route
Reference: D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters”, J. Soc. Indust. Appl. Math. 11, 431–441 (1963)

ENDF Nuclear Data

Resonance parameters are sourced from evaluated nuclear data libraries (ENDF/B from NNDC with IAEA fallback; the other libraries from IAEA):

Module: retrieval – download and cache
Module: parser – parse ENDF-6 File 2
Module: resonance – data structures

Supported libraries: ENDF/B-VIII.0, ENDF/B-VIII.1, JEFF-3.3, JENDL-5, TENDL-2023, CENDL-3.2.

NEREIDS Guide