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/`
R-Matrix Limited	LRF=7	`rmatrix_limited`	Manual Sec. II
Unresolved Resonance Region	LRU=2	`urr`	Manual Sec. VIII.A, `acs/` (FITACS)

The urr module computes energy-averaged Hauser-Feshbach cross-sections from the average resonance parameters. The width-fluctuation correction is not yet implemented: the AMUN/AMUF degrees of freedom are parsed from ENDF File 2 but not yet used in the cross-section computation.

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 – transmission-domain Poisson likelihood (projected damped Gauss-Newton); used for the transmission + PoissonKL combination
Reference: TRINIDI approach (trinidi/reconstruct.py)

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