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We derive an effective Reich-Moore approximation (RMA) of the Wigner-Eisenbud R-matrix formalism parameterized by complex-valued resonance energies and widths; this RMA exactly reproduces the total eliminated cross section. We show that resonance parameters evaluated for a conventional *** boundary conditions (BCs), Bc = Sc(E),are approximately equal to the R-matrix parameters in Park’s formalism by employing a linear approximation of the shift function therein [T.-S. Park, Phys. Rev. C 106 (2021) 064612]. We outline a method for converting Park’s observed reduced width amplitudes (RWAs) and their covariance matrix into Brune’s alternative R-matrix RWAs and their covariance matrix [C. Brune, Phys. Rev. C 66 (2002) 044611]. We extend the Park’s R-matrix formalism into the complex plane by introducing a complex-valued basis set of eigenfunctions of a complex-symmetric (non-Hermitian) Hamiltonian in the R-matrix interior. We observe that its R-matrix resonance energies and widths are directly related to the poles and residues, respectively, of Hwang’s sum-over-poles representation of cross sections [R.N. Hwang, Nucl. Sci. Eng. 96 (1987) 192].

Recently, a cold moderator was designed and developed for use at the Rensselaer Polytechnic Institute Linear Accelerator (RPI LINAC). This cold moderator proved to easily and safely couple to an existing neutron producing target, while enhancing neutron flux below 0.02 eV by up to a factor of 8 by cooling polyethylene down to 29 K. This cold moderator capability allowed for significantly improved counting statistics below 0.02 eV not previously possible due to a poor signal to background ratio. Additionally, testing was performed to characterize the energy resolution of the new cold moderator system and found the system easily capable of resolving resonances in Ta-181 at 4 and 10 eV, while also clearly resolving the Bragg edges found in Be metal below 0.01 eV. Following the design and development of a cold polyethylene moderator, a series of thermal total cross section measurements were performed for polyethylene, polystyrene, Plexiglas and yttrium hydride in the thermal region. These measurements serve to help validate thermal scattering law (TSL) evaluations in the 0.0005 – 1 eV energy range. For polyethylene and polystyrene, two sets of experiments were performed – one with the Enhanced Thermal Target (ETT) and another with the ETT plus the new cold moderator capability (ETTC). The yttrium hydride and Plexiglas measurements were only performed with the ETTC. The measurements for polyethylene help to validate the data processing methodology when using the ETTC, while extending the measured range of polyethylene down to 0.0005 eV. Two different Plexiglas, Plexiglas G and Plexiglas G-UVT, and two different concentrations of yttrium hydride, H/Y = 1.85 and 1.68, were measured. Overall, all materials had generally good agreement with their ENDF/B-VIII.0 TSL evaluations, though some discrepancies were noticed. In the case of the yttrium hydride, the high energy oscillations in the hydrogen cross section and the low energy Bragg edges in the yttrium cross section were clearly seen. These measurements represent the first total cross section measurements that encompass the entire thermal region from 0.0005 – 1 eV for polystyrene and yttrium hydride.

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.