Zero-range potentials with Inner structure: fitting parameters for resonance scattering

TL;DR

This paper develops a generalized zero-range potential model with inner structure to accurately describe low-energy neutron scattering, incorporating nuclear excitations and providing a method to determine model parameters from physical data.

Contribution

It introduces a zero-range potential model with an inner Hamiltonian and indefinite metric, extending Fermi's potential to include nuclear excitations and analyticity principles for parameter evaluation.

Findings

Model successfully incorporates nuclear excitations in scattering

Parameters can be determined from spectrum, scattering length, and radius

Provides a systematic way to fit resonance scattering data

Abstract

The solution of the classical Fermi problem of low-energy neutron scattering by nuclei, when the excitations of the nuclei in scattering processes are taken into account, is found by the method of zero-range potentials with inner structure. This model is a generalization of the Fermi zero-range potential obtained by adding a non-trivial inner Hamiltonian and inner space with indefinite metric. We propose a general principle of analyticity of the Caley-transform of the S-scattering matrix, written as a function of wave number. This permits us to evaluate all parameters of the model, including the indefinite metric tensor of the inner space, once the spectrum of the inner Hamiltonian, the scattering length and the effective radious are chosen.