Shell Model States in the Continuum

TL;DR

The paper introduces a novel method for calculating scattering phase shifts and resonance parameters using eigenenergies from variational oscillator basis calculations, validated with model potentials and applied to nuclear scattering problems.

Contribution

It presents a new approach combining variational eigenenergies with the HORSE formalism to efficiently determine scattering and resonance properties.

Findings

Accurate phase shifts and resonance widths obtained from eigenenergies.

Method validated with Woods--Saxon potential models.

Applied successfully to nα resonances and non-resonant scattering.

Abstract

We suggest a method for calculating scattering phase shifts and energies and widths of resonances which utilizes only eigenenergies obtained in variational calculations with oscillator basis and their dependence on oscillator basis spacing $\hbar\Omega$. We make use of simple expressions for the $S$-matrix at eigenstates of a finite (truncated) Hamiltonian matrix in the oscillator basis obtained in the HORSE ($J$-matrix) formalism of quantum scattering theory. The validity of the suggested approach is verified in calculations with model Woods--Saxon potentials and applied to calculations of $n\alpha$ resonances and non-resonant scattering using the no-core shell model.