Inverse scattering J-matrix approach to nucleon-nucleus scattering and the shell model

Abstract

The $J$-matrix inverse scattering approach can be used as an alternative to a conventional $R$-matrix in analyzing scattering phase shifts and extracting resonance energies and widths from experimental data. A great advantage of the $J$-matrix is that it provides eigenstates directly related to the ones obtained in the shell model in a given model space and with a given value of the oscillator spacing $\hslash \Omega$. This relationship is of a particular interest in the cases when a many-body system does not have a resonant state or the resonance is broad and its energy can differ significantly from the shell model eigenstate. We discuss the $J$-matrix inverse scattering technique, extend it for the case of charged colliding particles and apply it to the analysis of $n\alpha$ and $p\alpha$ scattering. The results are compared with the No-core Shell Model calculations of ${}^5$He and ${}^5$Li.

Some text is added following suggestions of a journal referee

References in corpus (9)

• Ab initio no-core full configuration calculations of light nuclei
• Many-body nuclear Hamiltonian: Ab exitu approach
• Large-basis shell model studies of light nuclei with a multi-valued G-matrix effective interaction
• Nucleon-nucleon interaction in the $J$-matrix inverse scattering approach and few-nucleon systems
• S-matrix and R-matrix determination of the low-energy He-5 and Li-5 resonance parameters
• Large-space shell-model calculations for light nuclei
• Novel NN interaction and the spectroscopy of light nuclei
• P-matrix and J-matrix approaches. Coulomb asymptotics in the harmonic oscillator representation of scattering theory
• Loosely bound three-body nuclear systems in the J-matrix approach

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• Structure of A = 7 - 8 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Role of diproton correlation in two-proton emission decay of the ${}^6$Be nucleus
• Nucleon-$\alpha$ Scattering and Resonances in ${}^5$He and ${}^5$Li with JISP16 and Daejeon16 $NN$ interactions
• Nuclear scattering via quantum computing
• SS-HORSE Extension of the No-Core Shell Model: Application to Resonances in ${}^7\mathrm{H}e$
• Scattering phase shifts from a quantum computer
• Nucleon-deuteron scattering with the JISP16 potential