Gamow shell model description of proton scattering onNe18

Abstract

Background: The structure of weakly bound/unbound nuclei close to particle drip lines is different from that around the valley of beta stability. A comprehensive description of these systems goes beyond the standard shell model (SM) and demands an open quantum system description of the nuclear many-body system.Purpose: For that purpose, we are using the Gamow shell model (GSM), which provides a fully microscopic description of bound and unbound nuclear states, nuclear decays, and reactions. We formulate the GSM in coupled-channel (GSM-CC) representation to describe low-energy elastic and inelastic scattering of protons on $^{18}\mathrm{Ne}$.Method: The GSM-CC formalism is applied to a translationally invariant Hamiltonian with an effective finite-range two-body interaction. We discuss in detail the GSM-CC formalism in coordinate space and give the description of the novel equivalent potential method for solving the GSM-CC system of integrodifferential equations. This method is then applied for the description of $(p,{p}^{\ensuremath{'}})$ reaction cross-sections. The reactions channels are built by GSM wave functions for the ground state ${0}^{+}$ and the first excited ${2}^{+}$ of $^{18}\mathrm{Ne}$ and a proton wave function expanded in different partial waves. The completeness of this basis is verified by comparing GSM and GSM-CC energies of low-energy resonant states in $^{19}\mathrm{Na}$. The differences between the two calculations provide a measure of the missing configurations in the GSM-CC calculation of low-energy states of $^{19}\mathrm{Na}$ due to the restriction on the number of excited states of $^{18}\mathrm{Ne}$.Results: We present the first application of the GSM-CC formalism for the calculation of excited states of $^{18}\mathrm{Ne}$ and $^{19}\mathrm{Na}$, the excitation function, and the elastic/inelastic differential cross-sections in the $^{18}\mathrm{Ne}$$(p,{p}^{\ensuremath{'}})$ reaction at different energies. This is the first unified description of the spectra and reaction cross-sections in the GSM formalism. The method is shown to be both feasible and accurate. The approximate equivalence of GSM and GSM-CC in describing spectra of $^{19}\mathrm{Na}$ has been demonstrated numerically.Conclusions: The GSM in the coupled-channel representation opens a possibility for the unified description of low-energy nuclear structure and reactions using the same Hamiltonian. While both GSM and GSM-CC can describe energies, widths, and wave functions of the many-body states, the GSM-CC can in addition yield reaction cross-sections. The combined application of GSM and GSM-CC to describe energies of resonant states allows to test the exactitude of calculated cross-sections for a given many-body Hamiltonian.