Gamow shell model description of proton scattering on ${}^{18}$Ne

Abstract

We formulate the GSM in coupled-channel (GSM-CC) representation to describe low-energy elastic and inelastic scattering of protons on ${}^{18}$Ne. The GSM-CC formalism is applied to a translationally-invariant Hamiltonian with an effective finite-range two-body interaction. We discuss in details the GSM-CC formalism in coordinate space and give the description of the novel equivalent potential method for solving the GSM-CC system of integro-differential equations. We present the first application of the GSM-CC formalism for the calculation of excited states of ${}^{18}$Ne and ${}^{19}$Na, excitation function and the elastic/inelastic differential cross-sections in the ${}^{18}$Ne$(p,p^{\prime })$ reaction at different energies.

14 pages, 11 figures

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