Gamow shell model description of proton scattering on ¹⁸Ne

Journal Article · Thu Mar 27 00:00:00 EDT 2014 · Physical Review. C. Nuclear Physics

DOI:https://doi.org/10.1103/physrevc.89.034624· OSTI ID:1565206

Jaganathen, Y. ^[1]; Michel, N. ^[2]; Płoszajczak, M. ^[2]

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1. Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Joint Inst. of Nuclear Physics and Applications
2. Grand Accélérateur National d'Ions Lourds (GANIL), Caen (France)

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) in this study, which provides a fully microscopic description of bound and unbound nuclear states, nuclear decays, and reactions. Here, we formulate the GSM in coupled-channel (GSM-CC) representation to describe low-energy elastic and inelastic scattering of protons on $$\mathrm{^{18}Ne}$$. 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 ($p, p'$) reaction cross-sections. The reactions channels are built by GSM wave functions for the ground state $$\mathrm{0^+}$$ and the first excited $$\mathrm{2^+}$$ of $$\mathrm{^{18}Ne}$$ 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 $$\mathrm{^{19}Na}$$. The differences between the two calculations provide a measure of the missing configurations in the GSM-CC calculation of low-energy states of $$\mathrm{^{19}Na}$$ due to the restriction on the number of excited states of $$\mathrm{^{18}Ne}$$. Results: We present the first application of the GSM-CC formalism for the calculation of excited states of $$\mathrm{^{18}Ne}$$ and $$\mathrm{^{19}Na}$$, the excitation function, and the elastic/inelastic differential cross-sections in the $$\mathrm{^{18}Ne}$$ ($p,p'$) 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 $$\mathrm{^{19}Na}$$ 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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Univ. of Tennessee, Knoxville, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: FG02-96ER40963; FG02-10ER41700
• OSTI ID: 1565206
• Journal Information: Physical Review. C. Nuclear Physics, Vol. 89, Issue 3; ISSN 0556-2813
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

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