Eur. Phys. J. A (2015) 51: 110
https://doi.org/10.1140/epja/i2015-15110-4

Regular Article - Theoretical Physics

A collective coupled-channel model and mirror state energy displacements

¹ Institute of Theoretical Physics, Curtin University, Bentley, 6102, Western Australia, Australia
² School of Physics, University of Melbourne, 3010, Melbourne, Victoria, Australia
³ Department of Physics, University of Johannesburg, P.O. Box 524, 2006, Auckland Park, South Africa
⁴ Sezione di Padova, Istituto Nazionale di Fisica Nucleare, via Marzolo 8, I-35131, Padova, Italia
⁵ Department of Physics and Astronomy, University of Manitoba, and Winnipeg Institute for Theoretical Physics, Winnipeg, R3T 2N2, Manitoba, Canada

^* e-mail: paul.fraser@curtin.edu.au

Received: 23 June 2015
Accepted: 14 August 2015
Published online: 11 September 2015

Abstract

The spectra of nucleon-nucleus mirror systems allow examination of charge symmetry breaking in nucleon-nucleus interactions. To date, such examination has been performed with studies using microscopic models of structure. Herein we seek characterisation with a coupled-channel model in which the nucleon-nucleus interactions are described using a collective model prescription with the Pauli principle taken into account. The neutron-nucleus Hamiltonian is chosen to give the best match to the compound system spectrum, with emphasis on finding the correct ground state energy relative to the neutron-nucleus threshold. The Coulomb interactions for the proton-nucleus partner of a mirror pair are determined using charge distributions that match the root-mean-square charge radii of the nuclei in question. With the Coulomb interaction so defined modifying the neutron-nucleus Hamiltonian, we then predict a spectrum for the relevant proton-nucleus compound. Discrepancies in that resulting spectrum with measured values we tentatively ascribe to charge-symmetry breaking effects. We consider spectra obtained in this way for the mirror pairs ¹³C and ¹³N, ¹⁵C and ¹⁵F, and ¹⁵O and ¹⁵N, all to ∼ 10 MeV excitation.