Neutron-proton ratio of collective excitations

Abstract

Using a harmonic oscillator model, it is shown that the isovector giant quadrupole resonance carries little isoscalar quadrupole strength while the isoscalar giant quadrupole resonance contains an isovector strength with $B(\mathrm{IV})/B(\mathrm{IS})\ensuremath{\approx}((N\ensuremath{-}Z)/A{)}^{2},$ when a consistency condition is fulfilled. Taking into account the consistency between the one-particle excitation spectra and the vibrational fields is of vital importance in the proper estimate of the ratio of the contribution by neutrons to that by protons to collective excitations of nuclei with $N\ensuremath{\ne}Z.$ The ratio may not be properly estimated in the models such as traditional shell models, in which the Coulomb potential (or interaction) is simulated by using the parameters ${\ensuremath{\omega}}_{p}<{\ensuremath{\omega}}_{n}$ for nuclei with a neutron excess.