Gamow shell-model calculations of drip-line oxygen isotopes

Abstract

We employ the Gamow shell model (GSM) to describe low-lying states of the oxygen isotopes $^{24}\mathrm{O}$ and $^{25}\mathrm{O}$. The many-body Schr\odinger equation is solved starting from a two-body Hamiltonian defined by a renormalized low-momentum nucleon-nucleon ($\mathit{NN}$) interaction and a spherical Berggren basis. The Berggren basis treats bound, resonant, and continuum states on an equal footing and is therefore an appropriate representation of loosely bound and unbound nuclear states near threshold. We show that the inclusion of continuum effects has a significant effect on the low-lying ${1}^{+}$ and ${2}^{+}$ excited states in $^{24}\mathrm{O}$. On the other hand, we find that a correct description of binding energy systematics of the ground states is driven by the proper treatment and inclusion of many-body correlation effects. This is supported by the fact that we get $^{25}\mathrm{O}$ unstable with respect to $^{24}\mathrm{O}$ in both oscillator and Berggren representations starting from a $^{22}\mathrm{O}$ core. Furthermore, we show that the structure of these loosely bound or unbound isotopes is strongly influenced by the ${}^{1}{S}_{0}$ component of the $\mathit{NN}$ interaction. This has important consequences for our understanding of nuclear stability.