Neutron decay width of one-particle resonant levels in deformed nuclei

Abstract

The neutron partial decay width of one-particle resonant levels that are the bandhead states in odd-$N$ deformed nuclei is estimated in the formalism with a real-energy variable, using the width of one-particle resonance calculated in terms of eigenphase. It is shown that because of the presence of various ($\ensuremath{\ell}j$) components in a given one-particle resonant level of deformed nuclei, the neutron decay width can be quite different from the one obtained from assuming a spherically symmetric nuclear shape. As a numerical example, the formalism is applied to the case of the nucleus ${}_{4}^{13}$Be${}_{9}$, which lies outside the neutron drip line by 100--200 keV. Considering that the core of the nucleus consisting of four protons and eight neutrons is most likely prolately deformed, we point out the possibility that two lowest lying levels have ${I}^{\ensuremath{\pi}}=1/{2}^{+}$ for the $N=9$ nucleus, and the higher lying one may have a neutron decay width that is much narrower than the one expected for an ${s}_{1/2}$ level at the same resonance energy. The structure of some ${\ensuremath{\Omega}}^{\ensuremath{\pi}}=1/{2}^{+}$ one-particle resonant levels, which are smoothly connected to weakly bound one-particle levels as the potential strength becomes stronger, is also analyzed using the present formalism.