Shell-structure of one-particle resonances in deformed potentials

TL;DR

This paper investigates the shell structure of low-lying neutron resonant levels in deformed nuclei near the neutron drip line, revealing how deformation influences resonance properties and correlates with experimental observations.

Contribution

It introduces an analysis of neutron resonant levels in deformed potentials, providing specific predictions for nuclei outside the neutron drip line, linking shell structure to deformation effects.

Findings

$^{39}$Mg likely prolately deformed with a 5/2$^{-}$ resonance.

$^{21}$C may be oblately deformed with a 1/2$^{+}$ resonance.

$^{21}$C is unlikely to be observed as a resonant state.

Abstract

Shell structure of low-lying neutron resonant levels in axially-symmetric quadrupole-deformed potentials is discussed, which seems analogous to that of weakly-bound neutrons. As numerical examples, nuclei slightly outside the neutron-drip-line, $^{39}_{12}$Mg$_{27}$ and $^{21}_{6}$C$_{15}$, are studied. For the lowest resonance I obtain $I^{\pi}$ = $\Omega^{\pi}$ = 5/2$^{-}$ for $^{39}$Mg which is likely to be prolately deformed, while $I^{\pi}$ = $\Omega^{\pi}$ = 1/2$^{+}$ may be assigned to the nucleus $^{21}$C which may be oblately deformed. Consequently, $^{21}$C will not be observed as a recognizable resonant state, in agreement with the experimental information.