Shell-structure of one-particle resonances in deformed potentials

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.