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, ${}_{12}^{39}$Mg${}_{27}$ and ${}_6^{21}$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.

Comments: 16 pages and 3 figures