Neutron drip line in odd and even mass calcium and nickel nuclei

Abstract

Neutron-rich Ca and Ni nuclei have been studied in a spherical relativistic mean-field formalism in coordinate space. A \ensuremath{\delta} interaction has been adopted to treat the pairing correlations for the neutrons. Odd nuclei have been treated in the blocking approximation. The effect of the positive-energy continuum and the role of pairing in the stability of nuclei have been investigated by use of the resonant-BCS approach. In Ca isotopes, $N=50$ is no longer a magic number, whereas in Ni nuclei, a new magic number emerges at $N=70$. There is a remarkable difference in the relative positions of the drip lines for odd and even isotopes. In Ca isotopes, the last bound even and odd nuclei are found to be $^{72}\mathrm{Ca}$ and $^{59}\mathrm{Ca}$, respectively. In Ni isotopes, the corresponding nuclei are $^{98}\mathrm{Ni}$ and $^{97}\mathrm{Ni}$, respectively. The origin of this difference in relative positions of the drip line in even and odd isotopes in the two chains is traced to the difference in the single-particle level structures and consequent modification in the magic numbers in the two elements. Pairing interaction is seen to play a major role. The effect of the width of the resonance states on pairing has also been investigated.