Varying shell gap and deformation inN∼20unstable nuclei studied by the Monte Carlo shell model

The structure of neutron-rich nuclei in the $N\sim 20$ region is studied by the Monte Carlo shell model based on the quantum Monte Carlo diagonalization method. We present a comprehensive description of even-even isotopes of O, Ne, Mg, and Si. It is demonstrated that, for different nuclei, various particle-hole excitations from the $\mathrm{sd}$ to $\mathrm{pf}$ shell are mixed in different ways, producing distinct effects sometimes, for instance, in ${}^{28}\mathrm{Ne}.$ The monopole interaction is examined and modified, resulting in the shell gap changing from nucleus to nucleus. The drip line of O isotopes is then reproduced. The interplay between the $T=0\mathrm{}$ and $T=1\mathrm{}$ monopole interactions is discussed from the viewpoint of the potential energy surface and the effective single-particle energy. The extension of the neutron drip line of Ne isotopes is explained, and the boundary of the “island of inversion” is shown to be rather indistinct.