Varying shell gap and deformation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mi>∼</mml:mi><mml:mn>20</mml:mn></mml:math>unstable nuclei studied by the Monte Carlo shell model

The structure of neutron-rich nuclei in the $N\ensuremath{\sim}20$ 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 $T=0$ and $T=1$ 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.

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