Effects of realistic tensor force on nuclear quadrupole deformation around the shore of the island of inversion

The M3Y-type semi-realistic interaction is applied to deformed nuclei for the first time. The constrained Hartree-Fock calculations assuming axial symmetry are implemented for the $N=20$ isotones $^{30}$Ne, $^{32}$Mg, $^{34}$Si and the $N=28$ isotones $^{40}$Mg, $^{42}$Si, $^{44}$S with the M3Y-P6 interaction. The results match the experimental data well. Effects of the realistic tensor force on the nuclear quadrupole deformation are investigated in relation to the loss of the $N=20$ and $28$ magic numbers. The tensor force is confirmed to favor the deformation for the $N=28$ nuclei owing to the closure of the $jj$-shell (\textit{i.e.}, $n0f_{7/2}$), while favoring the sphericity for the $N=20$ nuclei owing to the $\ell s$-closure of $N=20$.

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