Low-lying 2$^+$ states generated by $pn$-quadrupole correlation and $N=28$ shell quenching

The quadrupole vibrational modes of neutron-rich $N$=28 isotones ($^{48}$Ca, $^{46}$Ar, $^{44}$S and $^{42}$Si) are investigated using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory with several choice of energy density functionals, including nuclear pairing correlation. It is found that the quenching of $N$=28 shell gap and the proton holes in the $sd$-shell trigger quadrupole correlation and increase the collectivity of the low-lying 2$^+$ state in $^{46}$Ar. It is also found that the pairing correlation plays an important role to increase the collectivity. We also demonstrate that the same mechanism to enhance the low-lying collectivity applies to other $N$=28 isotones $^{44}$S and $^{42}$Si, and it generates a couple of low-lying 2$^+$ states which can be associated with the observed $2^+$ states.

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