Quenching of N = 28 shell gap and a low-lying quadrupole mode in the vicinity of neutron-rich N = 28 isotones

We investigate the low-lying 2$^+$ states of $N=28$ isotones ($^{48}$Ca, $^{46}$Ar, $^{44}$S and $^{42}$Si) with using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory in which the pairing is taken into account self-consistently. The quadrupole mode with very small excitation energies emerges in $^{46}$Ar, $^{44}$S and $^{42}$Si due to the strong quadrupole correlations triggered by the quenching of the $N=28$ shell gap. The importance of the quadrupole correlations between the protons and neutrons, and the role of the pairing correlation to reinforce the lowest 2$^+$ mode are discussed. It is also shown that the $B$(E2$\uparrow$) values of $^{48}$Ca and $^{46}$Ar are plausibly explained by our calculations.