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

The quadrupole vibrational modes of neutron-rich $N=28$ isotones (${}^{48}\mathrm{Ca}$, ${}^{46}\mathrm{Ar}$, ${}^{44}\mathrm{S}$, and ${}^{42}\mathrm{Si}$) are investigated by 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 the $N=28$ shell gap and the proton holes in the $sd$ shell trigger quadrupole correlation and increase the collectivity of the low-lying $2^{+}$ state in ${}^{46}\mathrm{Ar}$. 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 ${}^{44}\mathrm{S}$ and ${}^{42}\mathrm{Si}$, and it generates a couple of low-lying $2^{+}$ states which can be associated with the observed $2^{+}$ states.

Figure 1

Strength functions of quadrupole vibrational modes of ${}^{48}\mathrm{Ca}$ and ${}^{46}\mathrm{Ar}$. The strength functions in the IS (solid line) and IV (dotted line) channels are shown in panels (a) and (d), while those in the proton and neutron channels are shown in panels (b), (e) and (c), (f). The solid and dashed lines in the panels (b), (c), (e), and (f) compare the fully self-consistent and unperturbed results. The filled arrows show the experimental one- and two-neutron separation energies [50], while the open arrows show the calculated two-neutron separation energies.

Figure 2

Strength functions in proton (red) and neutron (blue) channels for ${}^{46}\mathrm{Ar}$ using ${\mathrm{SkM}}^{*}$. Fully self-consistent (thin solid line) and unperturbed (thin chain line) results are shown.

Figure 3

Strength functions in proton (red) and neutron (blue) channels for ${}^{46}\mathrm{Ar}{}^{\mathrm{II}}$ (solid line) and ${}^{46}\mathrm{Ar}{}^{\mathrm{III}}$ (dashed line), which are obtained by the fully self-consistent calculation.

Figure 4

Strength functions in the proton and neutron channels for ${}^{44}\mathrm{S}$ and ${}^{42}\mathrm{Si}$. $K=0$ and 2 modes are shown in panels (a) and (b), respectively. The experimental separation energies ${\mathrm{S}}_n$, ${\mathrm{S}}_{2n}$ are taken from Ref. [50].