Core polarization for the electric quadrupole moment of neutron-rich aluminum isotopes

The core polarization effects for the electric quadrupole moments of the neutron-rich ${}^{31}\mathrm{Al}$, ${}^{33}\mathrm{Al}$, and ${}^{35}\mathrm{Al}$ isotopes in the vicinity of the island of inversion are investigated by means of the microscopic particle-vibration coupling model in which the Skyrme Hartee-Fock-Bogoliubov and quasiparticle random-phase approximations are used to calculate the single-quasiparticle wave functions and the excitation modes. It is found that the polarization charge for the proton $1d_{5/2}$ hole state in ${}^{33}\mathrm{Al}$ is quite sensitive to coupling to the neutrons in the $\mathit{pf}$-shell associated with the pairing correlations and that the polarization charge in ${}^{35}\mathrm{Al}$ becomes larger due to the stronger collectivity of the low-lying quadrupole vibrational mode in the neighboring ${}^{36}\mathrm{Si}$ nucleus.

Figure 1

Response functions for the isoscalar (IS), isovector (IV), and proton quadrupole excitations in ${}^{32,34,36}\mathrm{Si}$. The transition strengths are smeared by a Lorentzian function with a width of $\Gamma =1$ MeV.

Figure 2

$B(E2;0^{+}\to 2_1^{+})$ values of Si isotopes as functions of neutron numbers. The calculated values (QRPA) are compared with the MCSM results [25] (SM) and the experimental results [26] (Exp.).

Figure 3

Same as Fig. 1 but for the RPA strengths in ${}^{34}\mathrm{Si}$.

Figure 4

Same as Fig. 1 but in ${}^{32}\mathrm{Mg}$.