Multipole modes of excitation in triaxially deformed superfluid nuclei

Background: The five-dimensional quadrupole collective model based on energy density functionals (EDFs) has often been employed to treat long-range correlations associated with shape fluctuations in nuclei. Our goal is to derive the collective inertial functions in the collective Hamiltonian by the local quasiparticle random-phase approximation (QRPA) that correctly takes into account time-odd mean-field effects. Currently, a practical framework to perform the QRPA calculation with the modern EDFs on the $(\beta ,\gamma )$ deformation space is not available.

Purpose: Toward this goal, we develop an efficient numerical method to perform the QRPA calculation on the $(\beta ,\gamma )$ deformation space based on the Skyrme EDF.

Methods: We use the finite amplitude method (FAM) for the efficient calculation of QRPA strength functions for multipole external fields. We construct a computational code of FAM-QRPA in the three-dimensional Cartesian coordinate space to handle triaxially deformed superfluid nuclei.

Results: We validate our new code by comparing our results with former QRPA calculations for axially symmetric nuclei. Isoscalar quadrupole strength functions in triaxial superfluid nuclei ${}^{110}\mathrm{Ru}$ and ${}^{190}\mathrm{Pt}$ are obtained within a reasonable computational cost.

Conclusions: QRPA calculations for triaxially deformed superfluid nuclei based on the Skyrme EDF are achieved with the help of the FAM. This is an important step toward the microscopic calculation of collective inertial functions of the local QRPA.

Figure 1

(a) Isoscalar quadrupole strengths of different $K$ modes as a function of $\omega$ for ${}^{24}\mathrm{Mg}$ calculated with ${\mathrm{SkM}}^{*}$ and (b) compared with those in Ref. [44].

Figure 2

(a) Isoscalar (IS) and isovector (IV) monopole strengths as a function of $\omega$ for ${}^{100}\mathrm{Zr}$ with SLy4 and with different pairing window energies $E_w=20\mathrm{MeV}$ (the solid line), 5 MeV (the cross), and 60 MeV (the diamond) and (b) compared with those in Ref. [35] (numerical data from Ref. [62]).

Figure 3

Isoscalar quadrupole strengths for spherical nuclei ${}^{92}\mathrm{Zr}$ (purple) and ${}^{94}\mathrm{Zr}$ (green). All the strengths with $K=0$, 1, and 2 (the solid, dashed, and dot-dashed lines) and $r_x=\pm 1$ are identical.

Figure 4

Isoscalar quadrupole strengths for triaxial nuclei (a) ${}^{110}\mathrm{Ru}$ and (b) ${}^{190}\mathrm{Pt}$.