Isovector giant monopole and quadrupole resonances in a Skyrme energy density functional approach with axial symmetry

Background: Giant resonance (GR) is a typical collective mode of vibration. The deformation splitting of the isovector (IV) giant dipole resonance is well established. However, the splitting of GRs with other multipolarities is not well understood.

Purpose: I explore the IV monopole and quadrupole excitations and attempt to obtain the generic features of IV giant resonances in deformed nuclei by investigating the neutral and charge-exchange channels simultaneously.

Method: I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states.

Results: I find the concentration of the monopole strengths in the energy region of the isobaric analog or Gamow-Teller resonance irrespective of nuclear deformation, and the appearance of a high-energy giant resonance composed of the particle-hole configurations of $2\hslash {\omega }_0$ excitation. Splitting of the distribution of the strength occurs in the giant monopole and quadrupole resonances due to deformation. The lower $K$ states of quadrupole resonances appear lower in energy and possess the enhanced strengths in the prolate configuration, and vice versa in the oblate configuration, while the energy ordering depending on $K$ is not clear for the $J=1$ and $J=2$ spin-quadrupole resonances.

Conclusions: The deformation splitting occurs generally in the giant monopole and quadrupole resonances. The $K$ dependence of the quadrupole transition strengths is largely understood by the anisotropy of density distribution.

Figure 1

Transition strengths of the non-spin-flip excitations in the $\mu =-1$ [(a), (d), (g)], $\mu =0$ [(b), (e), (h)], and $\mu =+1$ channels [(c), (f), (i)]. The Fermi (F), monopole (M), and quadrupole (Q) strengths are shown by the dotted, dashed, and long-dashed lines, respectively. The quadrupole strengths are multiplied by $1/25$ ($1/35$ for ${}^{208}\mathrm{Bi}$, Pb, Tl). The excitation energies $E_x$ are with respect to the ground state of the daughter nucleus. Arrows indicate the experimental data for the excitation energy.

Figure 2

As in Fig. 1 but for the deformed ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ nuclei. Instead of showing the total strengths, those for each $K$ component are shown for the quadrupole excitations. The quadrupole strengths are multiplied by $1/5$.

Figure 3

Monopole strengths in the (a) $\mu =-1$ channel and (b) $\mu =+1$ channel of the Sm isotopes (shifted), and the $K=0$ component of quadrupole strength distributions in the (c) $\mu =-1$ channel and (d) $\mu =+1$ channel (shifted). The excitation energies are with respect to the ground state of the target nuclei.

Figure 4

Fraction of the monopole strengths found in the peak energy region of the $K=0$ component of the quadrupole strength distribution as a function of the quadrupole deformation parameter in the deformed Sm isotopes with $N=86\text{–}92$.

Figure 5

Distributions of the monopole (upper) and the $K=0$ component of the quadrupole (lower) strengths in the $\mu =-1$ (a),(b), $\mu =0$ (c),(d), and $\mu =+1$ (e), (f) channels in ${}^{154}\mathrm{Sm}$. The unperturbed strengths are also shown.

Figure 6

As in Fig. 1 but for the spin quadrupole (SQ) strengths. The $J=1$, 2, and 3 states are depicted by the dotted, dashed, and solid lines, respectively.

Figure 7

As in Fig. 2 but for the Gamow-Teller and spin-monopole (SM) excitations. The strengths of $K=\pm 1$ are summed for $\left|K\right|=1$. The SM strengths are multiplied by $1/10$. The total strengths denoted by the solid lines include both the $J=1$ states with $K=0$ and those with $K=\pm 1$, while the dotted and dashed lines show the $K=0$ and $\left|K\right|=1$ states, respectively.

Figure 8

As in Fig. 2 but for the spin-quadrupole (SQ) excitations in the $\mu =+1$ channel.

Figure 9

As in Fig. 3 but for the spin-monopole (SM) excitations. The strengths for $K=0$ and $K=1$ are separately depicted by the dashed and solid lines, respectively.

Figure 10

Calculated distributions of the SM excitation in ${}^{144,154}\mathrm{Sm}$ obtained using the SkM* and SkP functionals.

Figure 11

As in Fig. 10 but for the SQ excitations in ${}^{144}\mathrm{Sm}$.

Figure 12

As in Fig. 11 but for ${}^{154}\mathrm{Sm}$.