Shape evolution of giant resonances in Nd and Sm isotopes

Giant multipole resonances in Nd and Sm isotopes are studied by employing the quasiparticle-random-phase approximation on the basis of the Skyrme energy-density-functional method. Deformation effects on giant resonances are investigated in these isotopes, which manifest a typical nuclear shape change from spherical to prolate shapes. The peak energy, the broadening, and the deformation splitting of the isoscalar giant monopole (ISGMR) and quadrupole (ISGQR) resonances agree well with measurements. The magnitude of the peak splitting and the fraction of the energy-weighted strength in the lower peak of the ISGMR reflect the nuclear deformation. The experimental data on ISGMR, isoscalar giant dipole (ISGDR), and ISGQR are consistent with the nuclear-matter incompressibility $K\simeq 210–230$ MeV and the effective mass $m_0^{*}/m\simeq 0.8–0.9$. However, the high-energy octupole resonance (HEOR) in ${}^{144}$Sm seems to indicate a smaller effective mass, $m_0^{*}/m\simeq 0.7–0.8$. A further precise measurement of HEOR is desired to determine the effective mass.

Figure 1

The IS dipole and octupole transition-strength distributions in ${}^{144}$Sm and in ${}^{154}$Sm in the low-energy region (upper panels) and the GR energy region (lower panels). The results obtained with ${\eta }_K=0$ and ${\eta }_K^{\left(3\right)}=0$ are shown by dotted lines.

Figure 2

The strength distributions (shifted) of ISGMR [(a), (b)] and ISGQR [(c), (d)] in Nd and Sm isotopes.

Figure 3

The centroid energies of the ISGQR in the Sm isotopes with a fitted line. The experimental data [40, 41] are denoted by open symbols.

Figure 4

The IS quadrupole transition-strength distribution in ${}^{154}$Sm for the $K^{\pi }=0^{+}$, $1^{+}$, and $2^{+}$ excitations. The eigenenergies obtained with use of the P+Q model are denoted by the arrows, and the peak position of the GQR was adjusted to the experimental data [42].

Figure 5

(a) The excitation energies of the ISGMR in the Sm isotopes. The experimental data [39] are denoted by open symbols with error bars. The energies of the upper and the lower peaks are indicated by squares and circles. (b) The energy difference of the upper peak and the lower peak of the ISGMR in ${}^{148,150,152,154}$Sm as a function of the deformation parameter ${\beta }_2$. The lines are results of the fluid dynamical and scaling models [45].

Figure 6

The strength distributions (shifted) of IVGMR [(a), (b)] and IVGQR [(c), (d)] in Nd and Sm isotopes.

Figure 7

Strength distributions (shifted) of ISGDR [(a), (b)] and ISGOR (HEOR) [(c), (d)] in Nd and Sm isotopes.

Figure 8

(a) The centroid energies of the low-energy and high-energy components of the ISGDR in the Sm isotopes. (b) The centroid energies of the HEOR and the LEOR in the Sm isotopes. The centroid energy of LEOR is evaluated in the energy range of $[E_a,E_b]=[3,10]$ MeV. The dotted line is obtained by fitting the results with an $A^{-1/3}$ line. The experimental data [39] are denoted by open symbols with error bars.

Figure 9

The low-energy IS dipole and octupole transition strengths in the Sm isotopes. The strengths with different $K$ are all identical for the spherical nuclei.

Figure 10

(a) The IS compression dipole strength distribution in the ISGDR energy region in ${}^{154}$Sm. (b) The IV dipole strength distribution in the GDR energy region. (c) The IS octupole strength distribution. (d) The IV octupole strength distribution.

Figure 11

The strength distributions (shifted) of IVGDR [(a), (b)] and IVGOR [(c), (d)] in Nd and Sm isotopes.

Figure 12

The excitation energies of the lowest $K^{\pi }=0^{+}$, $2^{+}$, $0^{-}$ and $1^{-}$ states in Nd and Sm isotopes. The experimental data for Nd and Sm isotopes [53] are denoted by open triangles and circles, respectively. The lines are drawn to guide the eyes.

Figure 13

The peak energies of the ISGMR and ISGQR, and the centroid energy of the ISGDR and HEOR in ${}^{144}$Sm and ${}^{154}$Sm obtained by employing the Skyrme functionals giving the different nuclear-matter properties. The continuous lines are drawn to guide the eyes. Experimental data are shown by the open squares [39] and the circles [40] with the error bars.