Systematic study of $L⩽3$ giant resonances in Sm isotopes via multipole decomposition analysis

Background-free inelastic scattering spectra have been obtained for five Sm isotopes with $386\text{−}\text{MeV}$ $\alpha$ particles at forward angles (including $0°$) to investigate the effect of deformation on the compressional-mode giant resonances. The strength distributions for the $L⩽3$ isoscalar giant resonances have been extracted via a multipole decomposition analysis using angular distributions calculated in the framework of the density-dependent single-folding model. We observed a splitting of the giant monopole resonance because of its mixing with the giant quadrupole resonance. For the isoscalar giant dipole resonance, the observed effects of deformation are different for the low- and high-excitation-energy components. Evidence has been obtained for the theoretically predicted mixing between the isoscalar giant dipole resonance and the high energy octupole resonance.

Figure 1

Schematic layout of the experimental setup. The beam path is shown by a thick solid line. (a) The experimental setup of the $0°$ measurement. (b) An enlarged view of the focal-plane detector. (c) The schematic view of the experimental setup for the $2°–6°$ measurements.

Figure 2

Vertical-position spectrum at the focal plane of Grand Raiden taken at $0°$. The central hatched region represents true + background events. The off-center regions represent only background events. The true events were extracted by subtracting the background events from the true + background events.

Figure 3

(a) Excitation-energy spectrum of the ${}^{144}\mathrm{Sm}\left(\alpha ,{\alpha }^{\prime }\right)$ reaction at $0°$ for the vertical center region at the focal plane. The hatched spectrum corresponds to the off-center region (see Fig. 2). (b) Excitation-energy spectrum after background subtraction.

Figure 4

Inelastic $\alpha$-scattering spectra at $0°\left({\theta }_{av}=0.7°\right)$ and $E_{\alpha }=386\text{MeV}$ for ${}^{144-154}\mathrm{Sm}$ obtained in the present work. These spectra have been subtracted from the background reasonably as shown in Fig. 3.

Figure 5

Differential cross sections of elastic $\alpha$-particle scattering from ${}^{144}\mathrm{Sm}$ at $386\text{MeV}$. The open circles show the measured cross sections. The solid line shows the result of the DW calculation with an optical-model potential obtained via a single-folded potential model.

Figure 6

Double-differential cross sections for selected energy bins in ${}^{144-154}\mathrm{Sm}$. The solid lines through the data show fits to the data from multipole decomposition. In each panel, the contributions from $L=0$ (thick-solid), $L=1$ $\left(T=0\right)$ (dot-dashed), $L=1$ $\left(T=1\right)$ (short-dashed), $L=2$ (long-dashed), $L=3$ (dotted), and $L⩾4$ (thin-solid) are also displayed.

Figure 7

The results of the MD analysis in ${}^{144}\mathrm{Sm}$ with various choices for $L_{max}$, ground-state density, and transition density. The solid lines connect data points. The closed circles, open circles, and open squares, respectively, show the results for $L_{max}$ (14, 16, and 19). The open triangles (UNFOLD) and open diamonds (FERMI) show the results of the MD analysis with the DWBA angular distributions calculated from the ground-state densities distributions in two alternative models. The closed triangles (BM) show the results with the DWBA angular distributions calculated from the Bohr-Mottelson transition density. The open stars show the results from the data of the ${\theta }_{\mathrm{c.m.}}<9°$ for ${}^{144}\mathrm{Sm}$. See text for more details.

Figure 8

The $L=0$ and $L=2$ strength distributions for ${}^{144-154}\mathrm{Sm}$ obtained from the multipole-decomposition analysis (see text). The thick solid lines show the results of a Breit-Wigner fit. The thin solid lines show the results of two-Breit-Wigner fits to the peak region. The low- and high-excitation-energy components of the GMR and the GQR are indicated by slashed areas. For the result of ${}^{154}\mathrm{Sm}$, the calculations of the adiabatic cranking model (dashed lines) [7] and the fluid-dynamical model (dash-dotted lines) [11] are shown.

Figure 9

The peak energies for the GMR and for the $K=0$ components of the GQR in ${}^{144-154}\mathrm{Sm}$ are plotted as a function of the deformation parameter $\delta$. The open squares are results of the fluid-dynamical model. The open triangles are results of the cranking model. The lines are drawn to guide the eye.

Figure 10

The ISGDR strength observed in the Sm isotopes. The dashed line indicates the division between the LE and HE components (see text). The results of two-Breit-Wigner fits are also shown.

Figure 11

The $L=3$ strength observed in the Sm isotopes. The dashed lines indicate the regions of the LE and HE parts, respectively (see text).