Isoscalar Giant Resonances in Highly-Deformed $^{172}$Yb

TL;DR

This work investigates isoscalar giant resonances in the highly deformed nucleus $^{172}$Yb using background-free $\alpha$-particle inelastic scattering at 386 MeV, extracting strength distributions for $L\le3$ via multipole-decomposition analysis. The results reveal deformation-driven features, including ISGMR splitting due to coupling with the $K=0$ ISGQR, a bimodal ISGDR, and an overtone in the ISGQR near $25$ MeV, all of which are well reproduced by the quasiparticle finite amplitude method (QFAM) alongside QRPA predictions for certain modes. Theoretical predictions based on axially deformed RHB+QFAM reproduce the main trends, confirming the role of ground-state deformation in shaping compressional modes and highlighting overtone excitations in a strongly deformed nucleus. These findings have implications for the understanding of nuclear incompressibility and the fragmentation of strength in deformed systems.

Abstract

To study the isoscalar giant resonances in a deformed case, background-free $α$-particle inelastic scattering measurements using a 386 MeV $α$ beam were performed on the highly-deformed $^{172}$Yb nucleus using the Grand Raiden spectrometer at the Research Center for Nuclear Physics (RCNP) at very forward angles, including $0^\circ$. The strength distributions for the isoscalar giant resonances up to $L \leq 3$ were obtained using multipole decomposition analysis. The isoscalar giant monopole resonance (ISGMR) strength exhibits a splitting into two components, interpreted as the coupling of the ISGMR with the $K=0$ component of the isoscalar giant quadrupole resonance (ISGQR). A \textit{bimodal} structure is observed in the strength distribution of the isoscalar giant dipole resonance. The ISGQR strength shows an enhancement near 25 MeV, attributed to the excitation of an overtone mode, while the broadening of the main-tone peak is associated with nuclear deformation. The experimental results are well reproduced by theoretical strength distributions calculated using the quasiparticle finite amplitude method for $L \leq 3$.

Figures (9)

• Figure 1: (a) Excitation-energy spectrum of $^{172}$Yb($\alpha, \alpha'$) measured at an average spectrometer angle of $\theta_{\mathrm{avg}}$ = 0.75$^{\circ}$, prior to instrumental background subtraction. The red histogram represents the total (true + background) events, while the blue-hatched area indicates the instrumental background. (b) Excitation-energy spectrum after instrumental background subtraction, where the black curve corresponds to the true inelastic scattering events.
• Figure 2: Two-dimensional spectrum of $^{172}$Yb($\alpha,\alpha$) elastic scattering at the GR angle of 11.2$^{\circ}$ without GR averaging. The red g-cut encloses the overlapping elastic peak and first-excited 2$^{+}$ state at 78 keV.
• Figure 3: Fitting of the EPFE2 peak for $^{172}$Yb($\alpha,\alpha$). The error bars are within the data points. The black filled data points are the measured experimental cross sections, while the red solid line shows the optical-model fit.
• Figure 4: Double-differential cross sections at 12, 15, 20, and 25 MeV for $^{172}$Yb are presented. The solid black curves represent fits from the MDA. Contributions from individual multipoles are shown: $L = 0$ (red), $L = 1$ (green), $L = 2$ (blue), $L = 3$ (cyan), $L\geq4$ (magenta), along with the IVGDR component (dashed black lines). The error bars are within the data points. The missing data points for angles between 4$^{\circ}$ and 8$^{\circ}$ in the different plots correspond to the regions where the hydrogen contamination was removed.
• Figure 5: ISGMR strength distribution in $^{172}$Yb extracted from MDA. The error bars on the data points include systematic uncertainties. The thick solid red line shows the double Lorentzian fit to the experimental data, with LE and HE components indicated by thick solid blue and green lines, respectively. The black dashed line represents the QFAM theoretical prediction, while the purple dashed line corresponds to the QRPA strength with the SV-bas interaction JKvasil2016.