Evolution of the giant monopole resonance with triaxial deformation

Background: The isoscalar giant monopole resonance (ISGMR) splits into two peaks in prolately deformed nuclei. When a nucleus is triaxially deformed, a peak appears in the middle between the two peaks.

Purpose: We investigate the mechanism of the appearance of the middle peak in the ISGMR in triaxial nuclei.

Method: We perform the constrained Skyrme-Hartree-Fock-Bogoliubov (CHFB) calculation for arbitrary triaxial shapes in ${}^{100}\mathrm{Mo}$. We calculate the strength functions of the isoscalar monopole (ISM) and IS quadrupole modes on the CHFB states. Furthermore, we investigate vibrations of matter distributions in $x$, $y$, and $z$ directions induced by the external ISM field, with the $z$ axis being the longest axis of the triaxial shape.

Results: The middle peak in the ISM strength evolves from the triaxial degree $\gamma =0^{\circ }$ to ${60}^{\circ }$. This is because the difference between the vibration in the $x$ direction and that in the $y$ direction is evident with an increase in $\gamma$, and the quadrupole $K=2$ component of the induced density of the ISM at the middle peak increases as $\gamma$ increases, where $K$ denotes the $z$ component of the angular momentum. This property is also obtained in the unperturbed ISM strength without the residual fields.

Conclusions: The mixing between the monopole and quadrupole modes is primarily determined by the ground-state deformation. Therefore, the ISM strength of the middle peak becomes strong as the triaxial degree in the ground state increases.

Figure 1

Potential energy surface in the $\beta \text{−}\gamma$ plane obtained by the CHFB calculation with the ${\mathrm{SkM}}^{*}$ EDF in ${}^{100}\mathrm{Mo}$.

Figure 2

(a) ISM strength and (b) ISQ strength as a function of $\omega$ for different $\gamma$ in ${}^{100}\mathrm{Mo}$ with $\beta =0.28$.

Figure 3

Fraction of the EWSR value for the middle peak in the ISM strength as a function of $\gamma$.

Figure 4

Response functions of ISM $\to x^2$ (a), ISM $\to y^2$ (b), and ISM $\to z^2$ (c) for different $\gamma$ in ${}^{100}\mathrm{Mo}$ with $\beta =0.28$.

Figure 5

Induced densities for the ISQ $K=2$ field at $\omega =16\mathrm{MeV}$ on the $z=0$ plane at $\gamma =0^{\circ }$ (a) and $\gamma ={30}^{\circ }$ (b), and for the ISM field at $\omega =16\mathrm{MeV}$ on the $y=0$ (c) and $z=0$ (d) planes and induced densities without the residual ISM field at $\omega =20\mathrm{MeV}$ on the $y=0$ (e) and $z=0$ (f) planes at $\gamma ={30}^{\circ }$ in ${}^{100}\mathrm{Mo}$. The dashed line indicates the contour of the isoscalar density $\rho =0.08{\mathrm{fm}}^{-3}$ obtained by the CHFB calculation at $\gamma ={30}^{\circ }$, except for (a) at $\gamma =0^{\circ }$.

Figure 6

$L=2$, $K=2$ component of the induced density by the ISM field for different $\gamma$. The nuclear radius is indicated in the arrow. The $L=0$ component of the induced density at $\gamma ={30}^{\circ }$ is plotted by the dotted line.

Figure 7

Same as Fig. 2, but for the unperturbed strength.