Giant dipole resonance and shape transitions in hot and rotating ${}^{88}\mathrm{Mo}$

The giant dipole resonance (GDR) observables are calculated within the thermal shape fluctuation model by considering the probability distributions of different angular momentum ($I$) and temperature ($T$) values estimated recently in the deexcitation process of the compound nucleus ${}^{88}\mathrm{Mo}$. These results are found to be very similar to the results obtained with the average $T$ ($T_{\mathrm{ave}}$) and average $I$ ($I_{\mathrm{ave}}$) corresponding to those distributions. The shape transitions in ${}^{88}\mathrm{Mo}$ at different $T$ and $I$ are also studied through the free energy surfaces calculated within the microscopic-macroscopic approach. The deformation of ${}^{88}\mathrm{Mo}$ is found to increase considerably with $T$ and $I$, leading to the Jacobi shape transition at $I\sim 50\hslash$. The combined effect of increasing deformation, larger fluctuations at higher $T$, and larger Coriolis splitting of GDR components at higher $I$, leads to a rapid increase in the GDR width.

Figure 1

GDR cross sections ($\sigma$) calculated within the TSFM for different daughter nuclei formed at different temperatures ($T$) in the deexcitation process of the compound nucleus ${}^{88}\mathrm{Mo}$ obtained with beam energy $E_{\mathrm{lab}}=300$ MeV. The solid line represents the ${\sigma }_{\mathrm{ave}}\left(T_{\mathrm{ave}}\right)$ obtained by considering an average $T_{\mathrm{ave}}$ and different angular momentum ($I$) probability distributions [Eq. (6)]. The dashed line and dash-dotted lines represent the $\sigma (T_{\mathrm{ave}},I_{\mathrm{ave}})$ obtained with an average $T_{\mathrm{ave}}$ and average $I_{\mathrm{ave}}$ given by Eq. (7), respectively. For the latter case, the results obtained by using free energies from the liquid drop model (LDM) are presented as the dash-dotted lines.

Figure 2

Same as Fig. 1, but for the beam energy $E_{\mathrm{lab}}=600$ MeV.

Figure 3

Experimental GDR cross sections (solid squares) of ${}^{88}\mathrm{Mo}$ at two different excitation energies taken from Ref. [1], compared with the TSFM results. The solid line represents the average of the GDR cross sections ($\sigma$) of daughter nuclei obtained by considering $T_{\mathrm{ave}}$ and $I$ probability distributions [Eq. (6)]. The dashed line represents the same obtained with the $T_{\mathrm{ave}}$ and $I_{\mathrm{ave}}$ with TSFM. For the latter case, the dotted lines represent the calculations with LDM free energies.

Figure 4

GDR width $\mathrm{\Gamma }$ of ${}^{88}\mathrm{Mo}$ calculated using TSFM at two different excitation energies as a function of $T$. The filled upward triangles connected with solid line represent $\mathrm{\Gamma }$ of the final $\sigma$ presented in Fig. 3, where $\sigma$ of the daughter nuclei are obtained by considering the $T_{\mathrm{ave}}$ and $I$ probability distributions [Eq. (6)]. The filled downward triangles connected with dashed line and filled circles connected with dash-dotted line represent the $\mathrm{\Gamma }$ of the final $\sigma$, where $\sigma$ of the daughter nuclei are obtained by considering the $T_{\mathrm{ave}}$ and $I_{\mathrm{ave}}$ within the TSFM with free energies obtained from the microscopic-macroscopic approach and LDM, respectively. The experimental results are taken from Ref. [1]. The widths obtained within the PDM and LSD taken from Ref. [1] are also shown with open circles and open triangles. The lines are drawn just to guide the eyes.

Figure 5

FES of ${}^{88}\mathrm{Mo}$ at $T=2$ MeV with different $I$. In this convention, $\gamma =0^{\circ }$ and $-{120}^{\circ }$ represent the noncollective and collective prolate shapes, respectively; $\gamma =-{180}^{\circ }$ and $-{60}^{\circ }$ represent the noncollective and collective oblate shapes, respectively. The contour line spacing is 0.2 MeV. The most probable shape is represented by a filled circle and first two minima are represented by thicker lines.

Figure 6

Same as Fig. 5, but at $T=2.5$ and 3 MeV.

Figure 7

Same as Fig. 5, but at $T=3.5$ MeV.