Temperature dependence of the giant dipole resonance width in ${}^{152}\mathrm{Gd}$

To investigate the dependence of giant dipole resonance (GDR) width on temperature $\left(T\right)$ and angular momentum $\left(J\right)$, high energy $\gamma$-ray spectra were measured in the reaction ${}^{28}\mathrm{Si}+{}^{124}\mathrm{Sn}$ at $E_{{}^{28}\mathrm{Si}}=135$ MeV. The $J$ information was deduced from multiplicity of low-energy $\gamma$ rays. The GDR parameters, namely, the centroid energy and width are extracted using statistical model analysis. The observed variation of the GDR width for $T\sim 1.2$–1.37 MeV and $J\sim 20\hslash$–$40\hslash$ is consistent with the universal scaling given by Kusnezov et al., which is applicable in the liquid-drop regime. The GDR input cross sections extracted from the statistical model best fits are compared with thermal shape fluctuation model (TSFM) calculations and are found to be in good agreement. The TSFM calculations predominantly favor the noncollective oblate shape, while the statistical model fit with both prolate and oblate shapes describes the data. The present data together with earlier measurements indicate a very slow variation of the GDR width for $T\sim 1.2$ to 1.5 MeV. The observed trend is well explained by the TSFM calculations, although the calculated values are $\sim 4$%–13% higher than the data.

Figure 1

Typical time-of-flight spectrum for the central ${\mathrm{BaF}}_2$ detector.

Figure 2

High energy $\gamma$-ray spectra with different fold windows, suitably scaled for better viewing.

Figure 3

The energy-gated (10–23 MeV) experimental fold distribution (blue dots) along with the statistical model fit (red line). The two-component Gaussian function fit is also shown (green dashed line) along with the individual components using black dotted and pink dash-dotted lines.

Figure 4

Divided plots of experimental $\gamma$-ray spectra (green solid circled) and statistical model best fits (red line) with prolate deformation for different fold windows.

Figure 5

Same as Fig. 4, but for the oblate deformed case.

Figure 6

The variation of reduced GDR width (${\mathrm{\Gamma }}_{\mathrm{red}}$) in ${}^{152}\mathrm{Gd}$ as a function of $\xi =J/A^{5/6}$ with ${\mathrm{\Gamma }}_0=3.6$ MeV, for $E^{*}\sim 71$ MeV (present data, for both prolate and oblate deformation) and for $E^{*}\sim 87$ MeV (data from Ref. [15]). The solid blue line represents the universal scaling given by Eq. (5).

Figure 7

Free energy surfaces of ${}^{152}\mathrm{Gd}$ at different $T$ and $J$ combinations corresponding to the data at $E^{*}\sim 71$ MeV. 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 solid red circle and the first two minimum energy contours are indicated by thick lines.

Figure 8

The best-fit statistical model input cross section for prolate deformation (solid circle) and ${\sigma }_{\mathrm{TSFM}}$ with $\eta =3.35$ (red line) for different fold windows.

Figure 9

Same as Fig. 8, but for oblate deformation.

Figure 10

Variation of the GDR width ($\mathrm{\Gamma }$) as a function of temperature for ${}^{152}\mathrm{Gd}$ and comparison with predictions of different models for $J=20\hslash$ and $40\hslash$. The data for $E^{*}=71$ MeV are from the present measurement and the data for $E^{*}=87$ and 116 MeV are taken from Refs. [15] and [6], respectively. The data span the range of $\langle J\rangle =23\hslash$–$42\hslash$. The top panel shows comparison with the PSF and the CTF, while TSFM calculations are shown in the bottom panel (see text for details).