Probing the Jacobi shape transition in hot and rotating ${}^{43}\mathrm{Sc}$

The evolution of the hot and rotating ${}^{43}\mathrm{Sc}$ nucleus to a highly deformed shape has been studied by measuring the high-energy $\gamma$ rays from the decay of the giant dipole resonance. The compound nucleus was populated at two initial excitation energies and average angular momenta of $\approx 26$ and $31\hslash$ by using ${}^{16}\mathrm{O}$ beam of energies $E_{\mathrm{lab}}$ = 120 and 142 MeV, respectively. The evaporated neutron energy spectra have been measured for proper determination of nuclear level density. The angular momentum has been determined by measuring the low-energy $\gamma$-ray multiplicities. The high-energy $\gamma$-ray and neutron spectra were analyzed simultaneously. At $\langle J\rangle \approx 26\hslash$ a near-oblate shape is observed, whereas at $\langle J\rangle \approx 31\hslash$ a sharp peak is observed at $E_{\gamma }\approx 10\mathrm{MeV}$ pointing towards the transition to the Jacobi shape with quadruple deformation parameter $\beta \approx 0.7$. The results have been corroborated by the theoretical calculations based on the rotating liquid drop model framework.

Figure 1

(a) Measured (symbols) and simulated (line) fold distributions, (b) fusion cross sections obtained from the pace4 code (symbols) and simulation (line) for $E_{\mathrm{lab}}=120\mathrm{MeV}$ and fold = 2.

Figure 2

Measured neutron energy spectra (symbols) along with the statistical model calculations (solid lines) for (a) $E_{\mathrm{lab}}=120\mathrm{MeV}$ and (b) $E_{\mathrm{lab}}=142\mathrm{MeV}$. The error bars are within the symbols.

Figure 3

Measured high-energy $\gamma$-ray spectra (symbols) along with the statistical model calculations (solid lines) for (a) $E_{\mathrm{lab}}=120\mathrm{MeV}$ and (c) $E_{\mathrm{lab}}=142\mathrm{MeV}$. The dashed lines are the bremsstrahlung components. (b) and (d) represent the corresponding linearized divided plots.

Figure 4

Contour plots of the free-energy surfaces at the specified angular momenta. The symbols represent the minima of the free-energy surfaces.

Figure 5

Position of the free-energy minimum (filled circles) as a function of $\beta$ and $\gamma$ at different angular momenta mentioned.

Figure 6

The $\gamma$-ray absorption cross section incorporated in the cascade code (long-dashed lines) along with the TSFM calculations (solid lines) for (a) $E_{\mathrm{lab}}=120\mathrm{MeV}$ and (b) $E_{\mathrm{lab}}=142\mathrm{MeV}$.