Signature of clustering in quantum many-body systems probed by the giant dipole resonance

The present experimental study illustrates how large deformations attained by nuclei due to cluster formation are perceived through the giant dipole resonance (GDR) strength function. The high energy GDR $\gamma$ rays have been measured from ${}^{32}\mathrm{S}$ at different angular momenta ($J$) but similar temperatures in the reactions ${}^4\mathrm{He}(E_{\text{lab}}=45\mathrm{MeV})+{}^{28}\mathrm{Si}$ and ${}^{20}\mathrm{Ne}(E_{\text{lab}}=145\mathrm{MeV})+{}^{12}\mathrm{C}$. The experimental data at lower $J$ ($\sim 10\hslash$) suggests a normal deformation, similar to the ground state value, showing no potential signature of clustering. However, it is found that the GDR lineshape is fragmented into two prominent peaks at high $J$ ($\sim 20\hslash$) providing a direct measurement of the large deformation developed in the nucleus. The observed lineshape is also completely different from the ones seen for Jacobi shape transition at high $J$ pointing towards the formation of cluster structure in superdeformed states of ${}^{32}\mathrm{S}$ at such high spin. Thus, the GDR can be regarded as a unique tool to study cluster formation at high excitation energies and angular momenta.

Figure 1

The experimental $\gamma$ spectra (symbols) for (a) ${}^{31}\mathrm{P}$ and (b) ${}^{32}\mathrm{S}$ are shown for 46 MeV excitation energy along with the statistical model calculation plus bremsstrahlung. The corresponding linearized GDR strength functions are shown in panels (c) and (d).

Figure 2

The statistical model calculation plus bremsstrahlung (solid lines) are compared to experimental data (symbols) at 145 MeV incident energy using (a) small mixing, (b) full mixing, and (c) including the pre-equlibrium effect. The individual cascade (dashed line) and bremsstrahlung (dashed-dotted line) are also shown.

Figure 3

The free energy surfaces for ${}^{32}\mathrm{S}$ at $T=2.0\mathrm{MeV}$ and different angular momenta. The thick white solid line corresponds to $\gamma =0$ (prolate).

Figure 4

The experimental GDR strength functions (symbols) for ${}^{32}\mathrm{S}$ are compared to TSFM calculation at (a) low and (b) high $J$. The normal (low $J$), Jacobi transition and cluster formation shapes are also shown on the right side.