Pairing Reentrance Phenomenon in Heated Rotating Nuclei in the Shell-Model Monte Carlo Approach

Rotational motion of heated ${}^{72}\mathrm{Ge}$ is studied within the microscopic shell-model Monte Carlo approach. We investigate the angular momentum alignment and nuclear pairing correlations associated with $J^{\pi }$ Cooper pairs as a function of the rotational frequency and temperature. The reentrance of pairing correlations with temperature is predicted at high rotational frequencies. It manifests itself through the anomalous behavior of specific heat and level density.

Figure 1

Neutron occupations of the individual $f_{7/2}$, $f_{5/2}$, and $g_{9/2}$ s.p. orbits as a function of cranking frequency $\omega$ in the wave function of ${}^{72}\mathrm{Ge}$ for temperatures $kT=0.47\mathrm{MeV}$ (a) and 1.6 MeV (b). The angular momentum alignment in the nucleus is generated by the gradual increase of occupations of positive-$m$ orbits (solid lines) at the expense of negative-$m$ states (dashed lines). The doubled magnetic quantum numbers, $2m$, of individual orbits are marked.

Figure 2

Neutron (top) and proton (bottom) $J=0$ pairing strength $⟨{\Delta }^{†}\Delta ⟩$ as a function of temperature for ${}^{72}\mathrm{Ge}$ at four values of $\omega$ (in MeV). At higher rotational frequencies, neutron pairing locally increases at low temperatures reaching a maximum (marked by arrows).

Figure 3

Angular momentum in ${}^{72}\mathrm{Ge}$ as a function of $kT$ at $\omega =0.25\mathrm{MeV}$ (a) and 0.50 MeV (b). Plotted are the following: average angular momentum $⟨J⟩$ (solid line); alignment $⟨J_z⟩$ (dashed line); $⟨J_{\perp }{⟩}_{\mathrm{r}.\mathrm{m}.\mathrm{s}.}$ (dash-dotted line); and $⟨J_z⟩$ (dotted line).

Figure 4

Specific heat calculated in SMMC for ${}^{72}\mathrm{Ge}$ as a function of temperature at $\omega =0.2$ and 0.5 MeV. At $\omega =0.5\mathrm{MeV}$, $C_v$ shows a local dip at low temperatures; this is a signature of the pairing reentrance. The inset shows the calculated level density. Again, at $\omega =0.5\mathrm{MeV}$, a low-temperature irregularity shows up.