Pairing phase transitions in nuclear wave functions

The exact solution of the nuclear shell model is used for studying the phase transition from superfluid to normal Fermi-liquid as a function of the pairing strength, excitation energy (or temperature), nuclear spin and the presence of other types of residual interactions. The phase transition in a finite system is seen through the change of properties of individual wave functions.

Figure 1

The pair correlator of Eq. (1) for $J^{\pi }T=0^{+}0$ states in the $\mathit{sd}$-model of ${}^{24}\mathrm{Mg}$, panels (a), (c), and (e), and ${}^{28}\mathrm{Si}$, panels (b), (d), and (f). The individual points correspond to the eigenstates ordered in increasing energy. Panels (a) and (b) show the results for the pure pairing interaction of Table , while panels (c) and (d) are calculated for the interaction where the pairing matrix elements are set to zero; the results for the full realistic interaction are given in panels (e) and (f).

Figure 2

The pair correlator for the ground state $J^{\pi }T=0^{+}0$ in the $\mathit{sd}$-model of ${}^{24}\mathrm{Mg}$ as a function of the pairing interaction of Table scaled with the aid of the overall factor $g$; other matrix elements are taken from the WB interaction [22].

Figure 3

The ground state band moment of inertia as a function of rotational frequency squared, for ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$, panels (a) and (b), respectively.

Figure 4

Comparison of yrast energies for isospin $T=0$ and $T=1$ in ${}^{24}\mathrm{Mg}$, panel (a), and ${}^{28}\mathrm{Si}$, panel (b).

Figure 5

The pair correlator for the yrast shell model states, in ${}^{28}\mathrm{Si}$, panels (a) ($T=0$) and (b) ($T=1$), and ${}^{24}\mathrm{Mg}$, panels (c) ($T=0$) and (d) ($T=1$).

Figure 6

The pair correlator in the $\mathit{sd}$ shell model of ${}^{28}\mathrm{Si}$ and ${}^{24}\mathrm{Mg}$ averaged over all states of given spin $J$ for $T=0$, panels (a) and (c), and $T=1$, panels (b) and (d).

Figure 7

The pair correlator in the $\mathit{sd}$ shell model of ${}^{24}\mathrm{Mg}$ averaged over all states of spins from $J=0$ to $J=8$ and $T=0$.

Figure 8

Pair correlator for $T=0$ yrast states in the $\mathit{sd}$ shell model for ${}^{24}\mathrm{Mg}$ (lower panel) and ${}^{28}\mathrm{Si}$ (upper panel) as a function of nuclear spin: full interaction, dashed line (a); pure pairing interaction case, thick solid line (b); only nonpairing parts of the interactions, dotted line (c); and the difference (a)–(c) of the full interaction and the nonpairing part, thin solid line (d).

Figure 9

Pair correlator for $J=0,T=0$ states in the $\mathit{sd}$-shell model of ${}^{24}\mathrm{Mg}$ calculated with the realistic single-particle energies and random matrix elements of residual interaction taken from the Gaussian distribution with zero mean.

Figure 10

Pair correlator for $J=0,T=0$ states in the $\mathit{sd}$ shell model of ${}^{24}\mathrm{Mg}$ calculated with the degenerate single-particle energies and realistic matrix elements of residual interaction (solid line) compared with the results of the full USD interaction (dashed line).