Microscopic Description of Nuclear Quantum Phase Transitions

The relativistic mean-field framework, extended to include correlations related to restoration of broken symmetries and to fluctuations of the quadrupole deformation, is applied to a study of shape transitions in Nd isotopes. It is demonstrated that the microscopic self-consistent approach, based on global effective interactions, can describe not only general features of transitions between spherical and deformed nuclei, but also the singular properties of excitation spectra and transition rates at the critical point of quantum shape phase transition.

Figure 1

Self-consistent RMF binding energy curves of ${}^{142–152}\mathrm{Nd}$, as functions of the mass quadrupole moment.

Figure 2

The particle-number projected GCM spectrum of ${}^{150}\mathrm{Nd}$ (left), compared with the data [12] (middle), and the $X(5)$-symmetry predictions (right) for the excitation energies, intraband and interband $B(E2)$ values (in Weisskopf units) of the ground-state ($s=1$) and ${\beta }_1$ ($s=2$) bands. The theoretical spectra are normalized to the experimental energy of the state $2_1^{+}$, and the $X(5)$ transition strengths are normalized to the experimental $B(E2;2_1^{+}\to 0_1^{+})$.

Figure 3

The particle-number projected GCM results for the excitation energies and intraband $B(E2)$ values (in Weisskopf units) of the ground-state bands of ${}^{148}\mathrm{Nd}$ (left) and ${}^{152}\mathrm{Nd}$ (right), are shown in comparison with the data [17, 18].

Figure 4

$B(E2;L\to L-2)$ values (upper panel) and excitation energies (lower panel) for the yrast states in ${}^{148}\mathrm{Nd}$, ${}^{150}\mathrm{Nd}$, and ${}^{152}\mathrm{Nd}$, calculated with the GCM and compared with those predicted by the $X(5)$, $SU(3)$, and $U(5)$ symmetries (open symbols).