γ-soft analog of the confined β-soft rotor model

A γ-soft analog of the confined β-soft rotor model is developed by using a γ-independent displaced infinite-well β potential in the Bohr Hamiltonian, for which exact separation of variables is possible. Level schemes interpolating between the E(5) critical point symmetry (with $R_{4/2}=E(4_1^{+})/E(2_1^{+})=2.20$) and the O(5) γ-soft rotor (with $R_{4/2}=2.50$) are obtained; these exhibit a crossover of excited $0^{+}$ bandheads that lead to agreement with the general trends of $0_2^{+}$ states in this region and is observed experimentally in ${}^{128,130}\mathrm{Xe}$.

Figure 1

Energy levels (normalized to the excitation energy of the $2_1^{+}$ state) and $B(E2)$ transition rates [normalized to $B(E2;2_1^{+}\to 0_1^{+})$] for two different values of the structural parameter $r_{\beta }={\beta }_m/{\beta }_M$ around the $0_{2,3}^{+}$ crossing.

Figure 2

Energy of $0^{+}$ states (normalized to the energy of the $2_1^{+}$ state), labeled as $R_{0/2}$, vs the ratio $R_{4/2}=E(4_1^{+})/E(2_1^{+})$. The parameter $r_{\beta }$ on each curve starts from zero at the left end, increasing to the right. The crossover of the ($\xi =2,\tau =0,L=0$) and the ($\xi =1,\tau =3,L=0$) curves occurs at $r_{{\beta }_c}\approx 0.171263,(R_{4/2},R_{0/2}){}_c\approx (2.27861,3.77797)$.

Figure 3

Comparison of the model predictions for $r_{\beta }=0.12$ (a) to the experimental data of ${}^{130}\mathrm{Xe}$ [26] (b), and of the model predictions for $r_{\beta }=0.21$ (c) to the experimental data for ${}^{128}\mathrm{Xe}$ [27] (d).