$\gamma$-soft rotor with configuration mixing in the O(6) limit of the interacting boson model

To describe obvious intruder states and nonzero quadrupole moments of $\gamma$-soft nuclei such as ${}^{194}\mathrm{Pt}$, a rotor extension plus intruder configuration mixing with $2n$-particle and $2n$-hole configurations from $n=0$ up to $n\to \infty$ in the O(6) ($\gamma$-unstable) limit of the interacting boson model is proposed. It is shown that the configuration mixing scheme keeps the lower part of the $\gamma$-unstable spectrum unchanged and generates the intruder states due to the mixing. It is further shown that almost all low-lying levels below 2.17 MeV in ${}^{194}\mathrm{Pt}$ can be well described by modifying the O(6) quadrupole-quadrupole interaction into an exponential form. The third-order term needed for a rotor realization in the interacting boson model seems necessary to produce nonzero quadrupole moments with the correct sign.

Figure 1

Low-lying level pattern of the solvable configuration mixing O(6) model with the Hamiltonian given by Eq. (2), where the left 10 levels are the same as those generated from the O(6)-limit of the IBM with the first term of Eq. (2) only, which, up to a constant, is typically given by ${\widehat{H}}_0=-\kappa \widehat{Q}·\widehat{Q}$ with eigenenergy $E_0=-\kappa [\sigma (\sigma +4)-\nu (\nu +3)]$, where $\kappa$ is a scale parameter, and $\nu$ is the seniority number of the O(5) group. Only levels of normal states with $(\sigma =N,\nu \le 3)$, $(\sigma =N-2,\nu \le 1)$, and intruder levels with $\nu \le 1$ are shown. $0_4^{+}$ is the intruder state of the model with ${\mathrm{\Delta }}_{\text{2p2h}}=2{({\mathrm{\Delta }}^2-g^2)}^{1/2}$.

Figure 2

The ground-state expectation value of the total number of bosons ${\overline{N}}_{\zeta =1}$ given by Eq. (23) (solid curve) and the expectation value of the total number of bosons of the first intruder $0_4^{+}$ state ${\overline{N}}_{\zeta =2}$ given by Eq. (25) (dashed curve) as functions of the mixing parameter $\overline{g}=g/{\mathrm{\Delta }}_0$, where ${\mathrm{\Delta }}_0$ is an arbitrary scale factor, and $\overline{\mathrm{\Delta }}=\mathrm{\Delta }/{\mathrm{\Delta }}_0$. $N=10$ and $\overline{\mathrm{\Delta }}=1$ are taken in the plot.

Figure 3

Detailed comparison of most of the excited level energies up to 3 MeV with known absolute $B\left(E2\right)$ values in W.u. obtained in this work to the experimental results [23, 24] for ${}^{194}\mathrm{Pt}$.