Prolate-to-oblate shape phase transitions in neutron-rich odd-mass nuclei

We investigate the prolate-to-oblate shape phase transitions in the neutron-rich Pt, Os, and Ir nuclei in the mass $A\approx 190$ region. The Hamiltonian of the interacting boson-fermion model, used to describe the odd-mass ${}^{185-199}\mathrm{Pt}, {}^{185-193}\mathrm{Os}$, and ${}^{185-195}\mathrm{Ir}$ isotopes, is partially constructed by using as a microscopic input the results of constrained self-consistent mean-field calculations within the Hartree-Fock-Bogoliubov method with the Gogny force. The remaining few parameters are adjusted to experimental data in the odd systems. In this way the calculations reasonably describe the spectroscopic properties of the odd-mass systems considered. Several calculated observables for the odd-mass nuclei, especially the low-energy excitation spectra and the effective deformation parameters, point to a prolate-oblate shape transition as a function of the neutron number for all the isotopic chains considered and similar to the one already observed in the neighboring even-even systems.

Figure 1

The Gogny-D1M HFB deformation energy surfaces in the $(\beta ,\gamma )$-deformation space for the ${}^{186-194}\mathrm{Pt}$ and ${}^{186-194}\mathrm{Os}$ nuclei are plotted up to 3 MeV from the global minimum. The energy difference between the neighboring contours is 100 keV.

Figure 2

The strength parameters ${\mathrm{\Gamma }}_{\nu }, {\mathrm{\Lambda }}_{\nu }$, and $A_{\nu }$, employed for the odd-$N$ Pt and Os nuclei are depicted as functions of the neutron number.

Figure 3

The strength parameters ${\mathrm{\Gamma }}_{\pi }, {\mathrm{\Lambda }}_{\pi }$, and $A_{\pi }$ for the odd-$Z$ Ir isotopes are depicted as functions of the neutron number.

Figure 4

Single-particle energies (plotted with respect to that of the $3p_{1/2}$ orbital) and occupation probabilities employed for the odd-$N$ Pt and Os nuclei as functions of the neutron number.

Figure 5

The same as in Fig. 4 but for the odd-$Z$ Ir isotopes. The single-particle energies are plotted with respect to $3s_{1/2}$ orbital.

Figure 6

Spectroscopic properties of the even-even ${}^{186-200}\mathrm{Pt}$ and ${}^{186-194}\mathrm{Os}$ nuclei plotted as functions of the neutron number: the energy ratios $R_{42}$ and $R_{4\gamma }$, spectroscopic quadrupole moment $Q_{2_1^{+}}$ and the $B\left(E2\right)$ value $B_{2\gamma }$. For more details, see the main text. Open circles, connected by lines, represent the theoretical values while solid diamonds represent the experimental data taken from Refs. [36, 37]. The symmetry limits $R_{42}=2.0$ [U(5)], 2.5 [O(6)], and 3.3 [SU(3)], and $R_{4\gamma }=1.0$ [O(6)] of the IBM [21] are also indicated.

Figure 7

The theoretical and experimental low-lying negative-parity ($\pi =-1$) yrast states in the odd-$N$ isotopes ${}^{185-199}\mathrm{Pt}$ are plotted as functions of the neutron number.

Figure 8

The same as in Fig. 7 but for the positive-parity states.

Figure 9

The same as in Fig. 7, but for the isotopes ${}^{185-193}\mathrm{Os}$.

Figure 10

The same as in Fig. 8 but for the isotopes ${}^{185-193}\mathrm{Os}$.

Figure 11

The same as in Fig. 7 but for the isotopes ${}^{185-195}\mathrm{Ir}$.

Figure 12

The same as in Fig. 8 but for the isotopes ${}^{185-195}\mathrm{Ir}$.

Figure 13

Comparison between the theoretical and experimental [36] low-lying positive- and negative-parity spectra for ${}^{195}\mathrm{Pt}$.

Figure 14

The same as in Fig. 13 but for ${}^{189}\mathrm{Os}$.

Figure 15

The same as in Fig. 13 but for ${}^{191}\mathrm{Ir}$.

Figure 16

Effective $\beta$ and $\gamma$ deformation parameters for the even-even nuclei ${}^{186-200}\mathrm{Pt}$ and ${}^{186-194}\mathrm{Os}$ obtained from the $E2$ transition matrix elements.

Figure 17

Effective $\beta$ and $\gamma$ deformation parameters for the odd-$N$ nuclei ${}^{185-199}\mathrm{Pt}$ and ${}^{185-193}\mathrm{Os}$ and the odd-$Z$ nuclei ${}^{185-191}\mathrm{Ir}$ for the $J^{\pi }={1/2}_1^{\pi }, {3/2}_1^{\pi }$, and ${5/2}_1^{\pi }$ states for normal-parity configurations ($\pi =-1$ for Pt and Os, and $\pi =+1$ for Ir) and $J^{\pi }={11/2}_1^{\pi }$ state for unique-parity configurations ($\pi =+1$ for Pt and Os, and $\pi =-1$ for Ir).