Investigating the prolate-to-oblate shape phase transition: Lifetime measurements and $\gamma$ spectroscopy of the low-lying negative parity structure in ${}^{193}\mathrm{Os}$

Excited states in ${}^{193}\mathrm{Os}$ were populated using a ${}^{192}\mathrm{Os}(n_{\text{th.}},\gamma ){}^{193}\mathrm{Os}$ thermal neutron capture reaction, with neutrons provided by the high-flux reactor of the Institut Laue-Langevin in Grenoble, France. Lifetimes of low-spin excited states were measured using the generalized centroid difference method. A total of eight mean lifetimes of low-lying excited states were determined for the first time, and limits for the lifetimes of three further excited states were established. Additionally, $\gamma \text{−}\gamma$ angular correlations were analyzed to assign spins to previously known excited states up to 1 MeV, and extract multipole mixing ratios for several transitions. The new spectroscopic information is compared to calculations in the framework of the interacting boson-fermion model, based on the nuclear density functional theory, to investigate the prolate-to-oblate shape phase transition, predicted to occur in the neutron rich $A\approx 190$ region.

Figure 1

(a) Angular correlation of the $1/2_C^{+}\to 3/2_3^{-}\to 1/2_1^{-}$ (5276-266 keV) cascade in ${}^{193}\mathrm{Os}$. The $1/2_C^{+}\to 3/2_3^{-}$ (5276 keV) primary transition is assumed to be pure $L=1$ [16]. Effective interaction angles and angular correlation coefficients are derived according to the method outlined in Ref. [25]. The derived attenuation coefficients are $q_2=0.979\left(1\right)$ and $q_4=0.927\left(3\right)$ and the extracted final angular correlation coefficients amount to $a_2=0.426\left(4\right)$ and $a_4=0\left(0\right)$. (b) Minimization of the mixing ratio $\delta$ for different cascades $1/2_C^{+}\to 3/2_3^{-}\to J$. The 42 keV state is clearly identified as a spin 1/2 state and the two minima correspond to ${\delta }_1=-0.253\left(7\right)$ and ${\delta }_2=-1.03\left(2\right)$ with $S_{\min }^2=15.4$. The 99% confidence limit [degrees of freedom (dof) = 17] is indicated by the dashed line and results above this limit are rejected.

Figure 2

(a) Combined $\mathrm{PRD}(E_{\gamma }$) curve of the experimental setup. The low-energy part is defined by the decays of the ${}^{152}\mathrm{Eu}$ and ${}^{187}\mathrm{W}$ sources; the high energy part is calibrated with the ${}^{48}\mathrm{Ti}(n,\gamma ){}^{49}\mathrm{Ti}$ reaction. The 40-1408 keV cascade, emitted following the electron capture (EC) decay of ${}^{152}\mathrm{Eu}$, is aligned using the 341-1381 keV cascade in ${}^{49}\mathrm{Ti}$. Mean lifetimes used for the calibration are adopted from Refs. [28, 29, 30, 31]. (b) Fit residuals of the low-energy $\mathrm{PRD}(E_{\gamma }$) curve with the $1\sigma$ uncertainty band plotted in gray. The inset (c) shows the separately fitted PRD for the high energy part between 2 and 6.7 MeV, calibrated using the ${}^{48}\mathrm{Ti}(n,\gamma ){}^{49}\mathrm{Ti}$ reaction. For the high-energy PRD, the $3\sigma$ standard deviation is adopted as uncertainty, and the corresponding uncertainty band is shown in gray.

Figure 3

Partial level scheme of the low-lying negative parity structure in ${}^{193}\mathrm{Os}$, investigated in this work. Level and transition energies were adopted from Ref. [14]. Spins of excited states assigned based on Refs. [14, 16] and the $\gamma \text{−}\gamma$ angular correlation analysis performed in this work. The relative $\gamma$-ray intensities of the different decay branches are listed in Table 4.

Figure 4

(a,b) Gated energy spectra used for the lifetime measurement of the $1/2_1^{-}$ at 42 keV state with the corresponding gates indicated in the figures. The gated LaBr (HPGe) spectrum is shown in black (red) and was generated using HPGe-LaBr-LaBr (HPGe-LaBr-HPGe) threefold coincidences. (a) The energy of the 42 keV transition is not sufficient to overcome the binding energy of the $K$-shell electrons, and the few visible $K\alpha$ and $K\beta$ x rays originate from random coincidences. (b) The observation of the $3/2_3^{-}\to 3/2_2^{-}$ (204 keV) transition in coincidence with the $1/2_1^{-}\to 3/2_{\mathrm{gs}}^{-}$ (42 keV) transition indicates the existence of a $3/2_2^{-}\to 1/2_1^{-}$ (61 keV) transition. For details see text. (c) Delayed (green) and antidelayed (red) time distributions generated for the $3/2_3^{-}\to 1/2_1^{-}\to 3/2_{\mathrm{gs}}^{-}$ (266-42 keV) cascade. The final resulting mean lifetime after correcting for time-correlated background contributions amounts to ${\tau }_{42}=586\left(19\right)$ ps.

Figure 5

Angular correlations of the (a) 4414-875 keV and (b) 875-254 keV $\gamma \text{−}\gamma$ cascades. The distinct shape of the $3/2^{(+)}\to 5/2_2^{-}\to 1/2_1^{-}$ (875-254 keV) cascade is only possible for a nearly pure $E2\text{−}E2$ cascade. From the significant $a_4$ component the 296 keV state can clearly be assigned as $5/2_2^{-}$.

Figure 6

Angular correlations of the (a) $1/2_4^{-}\to 3/2_4^{-}\to 3/2_{\mathrm{gs}}^{-}$ (619-435 keV) and (b) $1/2_4^{-}\to 3/2_4^{-}\to 1/2_1^{-}$ (619-394 keV) cascades. A direct fit to the angular correlations yields (a) $a_2=-0.85\left(3\right)$ and (b) $a_2=0.70\left(2\right)$. The corresponding mixing ratios cannot be precisely determined but only constrained in its range. For details see text.

Figure 7

Potential energy surfaces for the even-even core nucleus ${}^{194}\mathrm{Os}$ calculated for (left) the Gogny-HFB method and (right) the mapped IBM-2 Hamiltonian. The energy difference between the neighboring contours is 100 keV, with the minimum in blue.

Figure 8

Comparison of experimental (left) and calculated (right) level scheme of the low-lying negative parity states in ${}^{193}\mathrm{Os}$. The corresponding counterparts of the individual experimental and theoretical states are connected by dotted red lines to guide the eye. Experimental energies were adopted from [14].