Lifetime measurements in low yrast states and spectroscopic peculiarities in ${}^{182}\mathrm{Os}$

Lifetimes of the low-lying yrast states $2^{+}$, $4^{+}$, and $6^{+}$ of the unstable nucleus ${}^{182}\mathrm{Os}$ were measured using digital fast-timing techniques. The lifetimes of the $4^{+}$ and $6^{+}$ states were determined for the first time. The remeasured value for the lifetime of the $2_1^{+}$ state was taken into account to evaluate the discrepancy between two inconsistent literature values. The lifetimes and extracted $B\left(E2\right)$ values are presented and discussed in terms of collective signatures and transitional phenomena. The $B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ ratio of 1.39(7) supports the interpretation of ${}^{182}\mathrm{Os}$ as a rigid rotor. This value is discussed in the context of these of the neighboring isotopes and isotones and calculations in the framework of the interacting boson model 1. Additionally, competing influences from the near lying collective deformed region, $\gamma$-soft rotors, X(5) symmetry, and neighboring regions of shape coexistence in low excitation states are assumed to influence the structure of the nucleus of interest: The trend of the excitation energies of the $\gamma$- and $K^{\pi }=0$–bands in the osmium isotopic chain change remarkably at ${}^{182}\mathrm{Os}$. This consideration helps to us delimit and understand the structural transitions in the isotopic and isotonic chains that intersect at ${}^{182}\mathrm{Os}$.

Figure 1

Even-even isotopes around $A=180$. The regions of shape coexistence, $\gamma$ softness, X(5) critical point symmetry, and rotational prolate deformation are roughly identified by elliptic shapes. The nucleus of interest ${}^{182}\mathrm{Os}$ is indicated by a red circle. The chart is extracted from The colourful nuclide chart by Simpson [22]. The color code of the individual nuclei illustrate the $R_{4/2}$ ratios, which are taken from Ref. [11].

Figure 2

$R_{4/2}$ ratios of platinum, osmium, and tungsten isotopes. The neutron midshell and the expectation values for rotational and $\gamma$-soft limits are indicated in the plot. The lines connecting the data points are meant to guide the eyes. All values are taken from [11].

Figure 3

Spectrum of strongest observed $\gamma$ rays in coincidence with the $2_1^{+}\to 0_1^{+}$ ground state transition observed with HPGe detectors for both detector groups: LaBr in blue and HPGe in red. The transitions used for the lifetime analysis are labeled in red. The energy labels are rounded to full keV. The remaining coincidence contribution in the 127 keV $2_1^{+}\to 0_1^{+}$ transition is due to random coincidence. The HPGe detectors were shielded by 2 mm copper and lead plates to prevent high count rates due to intensive x rays in the sub-100 keV region.

Figure 4

Time-difference distribution obtained by a direct HPGe energy gate on the $6_1^{+}\to 4_1^{+}$ transition, feeding the $4_1^{+}$ state to clean the cascade of interest. The LaBr gates were applied to the $4_1^{+}\to 2_1^{+}$ (273.5 keV) and the $2_1^{+}\to 0_1^{+}$ (126.9 keV) transitions. The straight line represents the slope fit to the exponential part of the distribution.

Figure 5

Time walk calibration for the energy range between 240 and 1300 keV. The maximum time walk range is below 50 ps in the energy range under consideration. The uncertainty band in the lower plot represents the $1\sigma$ interval and is considered as the TW uncertainty throughout this work.

Figure 6

(a) Time-difference distribution obtained with energy gates applied to the $2_1^{+}$ state (127 keV) in HPGe detectors and to the $6_1^{+}$ state (393.8 keV) and $4_1^{+}$ state (273.5 keV) in LaBr detectors. (b) Time-difference distribution obtained with energy gates applied to the $2_1^{+}$ state (126.9 keV) in HPGe detectors and to the $8_1^{+}$ state (483.8 keV) and $6_1^{+}$ state (393.8 keV) in LaBr detectors. In both plots, the centroid position $C_D$ and the time reference of the system $T_0$ are indicated and the energy gates applied to the LaBr detectors are provided.

Figure 7

Exemplary lifetime analysis and background correction for the $4_1^{+}$ state. (a) LaBr spectrum and HPGe reference spectrum with energy gates applied to the $2_1^{+}\to 0_1^{+}$ (127 keV) transition in HPGe detectors and to the $6_1^{+}\to 4_1^{+}$ (393.8 keV) transition in LaBr detectors. The lower part of the figure shows the background correction procedure for the $4_1^{+}\to 2_1^{+}$ transition. The centroid positions taken in the background around the peak of interest and the fit are depicted in blue. The experimental centroid position $C_{\text{D,}\text{exp}}$ is indicated in green. (b) LaBr spectrum and HPGe reference spectrum with energy gates applied to the $2_1^{+}$ state (127 keV) in HPGe detectors and to the $4_1^{+}\to 2_1^{+}$ (273.5 keV) transition in LaBr detectors. The lower part of the figure shows the background correction procedure for the $6_1^{+}\to 4_1^{+}$ transition. The centroid positions taken in the background around the peak of interest and the fit are depicted in blue.

Figure 8

$B_{4/2}$ ratios for the osmium, platinum, and tungsten isotopic chains. The newly determined value of ${{}^{182}\mathrm{Os}}_{106}$ is indicated by a dashed box. The orange triangles represent the results of the IBM-1 calculations; see Sec. 4. The dashed lines connecting the data points are meant to guide the eyes. The theoretical limits of ideal rotors and vibrators as well as the neutron midshell are shown with grey dashed lines. The values for ${}^{172,176,180}\mathrm{Pt}$, ${}^{176,178,180}\mathrm{W}$, and ${}^{168,172,174,178}\mathrm{Os}$ are taken from Refs. [7, 17, 27, 28, 29]. All other values taken from nuclear data sheets [11].

Figure 9

(a) Evolution of level energies of the osmium isotopes around neutron midshell, $N=104$. The red dashed box marks the area of interest. The blue dots represent the level energies of the $2_1^{+},4_1^{+},6_1^{+}$ states of the ground state band. The orange squares are the energies of the $2_2^{+}$ states and the green squares are the energies of the $0_2^{+}$ state. (b) Energies of the first three yrast states and $2_2^{+}$ and $0_2^{+}$ states versus proton number $Z$ of the isotones with $N=106$. The lines connecting the data points are meant to guide the eyes. All values are taken from [11].

Figure 10

Experimental and theoretical level energies of first three ground state band states and $2_2^{+}$ and $0_2^{+}$ states of ${}^{180–186}\mathrm{Os}$. IBM values are illustrated with triangles of different colors. The theoretical values for the ground state bands and the $2_2^{+}$ states are taken from Ref. [12]. The theoretical values for the $0_2^{+}$ states were calculated in the scope of this paper. The lines are meant to guide the eyes.