Identification of excited states in ${}^{188}\mathrm{Bi}$ and ${}^{188}\mathrm{Po}$

The neutron-deficient ${}^{188}\mathrm{Bi}$ and ${}^{188}\mathrm{Po}$ isotopes have been studied by $\gamma$-ray spectroscopy using the recoil-decay tagging technique with the Argonne Gas-Filled Analyzer. A new 0.25(5)-$\mu \mathrm{s}$ isomeric state and a prompt cascade formed by 319-, 366-, and 462-keV $\gamma$ rays have been established on top of the (${10}^{-}$) $\alpha$-decaying isomer in ${}^{188}\mathrm{Bi}$. The first excited ($2^{+}$) state in ${}^{188}\mathrm{Po}$ was identified, its excitation energy of 242(2) keV continues the nearly constant trend for the first $2^{+}$ states in ${}^{190,192,194}\mathrm{Po}$. The state is most likely a member of a prolate rotational band built on the ground state, albeit mixing with other coexisting configurations cannot be excluded. The new results obtained in the present work provide new information to shape coexistence in bismuth and polonium isotopes near the neutron midshell at $N=104$. In this mass region, a reduction in the prompt $\gamma$-ray yield obtained with recoil decay tagging was observed for a few nuclides, and the possible reasons are presented.

Figure 1

(a) A part of the energy spectrum for $\alpha$ particles, registered in the DSSD only, following EVRs' implantation within 5 s. (b) The same, but for escaping $\alpha$ particles, being the sum of $\alpha$-particle energies measured in the DSSD and Sibox. The vertical dashed lines show the correspondence of the peaks in the two spectra. The approximate numbers of counts (DSSD only) for the full-energy $\alpha$ peaks of ${}^{188}\mathrm{Bi}^{g,m}$ and ${}^{189}\mathrm{Bi}$ are shown above each peak. The structure at 6220 to 6264 keV corresponds to the partial or full energy summing in the DSSD of the 6194-keV $\alpha$ decay of ${}^{187}\mathrm{Pb}^g$ and $\approx 54\text{–}64$ keV $L/M$-shell conversion electrons (CEs) resulting from the strong conversion of the known coincident 67-keV $E2$ transition [41].

Figure 2

(a) The delayed $\gamma$-ray energy spectrum obtained by tagging on the combined statistics of the 6815-keV $\alpha$ decay of ${}^{188}\mathrm{Bi}^m$ in DSSD only. (b) The same, but gated by the 6672-keV $\alpha$ decay of ${}^{189}\mathrm{Bi}$. The tagging time intervals are shown in the panel titles. The inset in (a) shows the overlay of the zoomed-in spectra from panels (a) (in black) and (b) (in red), after normalization to the same number of Bi $K_{\alpha }$ x rays as seen in panel (a). (c) The difference of the spectra from panels (a) and (b) after normalization to the same number of Bi $K_{\alpha }$ x-ray counts as seen in (a).

Figure 3

(a) The time difference $\mathrm{\Delta }T(\text{EVR}-\gamma (243\text{keV},{}^{188}\mathrm{Bi}^m))$, and the associated fit by an exponential function with a constant background using maximum likelihood method. (b) The same, but for the time difference $\mathrm{\Delta }T(\text{EVR}-\gamma (357\text{keV},{}^{189g}\mathrm{Bi}))$.

Figure 4

(a) The combined prompt $\gamma$-ray energy spectrum in GS obtained by tagging on the 6815-keV decay of ${}^{188}\mathrm{Bi}^m$ in DSSD only and DSSD $+$ Sibox. (b) The same, but gated by the 6991-keV peak of ${}^{188}\mathrm{Bi}^g$. (c) The same, but for the 6329-keV peak of ${}^{186}\mathrm{Pb}$ and after normalizing to approximately the same number of $\alpha$ decays as for ${}^{188}\mathrm{Bi}^{g,m}$ in panels (a) and (b). The partial level scheme of yrast states up to $6^{+}$ in ${}^{186}\mathrm{Pb}$ and the number of the 662-keV $\gamma$ rays are also shown in panel (c). The tagging time intervals are given in the panel titles. The $K_{\alpha ,\beta }$ x rays from element Nd in the target and the $K_{\alpha }$ x ray from Ta absorbers in front of the Ge detectors are also present. The 197-keV line is from the Coulomb excitation of ${}^{19}\mathrm{F}$ in the target.

Figure 5

(a)–(c) Recoil-gated $\gamma \gamma$ coincidence energy spectra tagged with the 6815-keV $\alpha$ decay of ${}^{188}\mathrm{Bi}^m$. The gating $\gamma$ rays are indicated in the panel titles.

Figure 6

Proposed level scheme for ${}^{188}\mathrm{Bi}^{g,m}$. The excitation energy of 153(30) keV for ${}^{188}\mathrm{Bi}^m$ is from Ref. [44]. The 165- and 188-keV transitions feeding the isomeric (${10}^{-}$) ${}^{188}\mathrm{Bi}^m$ are taken from Ref. [11]. The symbol “I” above the levels represents intensities for the isomer and cascade relative to the 6815-keV $\alpha$ decay. The panels to the leftmost and rightmost show partial level schemes for ${}^{187,189}\mathrm{Bi}$ [45].

Figure 7

(a) The prompt RDT $\gamma$-ray energy spectrum in GS obtained by tagging on the 7899-keV $\alpha$ decay of ${}^{188}\mathrm{Po}$; see main text for details. (b) The corresponding background RDT spectrum gated by the random time window between the EVRs and the $\gamma$ rays registered in GS, with the same condition on $\alpha$ decay. The tagging time windows for the RDT spectrum and background spectrum are indicated in the panel titles. The top and bottom panels in the inset show parts of the corresponding $\alpha$-decay spectra registered in the DSSD only and the DSSD $+$ Sibox, respectively.

Figure 8

Intensities are given for the isomeric 52-, 81-, 143-, and 243-keV $\gamma$ rays relative to the number of 6815-keV $\alpha$-decays of ${}^{188}\mathrm{Bi}^m$, which is taken as $100\%$ and shown by a solid horizontal line in the figure. The values are corrected for $\gamma$-ray efficiency and for respective internal conversion for each possible multipolarity considered.

Figure 9

The excitation energies for the lowest single-proton states in the odd-mass Bi isotopes, close to ${}^{188}\mathrm{Bi}$. The data are taken from Ref. [10].

Figure 10

Systematics of selected positive-parity near-yrast states for even-even polonium isotopes. Yrast states are indicated by filled circles. The non-yrast levels are indicated with empty circles. Tentative spin-parity assignment is given in parentheses. The data are taken from Refs. [13, 14, 15, 16, 17, 18, 48] and the present work (red symbol for ${}^{188}\mathrm{Po}$).

Figure 11

PES for ${}^{188}\mathrm{Po}$. Nearly spherical, oblate, and prolate minima are indicated by the circle, square, and triangle, respectively. We made the energy at the lowest point of the PES be zero and the energy separation between the contour lines is 100 keV. The axis of oblate deformation lies at $\gamma =-{60}^{\circ }$ and that of prolate deformation at $\gamma =0^{\circ }$.