Shape-changing particle decays of ${}^{185}\mathrm{Bi}$ and structure of the lightest odd-mass Bi isotopes

Proton and $\alpha$ decay of the proton-rich nuclide ${}^{185}\mathrm{Bi}$ has been restudied in more detail in the complete fusion reaction ${}^{93}\mathrm{Nb}\left({}^{95}\mathrm{Mo},3n\right){}^{185}\mathrm{Bi}$ at the velocity filter SHIP. The observed decay pattern of ${}^{185}\mathrm{Bi}$ and of the heavier odd-mass isotopes ${}^{187,189,191,193}\mathrm{Bi}$ are interpreted based on potential-energy surface calculations. It is shown that the experimental systematics of the particle decays and of the excited states in these nuclei (where known) can be explained by the prolate-oblate shape co-existence at low excitation energy. The observed state in ${}^{185}\mathrm{Bi}$ is proposed to be of prolate nature, which is in contrast with the previously proposed oblate interpretation.

Figure 1

Energy spectrum of proton and $\alpha$-decay events collected in the PSSD in the ${}^{95}\mathrm{Mo}+{}^{93}\mathrm{Nb}$ reaction at the beam energy of $E_{\mathrm{lab}}\left({}^{95}\mathrm{Mo}\right)=438\text{MeV}$ in middle of the target. The time interval of $\Delta T\left(\text{ER-decay}\right)⩽350\mu \mathrm{s}$ and anticoincidence condition with the signals from the TOF and BOX detectors were applied along with the time-dependent decay energy correction (see text). Position windows of $\pm 2\text{mm}$ and $\pm 0.6\text{mm}$ between the implantation and subsequent decay were used to produce the parts of the spectrum below and above $3\text{MeV}$, respectively (see text for details). Inset shows an expanded part of the spectrum for the energy region of $1300–1800\text{keV}$.

Figure 2

Energy spectra of $\alpha$ decays in the $6150–8400\text{keV}$ region collected in the PSSD in the ${}^{95}\mathrm{Mo}+{}^{93}\mathrm{Nb}$ reaction at the beam energy of $E_{\mathrm{lab}}=438\text{MeV}$ in front of the target. Part (a) shows all decay events, registered within $30\text{ms}$ after recoil implantation; (b) same, but within $350\mu \mathrm{s}$ after implantation (this is an expanded part of the corresponding region of Fig. 1; (c) spectrum of $\alpha$ decays observed within $3\mathrm{s}$ after the proton decay at $E_p=\left(1510–1670\right)\text{keV}$ of ${}^{185}\mathrm{Bi}$. Some peaks, relevant for the discussion, are labeled with the measured $\alpha$ decay energy (in keV) and the isotope to which the decay belongs.

Figure 3

Decay scheme of ${}^{185}\mathrm{Bi}$ deduced in this work. The proton energy is taken from Ref. 9, see text. The estimated excitation energy of the $9∕2^{-}$ state in ${}^{181}\mathrm{Tl}$ obtained by the extrapolation from known isotopes is shown in square brackets (see also Fig. 5). Data for ${}^{184}\mathrm{Pb}$ are from Ref. 26.

Figure 4

(a) $\alpha$-decay energy systematics for the $9∕2^{-}\to 9∕2^{-}$ (filled circles) and $1∕2^{+}\to 1∕2^{+}$ (open squares) decays in the odd-mass Bi isotopes. The parabolic fits of the systematics are shown by the solid lines. The positions of the 8030 and $8130\text{keV}$ $\alpha$ decays of ${}^{185}\mathrm{Bi}$ are shown by the filled squares; (b) reduced $\alpha$ widths for the $9∕2^{-}\to 9∕2^{-}$ and $1∕2^{+}\to 1∕2^{+}$ decays in the odd-mass Bi isotopes and for the $0^{+}\to 0^{+}$ decays in the even-mass Pb isotopes. The newly determined ${\delta }_{\alpha }^2\left({}^{185}\mathrm{Bi}\right)$ value is shown by an open diamond. Our new value of ${\delta }_{\alpha }^2\left({}^{184}\mathrm{Pb}\right)=47\left(5\right)\text{keV}$ was used in the plot for the even-mass Pb nuclei. A previous value of ${\delta }_{\alpha }^2\left({}^{184}\mathrm{Pb}\right)=13\left(8\right)\text{keV}$ from Ref. 9 is shown for comparison. Data are taken from Refs. 3, 4, 5, 6, 10, 19, 22.

Figure 5

Experimental (open symbols with solid lines) and calculated (filled symbols with dashed lines) excitation energies of the oblate $9∕2^{-}$ state (based on the $9∕2^{-}\left[514\right]$ Nilsson orbital) and of the prolate $13∕2^{+}$ state ($1∕2^{+}\left[660\right]$ Nilsson orbital) in Tl isotopes relative to the $1∕2^{+}$ ground state. Experimental excitation energies of the $1∕2^{+}$ states in Bi isotopes, relative to the $9∕2^{-}$ ground state, are shown by open squares. Calculated values were extracted from the PES data, see Sec. 4B. Experimental data are taken from Refs. 3, 4, 5, 6, 19, 37. The extrapolated value for the $9∕2^{-}$ state in ${}^{181}\mathrm{Tl}$ is connected to known data by a dashed line.

Figure 6

Potential-energy surfaces for the negative parity states in the $\alpha$-decaying isotopes ${}^{185–195}\mathrm{Bi}$. The near-spherical $9∕2^{-}$ ground states are indicated by the filled circles. Minima for oblate $7∕2^{-}\left[514\right]$ and prolate $1∕2^{-}\left[530\right]$ configurations, relevant for discussion, are shown by a filled diamond and by a star, respectively. A $\gamma$-soft prolate minimum in ${}^{187}\mathrm{Bi}$ is shown by the shaded area. See text for a detailed discussion of the minima. The distance between the contour lines is $50\text{keV}$.

Figure 7

Potential-energy surfaces for the positive parity states in the $\alpha$-decaying isotopes ${}^{185–195}\mathrm{Bi}$. Some minima, relevant for discussion, are indicated by filled symbols and discussed in detail in the text. The $\gamma$-soft minima with ${\beta }_2\approx 0.15$ are shown by a shaded area. The distance between the contour lines is $50\text{keV}$.

Figure 8

(a) Calculated (full symbols) and experimental (open symbols) excitation energies of some selected configurations in the odd-mass isotopes ${}^{185–205}\mathrm{Bi}$, relative to the near-spherical $9∕2^{-}$ g.s. (except for ${}^{185}\mathrm{Bi}$). (a) $13∕2^{+}$ states; (b) $7∕2^{-}$ states. See comment in the text on the bandhead state of the prolate $1∕2^{-}\left[530\right]$ Nilsson configuration; (c) $1∕2^{+}$ states. The oblate states are connected by the solid lines and the prolate ones by the dashed lines. Calculated energies are extracted from the PES data, shown in Figs. 6, 7. Experimental data are taken from Refs. 12, 58, 59 and references therein.

Figure 9

Spherical decomposition of the wavefunction of the $1∕2^{+}$ state as a function of (a) ${\beta }_2$ deformation along oblate and prolate axes; (b) as a function of $\gamma$ deformation at a fixed value of $\mid {\beta }_2\mid =0.15$. The contributions from the $2d_{3∕2}$ and $2d_{5∕2}$ orbitals are summed together and denoted as $\Sigma d_{3∕2,5∕2}$, while the sum of the contributions from the $1g_{7∕2},1g_{9∕2}$, and $1i_{13∕2}$ orbitals is denoted as $\Sigma g,i$.