Detailed high-spin spectroscopy and the search for the wobbling mode in ${}^{171}\mathrm{Ta}$

High-spin states in ${}^{171}\mathrm{Ta}$ were populated in the ${}^{124}\mathrm{Sn}$(${}^{51}\mathrm{V}$,$4n$) reaction at 228 MeV to search for evidence of stable triaxial deformation. Identification of a wobbling sequence based on the previously known $\pi i_{13/2}$ structure would provide a unique signature for this rarely observed shape. No such sequence was identified in these data, which suggests that the island of triaxial strongly deformed bands may be smaller than once thought. However, over 200 new transitions and two new bands were placed in the level scheme and the sequence based on the $\pi i_{13/2}$ orbital could be observed up to spin and parity $I^{\pi }=(101/2{}^{+}$). The relative excitations of all the sequences were determined and the ground state of ${}^{171}\mathrm{Ta}$ was found to have $5/2^{+}$ quantum numbers, contrary to previous reports. All of the previously known structures were extended to much higher spin and their high-frequency band crossings are interpreted within the framework of the cranked shell model.

Figure 1

Level scheme for ${}^{171}\mathrm{Ta}$. The width of the arrows is proportional to the relative intensity of the γ rays. Tentative transitions and levels are denoted with dashed lines.

Figure 2

Partial level scheme for ${}^{171}\mathrm{Ta}$ highlighting the low-spin states. Note that the band-head energies are indicated in italics.

Figure 3

Unless otherwise indicated, the spectra shown are the result of a sum of all triple coincidence gates using $E2$ transitions. (a) Spectrum of Band 1 ([402]5/2), where the crosses indicate transitions from Band 2. (b) Spectrum of Band 2 ([404]7/2), where the asterisks denote transitions from Band 1. All triple combinations with the 627- and 630-keV transitions were summed to produce this spectrum. The inset displays the high-energy transitions and was produced by triple gates on the highest energies within the band. (c) Spectrum of the $\alpha =-1/2$ signature of Band 3 ([411]1/2), where the pluses indicate transitions from Band 5 and the transitions marked with C are known contaminants. (d) Spectrum of the $\alpha =+1/2$ signature of Band 3.

Figure 4

(a) Spectrum of Band 4 ([660]1/2), which results from summing all triple coincidence gates on in-band transitions. Peaks marked with an asterisk or a cross indicate the transition is from Band 1 or 2, respectively. Transitions denoted with a filled circle are linking transitions. (b) Spectrum of the $\alpha =+1/2$ signature of Band 5 ([541]1/2) produced in a similar manner as panel (a). The inset displays the $\alpha =-1/2$ signature of Band 5, where linking transitions are denoted with filled circles.

Figure 5

Excitation energies of the observed levels minus a rigid-rotor reference where this reference was assumed to have a moment of inertia parameter $A=0.0077$ MeV. The positive-parity sequences are displayed in (a), whereas the negative-parity structures are in (b). Band 4 is also displayed in (b) as a dashed line for reference. Positive (negative) signatures are represented with filled (open) symbols.

Figure 6

(a) Spectrum of band 6 from summing triple gates using any two of the 197-, 298-, 389-, 465-, and 524-keV transitions with the 562-, 598-, and 637-keV transitions. The inset is from the same spectrum and displays the linking transitions. (b) Spectrum of Band 7 ([514]9/2) resulting from the sum of two double gates (538/556 + 539/560). The inset shows the extension of the band to its highest spins and results from the summing of many triple gates at the top of the band.

Figure 7

Alignments for the bands in ${}^{171}\mathrm{Ta}$. Harris parameters of ${\mathcal{J}}_0=29$ $\hslash {}^2$/MeV and ${\mathcal{J}}_1=60$ $\hslash {}^4$/MeV${}^3$ were used to subtract the angular momentum of the rotating core. Observed crossings are designated in the figure. Filled (empty) symbols denote a $\alpha =+1/2$ ($-1/2$) sequence.

Figure 8

$B(M1)/B(E2)$ ratios for Bands 1, 2, 3, and 7 in ${}^{171}\mathrm{Ta}$. Filled (empty) symbols represent the experimental values for the $\alpha =+1/2$ ($-1/2$) sequence. (a) The positive-parity bands and the lines represent calculated values for the following configurations: [402]5/2 solid; dotted [404]7/2; $\pi g_{7/2}\nu \mathit{AB}$ dot-dashed; $\pi h_{11/2}\nu \mathrm{AEBC}$ long dashed; [411]1/2 dashed. (b) Band 7 with the calculated for the [514]9/2 (solid line) and $\pi h_{11/2}\nu \mathit{AB}$ (dotted line) configurations.

Figure 9

$B(M1){}_{\mathrm{inter}}/B(M1){}_{\mathrm{intra}}$ ratios for linking transitions between Band 1 and 2 deduced from branching ratios.

Figure 10

Cranked shell-model calculations for quasiprotons of ${}^{171}\mathrm{Ta}$. Deformation parameters of ${\beta }_2=0.24,{\beta }_4=0$, and $\gamma =1^{°}$ were used. The two lowest frequency crossings are denoted in the figure.

Figure 11

Dynamic moments of inertia of the $\pi i_{13/2}$ band in the $A\approx 175$ region.