Possible deformation evolution in the $\pi i_{13/2}$ structure of ${}^{171}$Re

The phenomenon of wobbling can only occur for a nuclear shape with stable triaxial deformation. To date, only a few examples of this exotic collective mode have been observed in lutetium and tantalum isotopes. A search for a wobbling sequence was performed in ${}^{171}$Re to determine if this feature can be observed in $Z>73$ nuclei. No evidence was found for wobbling; however, an interaction between the $\pi i_{13/2}$ sequence and another positive-parity band may give an indication on why wobbling may not occur in this nucleus. The level scheme for ${}^{171}$Re was significantly extended and interpretations for the decay sequences are proposed within the context of the cranked shell model.

Figure 1

Partial level scheme for ${}^{171}$Re from the present analysis. The widths of the arrows are proportional to the relative intensities of the $\gamma$ rays. Tentative levels and $\gamma$ rays are indicated as dashed lines.

Figure 2

Partial level scheme for ${}^{171}$Re from the present analysis. The widths of the arrows are proportional to the relative intensities of the $\gamma$ rays. Tentative levels and $\gamma$ rays are given as dashed lines.

Figure 3

(a) Spectrum for band 1 in ${}^{171}$Re. The main spectrum results from a sum of all triple coincidence spectra between all $\Delta I=1$ transitions in the band from the 31/2 to the 49/2 state. The first high-energy inset is a summation of all triple coincidence gates using a list of $E2$ transitions in the $\alpha =+1/2$ sequence from the 57/2 to the 81/2 state. In a similar manner, the second inset results from a list of $E2$ transitions in the $\alpha =-1/2$ structure from the 55/2 to the 67/2 level. (b) This spectrum for the $\alpha =+1/2$ signature of band 2 displays the transitions that are in coincidence with any two of the $\gamma$ rays in the $\alpha =+1/2$ signature of band 2 between 37/2 and 61/2 along with a transition in the same sequence below the 33/2 state in the same structure. The high-energy inset shows the $\gamma$ rays at the top of the sequence. (c) In a similar manner to panel (b), this spectrum of the $\alpha =-1/2$ signature of band 2 is a sum of spectra where coincident transitions with any two $\gamma$ rays in the $\alpha =-1/2$ signature of band 2 between spins 31/2 and 55/2 along with a transition in the same sequence below the 23/2 level. The high-energy inset displays the transitions at the top of the structure.

Figure 4

Excitation energies of the observed levels minus a rigid-rotor reference, where this reference was assumed to have a moment of inertia parameter $A=0.007$ MeV. Positive (negative) signatures are represented with filled (open) symbols.

Figure 5

(a) Spectrum for band 3 in ${}^{171}$Re generated by summing all spectra when requiring $\gamma$ rays to be in coincidence with two transitions in the $\alpha =+1/2$ sequence of band 2 (below the 29/2 level) and the 693-keV transition. (b) The summed spectrum created for band 5 displaying $\gamma$ rays in coincidence with two transitions from the $\alpha =+1/2$ structure of band 2 (below the 37/2 level) and with the lowest dipole transitions in band 5. (c) Summed spectrum of all possible triple combinations in the hypercube from a list of the dipole transitions between the 25/2 and 53/2 states of band 6. Transitions denoted in the panels with filled triangles and filled circles result from bands 2 and 8, respectively.

Figure 6

(a) Spectrum for band 7 in ${}^{171}$Re composed of the sum of the cleanest spectra resulting from a coincidence with a multitude of combinations of three in-band transitions. The inset was constructed in a similar format as the main spectrum. (b) Summed spectrum of all possible triple combinations in the hypercube from a list of transitions between the 39/2 and 79/2 states of band 11. Transitions marked with filled triangles, diamonds, crosses, and circles result from coincidences with bands 2, 6, 7, and 8, respectively.

Figure 7

(a) Transitions in band 8 resulting from a sum of spectra generated by requiring a coincidence with any two transitions in the band below the 41/2 level with a transition between the 45/2 and 77/2 states. (b) Summed spectrum of all possible triple combinations in the hypercube from a list of transitions between the 29/2 and 61/2 states of band 9. (c) Spectrum for band 10 where coincidences between all possible triple combinations of transitions from the 49/2 to the 73/2 states were summed together. For the spectra in these panels, transitions denoted with a filled triangle, filled diamond, and filled circle result from coincidences with bands 2, 6, and 8, respectively.

Figure 8

Alignments of the bands in ${}^{171}$Re plotted vs the rotational frequency $\hslash \omega$, where Harris parameters of ${\mathcal{J}}_0=23$ ${\hslash }^2$/MeV and ${\mathcal{J}}_1=65$ ${\hslash }^4$/MeV${}^3$ were used for the rotation of the core. Filled (open) symbols denote the $\alpha =+1/2$ ($-1/2$) sequences. Several bands from the neighboring even-even nucleus ${}^{170}$W are also displayed (see text for details).

Figure 9

Quasiparticle Routhian energies for ${}^{171}$Re from the cranked shell model. A quadrupole deformation of ${\beta }_2=0.209$ and pairing energies of ${\Delta }_p={\Delta }_n=1.26$ MeV were assumed. The solid (dotted) lines represent positive parity and $\alpha =+1/2$ ($\alpha =-1/2$) Routhians, while the dashed (dash-dotted) lines represent negative parity with $\alpha =-1/2$ ($\alpha =+1/2$) Routhians.

Figure 10

$B\left(M1\right)/B\left(E2\right)$ ratios for the strongly coupled sequences in ${}^{171}$Re. Calculations of the theoretical values are described in the text and the parameters used are listed in Table .

Figure 11

Dynamic moments of inertia for the $\pi i_{13/2}$ bands in (a) ${}^{169,171,173}$Re and (b) ${}^{167,169,171}$Ta.