High-spin states and signature inversion in odd-odd ${}^{168}\mathrm{Lu}$

High-spin states of the odd-odd nucleus ${}^{168}\mathrm{Lu}$ were populated in the ${}^{123}\mathrm{Sb}({}^{48}\mathrm{Ca},3\mathrm{n}){}^{168}\mathrm{Lu}$ reaction at a beam energy of 203 MeV and decay $\gamma$ rays measured using the Gammasphere spectrometer array. The level scheme has been extended from spin 27 to 50 $\hslash$, and three new rotational bands have been added. A number of interband linking transitions were revealed, so that all but two bands could be connected with each other. High-spin band crossings, above the first $\nu i_{13/2}$ alignment, are delineated in most bands. Significant signature inversions are identified for the first time in the bands involving both favored and unfavored signatures of the $\pi h_{9/2}$ orbital, which are likely caused by a residual proton-neutron interaction. A signature inversion with small amplitude is also observed in the $\pi d_{5/2}\otimes \nu i_{13/2}$ band. Configurations are suggested for all bands based on their experimental properties, with the help of Cranked Shell Model calculations. No evidence is found for triaxial strongly deformed structures that were predicted by the calculations.

Figure 1

Partial level scheme of ${}^{168}\mathrm{Lu}$, deduced from the present data. Gamma-ray energies are in units of keV. Arrow widths indicate transition intensities. Tentative assignments are in parentheses. The labels shown below each $\gamma$-ray sequence represent the proposed quasiparticle configurations that will be discussed in Sec. 4.

Figure 2

Partial level scheme of ${}^{168}\mathrm{Lu}$ (continued from Fig. 1).

Figure 3

Summed fourfold coincidence spectra for Band 1. (a) Spectrum for the $\alpha =1$ signature, obtained by summing triple gates set on the transitions between ${13}^{+}$ and ${41}^{+}$. (b) Spectrum for the $\alpha =0$ signature, obtained by summing triple gates set on the transitions between ${16}^{+}$ and ${44}^{+}$, but excluding 1005 keV. In all the following spectra coincidence $\gamma$ rays in other known bands are labeled with asterisks $(*)$, and important interband linking transitions with plus $(+)$ signs.

Figure 4

Coincidence spectra for Band 2. Panel (a) shows summed fourfold coincidence spectra gated on transitions in the $\alpha =0$ signature, between ${14}^{-}$ and ${46}^{-}$. The 609-, 642-, and 657-keV transitions linking Bands 2 and 4 can be seen clearly. The inset, which emphasizes the high-spin transitions, shows the sum of double gates set on transitions between ${26}^{-}$ and ${50}^{-}$. Panel (b) shows summed fourfold coincidence spectra gated on transitions in the $\alpha =1$ signature, between ${19}^{-}$ and ${41}^{-}$. The 568-, 600-, 642-, 657-, and 716-keV transitions linking Bands 2 and 4 are visible.

Figure 5

Summed fourfold coincidence spectra for Band 4, with insets emphasizing the high-spin band members. (a) Spectrum for the $\alpha =1$ signature, obtained by summing triple gates set on the transitions between $9^{-}$ and ${37}^{-}$, but excluding 760 and 824 keV. The 716-keV linking transition between this band and Band 2 is seen clearly. The inset is a sum of spectra double-gated on transitions between ${27}^{-}$ and ${37}^{-}$. (b) Spectrum for the $\alpha =0$ signature, obtained by summing triple gates set on the transitions between ${14}^{-}$ and ${34}^{-}$ but excluding 863 keV. The 642-, 657-, and 703-keV linking transitions between this band and Band 2 are clearly visible. The peak at 1035 keV is a contamination. The inset is a sum of spectra double-gated on transitions between ${22}^{-}$ and ${36}^{-}$.

Figure 6

Summed fourfold coincidence spectra for Band 5. (a) Spectrum for the $\alpha =0$ signature, obtained by summing triple gates set on the transitions between $8^{-}$ and ${34}^{-}$. The 419-, 502- and 567-keV decays to Band 4 are clearly visible. (b) Spectrum for the $\alpha =1$ signature, obtained by summing triple gates set on the transitions on the decay path from $\left({33}^{-}\right)$ in Band 5 to ${14}^{-}$ in Band 4, but excluding 634 keV. The 582-keV decay to Band 4 is clearly visible.

Figure 7

Summed fourfold coincidence spectra for Bands 6 and 7. (a) Spectrum for the $\alpha =1$ signature of Band 6, obtained by summing triple gates set on the transitions between $\left({17}^{+}\right)$ and $\left({37}^{+}\right)$. (b) Spectrum for the $\alpha =0$ signature of band 6, obtained by summing triple gates set on the transitions between $\left({16}^{+}\right)$ and $\left({36}^{+}\right)$. The 938-keV transition linking this band to Band 7 is clearly visible. The inset shows the spectrum for Band 7 obtained by summing triple gates on all transitions on the decay path from $\left({44}^{+}\right)$ in Band 7 and $\left({16}^{+}\right)$ in Band 6.

Figure 8

Summed fourfold coincidence spectra for Band 8, with insets emphasizing high-spin band members. (a) Spectrum for the $\alpha =1$ signature, obtained by summing triple gates set on the transitions between $\left({11}^{+}\right)$ and $\left({39}^{+}\right)$. The inset was obtained by summing double gates set on band members between $\left({17}^{+}\right)$ and $\left({39}^{+}\right)$, but excluding 760 and 1006 keV. (b) Spectrum for the $\alpha =0$ signature, obtained by summing triple gates set on the transitions between $\left({10}^{+}\right)$ and $\left({42}^{+}\right)$. The inset was generated by summing double gates set on band members between $\left({40}^{+}\right)$ and $\left({26}^{+}\right)$.

Figure 9

Quasiparticle Routhians as a function of rotational frequency for protons (upper panel) and neutrons (lower panel), generated with the code ultimate cranker [14, 15] for ${}^{168}\mathrm{Lu}$ for an axially symmetric potential with a quadrupole deformation of $\epsilon =0.25$. Solid lines denote quasiparticle levels with $(\pi ,\alpha )=(+,+\frac{1}{2})$; dotted lines denote $(+,-\frac{1}{2})$; dash-dotted lines denote $(-,+\frac{1}{2})$ and dashed lines $(-,-\frac{1}{2})$. Upper case letters identify relevant neutron orbitals, and lower case letters proton orbitals. The labeling convention is explained in Table 2.

Figure 10

Aligned angular momenta of bands in ${}^{168}\mathrm{Lu}$. The curve for the yrast band of the even-even ${}^{166}\mathrm{Yb}$ has been superimposed on each panel as a reference. Open symbols represent $\alpha =0$ sequences and closed symbols $\alpha =1$ sequences. A reference with Harris parameters $J_0=30{\hslash }^2{\text{MeV}}^{-1}$ and $J_1=45{\hslash }^4{\text{MeV}}^{-3}$ was subtracted from the data.

Figure 11

Excitation energies less a rigid rotor reference ($A=7.4$ keV) as a function of spin. Open symbols represent $\alpha =0$ and filled symbols $\alpha =1$ sequences. The $\alpha =0$ signature of Band 2 has been duplicated in the lower panel to provide a reference.

Figure 12

Dynamical moments of inertia, $J^{\left(2\right)}$, for bands in ${}^{168}\mathrm{Lu}$. Open (filled) symbols represent $\alpha =0$ ($\alpha =1$) sequences.

Figure 13

Experimental (data points) and theoretical (lines) $B\left(M1\right)/B\left(E2\right)$ ratios for bands in ${}^{168}\mathrm{Lu}$. The values for positive- and negative-parity bands are plotted in the upper and lower panels, respectively. Open (filled) symbols represent the experimental values for the $\alpha =0$ ($\alpha =1$) sequences. The spins of Bands 6 and 8 are uncertain. See text for discussion.

Figure 14

Experimental Routhians of Bands 4 and 5. Open (filled) symbols represent $\alpha =0$ ($\alpha =1$) rotational sequences. A reference with Harris parameters $J_0=30{\hslash }^2{\text{MeV}}^{-1}$ and $J_1=45{\hslash }^4{\text{MeV}}^{-3}$ was subtracted from the data.

Figure 15

Signature splitting functions for bands in ${}^{168}\mathrm{Lu}$. Open symbols represent $\alpha =0$ sequences and closed symbols $\alpha =1$ sequences. The spins of Bands 6 and 8 are uncertain. See text for discussion.