Return of backbending in ${}^{169}\mathrm{Tm}_{}$ and the effect of the $N=98$ deformed shell gap

The high spin excited states of ${}^{169}\mathrm{Tm}_{}$ have been studied via the ${}^{169}\mathrm{Tm}_{}$(${}^{32}\mathrm{S}_{}$, ${}^{32}\mathrm{S}^{\prime }$)${}^{169}{\mathrm{Tm}}^{*}_{}$ reaction at a beam energy of 164 MeV. The $\gamma$ rays were detected using an array of 19 Compton-suppressed clover HPGe detectors. The band based on the $\left[411\right]1/2^{+}$ Nilsson orbital has been extended to observe the band crossing for the first time in this nucleus. A sharp backbending, similar to ${}^{165}\mathrm{Tm}_{}$, is observed in this nucleus which is in complete contrast with its immediate neighbor ${}^{167}\mathrm{Tm}_{}$. The data were interpreted in the cranked shell model approach by calculating the total Routhian surfaces, crossing frequencies, and the interaction strengths for these nuclei which are in excellent agreement with the experimental data. It is suggested that the $N=98$ deformed shell gap has larger effect in determining the nature of alignment than its shape driving effect.

Figure 1

$\gamma$-ray spectra of ${}^{169}\mathrm{Tm}_{}$ obtained by sum of double gates. The new $\gamma$ peaks are marked by asterisks (*).

Figure 2

Proposed level scheme of ${}^{169}\mathrm{Tm}_{}$ in the present work. The new $\gamma$ rays are marked by asterisks (*).

Figure 3

Quasiparticle aligned angular momenta ($i_x$) as a function of rotational frequency ($\hslash \omega$) for odd-$A$ Tm isotopes. Haris parameters $J_0=35{\hslash }^2{\mathrm{MeV}}^{-1}$ and $J_1=43{\hslash }^4{\mathrm{MeV}}^{-3}$ are taken.

Figure 4

TRS calculations of ${}^{165}\mathrm{Tm}_{}$ (a), ${}^{167}\mathrm{Tm}_{}$ (b), and ${}^{169}\mathrm{Tm}_{}$ (c) nuclei at $\hslash \omega =0.2$ MeV. The contours are 250 keV apart.

Figure 5

Calculated quasineutron energy levels for $N=96,98$, and 100 corresponding to ${}^{165}\mathrm{Tm}_{}$ (a), ${}^{167}\mathrm{Tm}_{}$ (b), and ${}^{169}\mathrm{Tm}_{}$ (c) nuclei.