Deformation and shape changes in ${}^{167}\mathrm{W}$

Lifetime measurements of yrast levels in ${}^{167}\mathrm{W}$ were measured using the recoil-distance Doppler-shift method. The differential decay-curve method was applied for a lifetime determination. Excited states of the nucleus ${}^{167}\mathrm{W}$ were populated by the reaction ${}^{142}\mathrm{Nd}$ (${}^{28}\mathrm{Si}, 3n$) at a beam energy of 144 MeV. The energy spectra and measured transition quadrupole moments inferred from the lifetimes of ${}^{167}\mathrm{W}$ are compared with the predictions of the cranked Nilsson-Strutinsky-Bogoliubov calculations. The changes of deformations and shapes with increasing spin due to the $\gamma$-polarization effect of aligned particles are discussed. The signature inversion visible in the negative parity yrast band is explained to be related to the triaxial shapes.

Figure 1

Partial level scheme of ${}^{167}\mathrm{W}$ according to Refs. [32, 33].

Figure 2

Sample $\gamma -\gamma$ coincidence spectra and simultaneous fits for $17/2^{+}, 21/2^{+}$, and $25/2^{+}$ transitions in the yrast band of ${}^{167}\mathrm{W}$. Gates are placed on the shifted components of $21/2^{+}\to 17/2^{+}, 25/2^{+}\to 21/2^{+}$, and $29/2^{+}\to 25/2^{+}$ transitions respectively showing the shifted and unshifted components of the $17/2^{+}, 21/2^{+}$, and $25/2^{+}$ transitions. The corresponding target-degrader separations are indicated. Spectra are from the detectors at backward angles (${153}^{\circ }$). The peak position of the fully Doppler-shifted and degraded components of the $\gamma$-ray transitions is indicated with blue solid line.

Figure 3

DDCM analysis of the $17/2^{+}\to 13/2^{+}$ (left), $21/2^{+}\to 17/2^{+}$ (middle), and $25/2^{+}\to 21/2^{+}$ (right) transitions in ${}^{167}\mathrm{W}$ gated by the direct feeders. In the upper panels the $\tau$ curves are displayed, including the resulting lifetimes and their statistical errors. The middle and bottom panels depict the intensities of the shifted, and unshifted, respectively, components of the $\gamma$ transitions of interest.

Figure 4

Calculated PESs for ${}^{167}\mathrm{W}$ at $I^{\pi }=13/2^{+},41/2^{+},9/2^{-},33/2^{-},11/2^{-}$, and $35/2^{-}$, which correspond to the configurations: $(+,0)(+,-1/2)$, top row; $(+,0)(-,+1/2)$, middle row; $(+,0)(-,-1/2)$, bottom row. The global minima are marked by stars. The energy interval of contour lines is 0.2 MeV.

Figure 5

The experimental and theoretical transitional quadrupole moments of the positive parity yrast band.

Figure 6

The experimental (a) and theoretical (b) energies relative to a rotating liquid drop (rld) reference in ${}^{167}\mathrm{W}$. The microscopic liquid drop energies were calculated using the Lublin-Strasbourg drop (LSD) model [48]. The lower panel shows the difference between calculations and experiment. Full (open) lines are used for positive (negative) parity and closed (open) symbols for signature $\alpha =1/2(\alpha =-1/2)$. The experimental bands are labeled by $(\pi ,\alpha )$ while the theoretical results are labeled by $({\pi }_p,{\alpha }_p)({\pi }_n,{\alpha }_n)$.

Figure 7

The energy staggering of the negative parity bands. The $\alpha =1/2$ and $-1/2$ states are denoted by circles and squares, respectively. The solid and open symbols correspond to experimental and theoretical values.