Magnetic properties of ${}^{177}\mathrm{Hf}$ and ${}^{180}\mathrm{Hf}$ in the strong-coupling deformed model

This paper reports NMR measurements of the magnetic dipole moments of two high-$K$ isomers, the 37/2${}^{-}$, 51.4 m, 2740 keV state in ${}^{177}\mathrm{Hf}$ and the $8^{-}$, 5.5 h, 1142 keV state in ${}^{180}\mathrm{Hf}$ by the method of on-line nuclear orientation. Also included are results on the angular distributions of $\gamma$ transitions in the decay of the ${}^{177}\mathrm{Hf}$ isotope. These yield high precision $E2/M1$ multipole mixing ratios for transitions in bands built on the 23/2${}^{+}$, 1.1 s, isomer at 1315 keV and on the 9/2${}^{+}$, 0.663 ns, isomer at 321 keV. The new results are discussed in the light of the recently reported finding of systematic dependence of the behavior of the $g_R$ parameter upon the quasiproton and quasineutron make up of high-$K$ isomeric states in this region.

Figure 1

${}^{177}$Hf${}^{\mathrm{m}2}$ decay scheme. Taken from [19].

Figure 2

Warm and cold spectra from $0^{\circ }$ and ${90}^{\circ }$ detectors for two series of $E2/M1$ transitions. Black/dark energy labels—in band built on 9/2${}^{+}$ [624] state—note increases at $0^{\circ }$. Blue/pale energy labels—in band built on 23/2${}^{+}$ three-quasiparticle isomer—note decreases at $0^{\circ }$.

Figure 3

Anisotropy of the 606.5 keV 29/2${}^{+}$–25/2${}^{+}$ pure $E2$ transition in band built on 23/2${}^{+}$ isomer. Fitted curve with shaded band is for $f$ = 0.786(12).

Figure 4

Anisotropy of the 228.5 keV 23/2${}^{+}$–19/2${}^{+}$ pure $E2$ transition from the 23/2${}^{+}$ isomer to the band built on the 9/2${}^{+}$ [624] band. Fitted curve with shaded band is for $f$ = 0.773(6).

Figure 5

Anisotropy of the 277.3 keV 25/2${}^{+}$–23/2${}^{+}$ mixed $E2/M1$ transition in band built on 23/2${}^{+}$ isomer. Fitted curve with shaded band is for $\delta$ $[E2/M1]=+0.302\left(4\right)$.

Figure 6

Anisotropy of the 153.1 keV 15/2${}^{+}$–13/2${}^{+}$ mixed $E2/M1$ transition in band built on 9/2${}^{+}$ [624] band. Fitted curve with shaded band is for $\delta$ $[E2/M1]=-0.317\left(13\right)$.

Figure 7

Resonance observed in a combined signal from the stretched $E2$ transitions in the decay of the 37/2${}^{-}$ isomer in ${}^{177}$Hf.

Figure 8

Resonance observed in percentage destruction of anisotropy of the 8${}^{-}$ isomer in ${}^{180}$Hf.

Figure 9

Plot of the collective $g_R$ as a function of $\Delta =N_p-N_n$. For ease of viewing the three data points at $-1$ have been slightly off-set along the $x$ axis. For discussion see text and Ref. [3].