Configuration mixing and $K$-forbidden $E2$ decays

Hindrance factors for $K$-forbidden $E2$ decays from multiquasiparticle isomers are analyzed in relation to mixing matrix elements that are often associated with chance near degeneracies, and a functional relationship is established. Focusing on effective matrix elements for $\mathrm{\Delta }K=6$ decays from three-quasiparticle isomers, significant configuration dependence is demonstrated.

Figure 1

Schematic level scheme illustrating a multi-$qp$ isomer, which decays by a $\mathrm{\Delta }K=6$, $E2$ transition into a rotational band.

Figure 2

Correlation plot for isomeric $E2$ transitions, showing how the product of the mixing strength and the square root of the Weisskopf hindrance factor, $\left|V\right|\sqrt{F_W}$, varies with the energy separation, $\mathrm{\Delta }E$, between the isomer and the state with the same spin and parity that is a member of the band to which the isomer decays. The straight line through the data is to guide the eye.

Figure 3

Reduced hindrance, $f_{\nu }$, as a function of isomer energy relative to a rigid rotor, $E_K-E_R$, for $\mathrm{\Delta }K=6$, $E2$ decays from 3-$qp$ isomers in the $Z\approx 70$ region. The subtracted rotor energy, $E_R$, has a moment of inertia that is 85% of the full rigid-body value (see text). Table 1 has the numerical values. Note that there are two data points for each of ${}^{175}\mathrm{Ta}$ and ${}^{177}\mathrm{Ta}$. The statistical uncertainties are smaller than the data points.

Figure 4

Inverse interaction matrix element, $1/\left|V\right|$, as a function of energy relative to a rigid rotor, $E_K-E_R$, for $\mathrm{\Delta }K=6$, $E2$ decays from 3-$qp$ isomers in the $Z\approx 70$ region. The Nilsson configurations of the populated 1-$qp$ bands are indicated. The subtracted rotor energy, $E_R$, has a moment of inertia that is 85% of the full rigid-body value. Table 1 has the numerical values. Note that the ${}^{181}\mathrm{W}$ and ${}^{181}\mathrm{Re}$ data points are overlapping. The filled circle is for ${}^{179}\mathrm{Ta}$, replotted according to a three-level-mixing analysis (see text). The statistical uncertainties are smaller than the data points.