Effect of Coriolis mixing on lifetime of isomeric states in heavy nuclei

The effect of Coriolis $K$ mixing on the $\gamma$ decay of one-quasiparticle isomeric states is examined in transfermium nuclei with neutron number $N=153$. We consider a core-plus-quasiparticle coupling in which the $K$ mixing sharply increases if the isomeric quasiparticle state closely approaches the rotational state with the same angular momentum $I$, but built on another quasiparticle state which is either directly coupled to the isomeric ($\mathrm{\Delta }K=1$) or connected with it through the intermediate mixing quasiparticle orbitals ($\mathrm{\Delta }K>1$). This mechanism is likely to explain the 38-ns $K^{\pi }=7/2^{+}$ isomer in ${}^{251}\mathrm{Cf}$ which is quasidegenerated with an $I^{\pi }=7/2^{+}$ rotation state built on $K^{\pi }=1/2^{+}$. Our model explains the enhancement of its decay by three orders of magnitude compared to the $K^{\pi }=7/2^{+}$ isomer in ${}^{249}\mathrm{Cm}$. We suggest that the same mechanism could be of general importance for the isomer decay properties in a wide range of heavy odd-mass nuclei.

Figure 1

Schematic presentation of two-level ($K$ and $K^{\prime }$) mixing through two intermediate states produced by the couplings of $K$ and $K+1$ states and $K^{\prime }$ and $K^{\prime }-1$ states. These intermediate states have the components with $\delta K=1$ and are coupled by the Coriolis interaction.

Figure 2

The calculated one-quasiparticle spectra for indicated nuclei of the $N=153$ isotonic chain. The calculations were performed with the TCSM. The experimental values [28] for ${}^{249}\mathrm{Cm}$ are shown by blue lines.

Figure 3

Energies of one-quasiparticle states in ${}^{251}\mathrm{Cf}$ calculated by the TCSM (th1) and axially symmetric deformed shell model (th2) compared with available experimental data [28].

Figure 4

The energy interval between the two lowest $7/2^{+}$ states: $\mathrm{\Delta }=E(7/2_2^{+})-E(7/2_1^{+})$ as a function of the moment of inertia of the core. The closest approach, $\mathrm{\Delta }\approx 0.02$ keV, occurs at ${\hslash }^2/\Im =12.44\mathrm{keV}$ ($x\approx 0.559$). The value $x_{\text{exp}}=0.564$ which corresponds to the experimentally measured energy distance between these states is marked by arrow.

Figure 5

Weights of components contributing to the wave function of the $7/2_2^{+}$ state. Only components with $K_{\gamma }=0$ and $K_p=1/2$, 3/2, 5/2, and 7/2 are shown.

Figure 6

Reduced transition probability $B(E2,7/2_2^{+}\to 3/2_1^{+})$ is shown as a function of $x=\Im /{\Im }_{r.b.}$. The value $x_{\text{exp}}=0.564$, which corresponds to the experimentally measured energy distance between the levels, is marked by arrow.