Competition between $\alpha$ and $\beta$ decays for heavy deformed neutron-deficient Pa, U, Np, and Pu isotopes

The competition between $\alpha$ and $\beta$ decays is investigated for neutron-deficient Pa, U, Np, and Pu isotopes. ${\beta }^{+}$/electron-capture (EC) decay rates are calculated within the deformed quasiparticle random-phase approximation with realistic nucleon-nucleon $\left(NN\right)$ interactions. Contributions from allowed Gamow-Teller and Fermi transitions as well as first-forbidden transitions are considered. $\alpha$-decay calculations are performed within the generalized density-dependent cluster model. Effects of differences between neutron and proton distributions and nuclear deformation are taken into account. In the calculations, Reid-93 $NN$ interactions are used for ${\beta }^{+}/\mathrm{EC}$ decays, while Michigan three-range Yukawa effective interactions, based on the $G$-matrix elements of Reid $NN$ potentials, are used for $\alpha$ decay. The calculated $\beta$-decay half-lives show good agreement with the experimental data over a range of magnitude from ${10}^2$ to ${10}^5$ s. The resulting total half-lives including $\alpha$ and $\beta$ contributions are found to be in good agreement with the experimental data, together with the $\alpha /\beta$-decay branching ratios.

Figure 1

Sensitivity of the calculated half-life to the decay energy used in calculations for the ${\beta }^{+}/\mathrm{EC}$ and $\alpha$ decays of ${}^{233}\mathrm{Pu}$. The ${\beta }^{+}/\mathrm{EC}$-decay results are shown by black solid lines (left axis: calculated $\beta$-decay half-life, bottom axis: $\beta$-decay energy), while the $\alpha$-decay results are shown by red dashed lines (right axis: calculated $\alpha$-decay half-life, top axis: $\alpha$-decay energy). Also, the experimental ${\beta }^{+}/\mathrm{EC}$-decay and $\alpha$-decay energies are, respectively, indicated by black and red dotted lines.

Figure 2

Percentage of the contributions of FF transitions to the ${\beta }^{+}/\mathrm{EC}$ decay rates of the neutron-deficient Pa, U, Np, and Pu isotopes.

Figure 3

Comparison of the calculated $\alpha$-decay half-lives with the experimental values versus the neutron number $N$ of parent nuclei for the $\alpha$ decays of the neutron-deficient Pa, U, Np, and Pu isotopes. $\alpha$-decay calculations are performed with the neutron skin type distribution. Experimental $\alpha$-decay data are not explicitly determined for some extremely neutron-deficient nuclei and deduced values suggested in Refs. [14, 49] are illustrated instead. These cases are indicated by blue dotted squares and recognized by quite large uncertainties.

Figure 4

Deviations of the calculated total half-lives (including ${\beta }^{+}/\mathrm{EC}$ and $\alpha$ contributions) from the experimental half-lives for the neutron-deficient Pa, U, Np, and Pu isotopes.