Additional hindrance of unfavored $\alpha$ decay between states of different parity

We study the influence of the parity configuration of the parent and daughter nuclei on the $\alpha$-decay process. We consider the ground-state to ground-state favored and unfavored decays, as well as the decay modes to different excited states of the daughter nucleus. The experimental half-life and the calculated decay width based on the realistic M3Y-Paris and the Skyrme-SLy4 effective nucleon-nucleon interactions, within the Wentzel-Kramers-Brillouin approximation, are used to estimate the $\alpha$-preformation factor for each decay mode. The experimental partial half-lives and $\alpha$-decay intensities indicate a somewhat larger hindrance of the unfavored decay modes between states of different parities than that of the unfavored decays between states of different spin but with the same parity. This hindrance overcomes the enhancement from a likely increase in the $Q_{\alpha }$ value of the odd-A isotopes relative to the even-even ones, leading to an increase (decrease) in the half-life (decay intensity) of the decay modes involving a change in parity. We also find that if the states among which the unfavored decay occurs have different parities, the preformation factor of the $\alpha$ cluster inside the parent nucleus becomes less than it would be if the involved states are of the same parity.

Figure 1

The observed partial half-lives $T_{\alpha }$ (s) [53], on a logarithmic scale, for the GS to GS $\alpha$-decay modes of the (a) ${}^{228-242,244}\mathrm{Pu}$, (b) ${}^{233,234,236,238-248,250}\mathrm{Cm}$, (c) ${}^{237,238,240-254,256}\mathrm{Cf}$, and (d) ${}^{241,243,244,246-257}\mathrm{Fm}$ isotopes, as a function of the mass number $A$. While the favored decay modes between ground states of the same spin parity are shown as solid squares, the unfavored decay modes between ground states of the same (different) parities are shown as open circles (squares). The straight lines show the trendline for the different decay types.

Figure 2

The $\alpha$ preformation factor $S_{\alpha }$ ($T_{\alpha }^{\exp },{\mathrm{\Gamma }}_{\alpha }^{\mathrm{cal}}$), on a logarithmic scale, for the $\alpha$-decay modes of the even-even ${}^{226,228,230}\mathrm{Th}\left(0^{+}\right)$ isotopes to the different states of the ${}^{222,224,226}\mathrm{Ra}$ daughter isotopes, as extracted from the experimental partial half-life $T_{\alpha }^{\exp }$ and the calculated decay width ${\mathrm{\Gamma }}_{\alpha }^{\mathrm{cal}}$ based on (a) M3Y-Paris and (b) Skyrme-SLy4 NN interactions. $S_{\alpha }$ is plotted versus the quantum number ${\ell }_{\text{min}}$ defining the minimum angular momentum transferred by the $\alpha$ particle. While the solid symbols represent the unfavored decays between states of the same parity (even ${\ell }_{\text{min}}$), the open ones represent unfavored decays between states of different parities (odd ${\ell }_{\text{min}}$). (c) The intensity $I_{\alpha }$ of the $\alpha$-decay modes of ${}^{228}\mathrm{Th}\left(0^{+}\right)$ to the different states of ${}^{224}\mathrm{Ra}$, as a function of ${\ell }_{\text{min}}$. The solid curves show the average values of $S_{\alpha }$ (${\ell }_{\text{min}}$) and $I_{\alpha }$ (${\ell }_{\text{min}}$).

Figure 3

(a) Same as Fig. 2, but for the even-odd nuclei of ${}^{225}\mathrm{Th}(3/2^{+}),{}^{251}\mathrm{Cf}(1/2^{+})$, and ${}^{255}\mathrm{Fm}(7/2^{+})$. (b) Same as Fig. 2, but for the ${}^{255}\mathrm{Fm}(7/2^{+})$ isotope.

Figure 4

(a) Same as Fig. 2, but for the even-odd nuclei of ${}^{235}\mathrm{U}(7/2^{-}),{}^{243}\mathrm{Am}(5/2^{-})$, and ${}^{247}\mathrm{Cm}(9/2^{-})$. (b) Same as Fig. 2, but for the ${}^{243}\mathrm{Am}(5/2^{-})$ isotope.