Simple relations for $\alpha$-decay energies of neighboring nuclei

Based on the longitudinal Garvey-Kelson relation and its odd-even features recently discerned, we construct simple relations of $\alpha$-decay energies (denoted by $Q$) for four neighboring nuclei. These relations are found to yield very small deviations from available experimental data. We apply these new relations to both description of experimental $\alpha$-decay energies and prediction of the unknown $Q$ values of heavy nuclei.

Figure 1

Schematic plot of our relations of $\alpha$-decay energies. Panels (a), (b), (c), and (d) correspond to Eqs. (5), (6), (7), and (8), respectively.

Figure 2

Deviations of our predicted $Q$ values in comparison with experimental data, denoted by $\Delta Q=Q^{\exp }-{\overline{Q}}^{\mathrm{th}}$, versus neutron number $N$. Panel (a) corresponds to results by using Eq. (5); and panel (b) corresponds to simultaneous use of Eqs. (5, 6, 7), namely, (B) in Table 1. Results in black (red) are obtained without (with) the refinements by using the LRBF method. See the text for details.

Figure 3

The correlation between $\Delta Q(N,Z)$ (in keV) and $\overline{\Delta Q}(N,Z)$. Panel (a) is obtained by using Eq. (5), and panel (b) is obtained by simultaneous use of Eqs. (5, 6, 7).

Figure 4

Theoretical uncertainty $\sigma$ of predicted $Q$ values for the $Z=108$ and $Z=118$ isotopes. The solid circles in red represent experimental error bars, and the solid squares in black represent theoretical uncertainty.

Figure 5

The $\alpha$-decay energies (in MeV) for nuclei with $Z$ ranging from 89 to 118. Panel (a) corresponds to nuclei with even $Z$, and panel (b) corresponds to nuclei with odd $Z$.