Examining the Impact of Α -Decay Energies on the Odd-Even Staggering in Half-Lives: Α -Decay Spectroscopy of Ac207–209

The $\ensuremath{\alpha}$ decays of $^{207--209}\mathrm{Ac}$, located near the proton drip-line, were reinvestigated by means of $\ensuremath{\alpha}$-decay spectroscopy. They were produced in the fusion reaction $^{36}\mathrm{Ar}+^{176}\mathrm{Hf}$ and separated in flight using the gas-filled recoil separator SHANS. A new $\ensuremath{\alpha}$-decay line at 7483(15) keV was observed and assigned as the decay from the ground state of $^{208}\mathrm{Ac}$ to the excited (${2}^{+}$) or (${4}^{+}$) state in $^{204}\mathrm{Fr}$. In addition, the previously known $\ensuremath{\alpha}$-decay properties of $^{207--209}\mathrm{Ac}$ were measured with improved precision. The half-lives obtained, together with the existing decay data of other $N\ensuremath{\le}126$ actinium isotopes, were compared with the values calculated with the Wentzel-Kramers-Brillouin approximation and without considering the $\ensuremath{\alpha}$-preformation factors. It is shown that the calculated half-lives exhibit a distinct odd-even staggering (OES) following the same trend as the experimental data, whereas the amplitudes of the exhibited OES are 30--60 % of the real ones. This implies that apart from the $\ensuremath{\alpha}$-preformation factors, the $\ensuremath{\alpha}$-decay energies also contribute significantly to the OES of $\ensuremath{\alpha}$-decay half-lives.