Systematics of α -decay energies in the valence correlation scheme

We study the $\ensuremath{\alpha}$-decay energies (${Q}_{\ensuremath{\alpha}}$) taken from the Atomic Mass Evaluation 2016 within the valence correlation scheme (VCS). A linear trajectory of $\ensuremath{\alpha}$-decay energies, derived from the VCS for nucleon separation energies, is put forward in terms of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\alpha}{N}_{\mathrm{p}}\ensuremath{\mp}\ensuremath{\beta}{N}_{\mathrm{n}}({N}_{\mathrm{p}}$ and ${N}_{\mathrm{n}}$ are the valence proton and neutron numbers, respectively, counted as particles or holes from the nearest shell closure). It is applicable well to all available $\ensuremath{\alpha}$ emitters including even-even, odd-$A$, and odd-odd nuclei. This relationship can be understood via the Taylor expansion method based on the Bethe-Weizs\"acker (BW) mass formula, leading to the recognition on the origin of the $\ensuremath{\alpha}$-decay energy to some extent as well. In fact, the present study can not only reconfirm the similar linear dependence of nucleon separation energies in the VCS, but also exhibit a regular pattern of $\ensuremath{\alpha}$-decay energy and provide a reasonable estimation on unknown ${Q}_{\ensuremath{\alpha}}$ values.