From local correlations to regional systematics

Local correlations of $2_1{}^{+}$ excitation energies and $B(E2,2_1{}^{+}\to \text{g.s.})$ values require linear $N_p{N}_n$ systematics in a logarithmic scale, as confirmed by an experiment survey. Based on local correlations of $\alpha$-decay energies, neutron separation energies, and proton separation energies, one can decouple them into their proton and neutron contributions separately. These contributions exhibit smooth regional systematics beyond the $N_p{N}_n$ scheme.

Figure 1

$E2$ values plotted vs the logarithmically scaled $N_p{N}_n$ product. All the data are from the ENSDF [15] compilation. Solid lines represent the results of fitting to Eqs. (4) and (6) with the best-fit results listed in Table 2. Three abnormal branches due to the $Z=64$ subshell are highlighted by circles in (c).

Figure 2

$B\left(E2\right)$ against the logarithmically scaled $N_p{N}_n$ product. All the data are from Ref. [16]. Solid lines demonstrate the linear relation with best-fit variables listed in Table 3. The fitting of (a) is not convergent due to lack of data. Still, we present this divergent fitting result with a dotted line as a guide to the eye.

Figure 3

Final results of the decoupling analysis of the $Q_{\alpha }, S_n$, and $S_p$ experimental data in $82<Z\le 104,126<N\le 155$ region. The data are extracted from the AME2012 [14] mass table. In (a)–(c), the experimental $Q_{\alpha }, S_n$, and $S_p$ values are plotted against the decoupled $f_p\left(N_p\right)+f_N\left(N_n\right)$, respectively. The diagonal dotted lines in (a)–(c) correspond to the exact $F(N_p,N_n)=f_p\left(N_p\right)+f_n\left(N_n\right)$ relation. Panels (d)–(f) illustrate the evolution of the decoupled $f_p\left(N_p\right)$ and $f_n\left(N_n\right)$ results for $Q_{\alpha }, S_n$, and $S_p$, respectively. The results exhibit smooth regional systematics with the expected odd-even staggering for $S_n$ and $S_p$.