Local mass relations and the $N_p{N}_n$ scheme

In this paper we show that $ip-jn$ relations for nuclear masses and charge radii of four neighboring nuclei reconcile with Casten's $N_p{N}_n$ scheme.

Figure 1

$\delta F/\overline{F}$ vs neutron number $N$, for $i=j=2$. Here $\overline{F}$ is the average of $F$ for corresponding four nuclei involved in Eq. (1). (a) $F$ corresponds to experimental values of $E_{2_1^{+}}$, taken from Ref. [11]. (b) $F$ corresponds to experimental values of $B\left(E2\right) [E2$ transition rates], from Ref. [11]. One sees that both $\delta F/\overline{F}$ here are small, with a few exceptions for nuclei with small mass numbers or very close to the magic numbers.

Figure 2

$F$ vs $N_p{N}_n$ for nuclei with $82<Z\le 104$ and $126<N\le 155$. (a) $F$ corresponds to $R$, experimental values of nuclear charge radii, from Ref. [12]. (b) $F$ corresponds to $B$, nuclear binding energy, from Ref. [13]. Both $F$ in this figure exhibit good correlations in the $N_p{N}_n$ scheme.

Figure 3

Experimental values of $\alpha$ decay energy $Q_{\alpha }$ (from Ref. [13]) vs $N_p{N}_n$ for nuclei with $82<Z\le 104$ and $126<N\le 155$.