Correlations of experimental isotope shifts with spectroscopic and mass observables

Experimental differential observables relating to mean square charge radii, spectroscopic, and mass observables of even-even nuclei are presented for different regions in the nuclear chart. They exhibit remarkable correlations, not heretofore recognized, that provide a new perspective on structural evolution, especially in exotic nuclei. This can also be a guide for future measurements of charge radii, spectroscopic observables, and masses, as well as for future theoretical approaches.

Figure 1

(Left): Experimental $\langle r^2\rangle$, $E(2_1^{+})$, $R_{4/2}$, $B(E2:2_1^{+}\to 0_1^{+})$, and $S_{2n}$ values with $N=70–104$ [1, 2]. (Right): Differential values of these observables defined by $\delta \langle r^2\rangle (N)=\langle r^2\rangle {}_N-\langle r^2\rangle {}_{(N-2)}$, $\delta E(2_1^{+})(N)=(E_{(N-2)}-E_N)/(E_{(N-2)}+E_N)$, $\delta R_{4/2}(N)=R_N-R_{(N-2)}$, $\delta B(E2:2_1^{+}\to 0_1^{+})(N)=B(E2){}_N-B(E2){}_{(N-2)}$, $\delta S_{2n}(N)=S_N-S_{(N-2)}$. Note that the definition of $\delta E(2_1^{+})$ is inverted in $N$ and $(N-2)$ since its overall trendline is opposite to most of the other observables. Error bars are shown only if larger than the symbols. Large errors only occur for a few $\delta B(E2)$ values: to avoid cluttering the plots with essentially content-free points, we omitted cases (five in total in Figs. 1 and 2) where the error in $\delta B(E2)>50\%$ and $>20$ W.u. In the single, important case of ${}^{98}\mathrm{Zr}$, whose $B(E2)$ value gives $\delta B(E2)$ values for ${}^{98,100}$ Zr, we used the Grodzins rule [3] to estimate the $B(E2)$ value, giving it a conservative uncertainty of $\pm 100\%$.

Figure 2

Similar to Fig. 1 but for the $A~100$, 130, and 190 regions [1, 2].

Figure 3

Similar to Fig. 1 but for the $A~35$ region and with three observables [1, 2].