Correlating double-difference of charge radii with quadrupole deformation and $B\left(E2\right)$ in atomic nuclei

A good linear correlation is found between the double-difference of charge radius $\delta R_{2p-2n}(Z,N)$ with that of quadrupole deformation data in even-even nuclei. This results in a further improved charge radius relation that holds in a precision of about $5\times {10}^{-3}$ fm. The new relation can be generalized to the reduced electric quadrupole transition probability $B\left(E2\right)$ between the first $2^{+}$ state and the $0^{+}$ ground state, and the mean lifetime $\tau$ of the first $2^{+}$ state. Same correlations are also seen in global nuclear models such as Hartree-Fock-Bogoliubov (HFB-24) and relativistic mean field (RMF); however, they are not consistent with the experimental data.

Figure 1

$\delta R(Z,N)$ as a function of $\delta R(Z,N)\left({\beta }_2^2\right)$ for all experimentally known cases. The linear fit is indicated by the dashed line. The relevant point for ${}^{98}\mathrm{Sr}$ is labeled.

Figure 2

Same as Fig. 1 but for the data with $A<130$ (a), $A\ge 130$ (b), and $\delta R(Z,N)<0.007$ fm and $\delta R{(Z,N)}_{\mathrm{def}}<0.007$ fm (c). Experimental uncertainties are not shown. Linear fits to the relevant experimental data are indicated by dashed lines.

Figure 3

Experimentally known $\delta R(Z,N)$ (filled circles) and $\delta R{(Z,N)}_{\mathrm{def}}$ (open squares) for the Sr isotopic chain.

Figure 4

Same as Fig. 1 but using the predicted $\delta R(Z,N)$ and $\delta R{(Z,N)}_{\mathrm{def}}$ in the RMF model (a), and using experimental $\delta R(Z,N)$ and predicted $\delta R{(Z,N)}_{\mathrm{def}}$ in the RMF model (b). Error bars are not shown for experimental data.