${\beta }^2$ corrections to spherical energy-density functional calculations for root-mean-square charge radii

Root-mean-square charge radii are discussed in terms of spherical energy-density functional (EDF) models corrected for quadrupole deformations. We discuss the specific examples for the isotope shifts of the calcium isotopes and the isotonic shift between tin and cadmium.

Figure 1

Measured rms charge radii for nuclei from $Z=20$ (calcium) to $Z=52$ (tellurium). The data are taken from compilations [22] and [23] with updated results for Ca [6, 18], Fe [24], Ni [25], Cd [20], and Sn [19].

Figure 2

${\mathrm{\Delta }}_{ch}=R_{ch}\left(\exp \right)-R_{ch}\left(2\mathrm{p}\right)$ with the two-parameter formula $R_{ch}\left(2\mathrm{p}\right)=r_0{A}^{1/3}+r_1{A}^{-1/3}$ with $r_0=0.9071\mathrm{fm}$ and $r_1=1.105\mathrm{fm}$ from [5].

Figure 3

$\mathrm{\Delta }{R}_{ch}$ for the calcium isotopes. The black circles are the experimental results from [6] with error bars about the size of the circles. The calculations shown in panel (c) are the results from the EDF calculations with the Sv-min and $\mathrm{Fy}(\mathrm{\Delta }r,\mathrm{HFB})$ EDFs as given in [18]. The red crosses in panels (a) and (b) are based on experimental $B\left(E2\right)$ values in the text. The lines shown in panels (a) and (b) are based on the $B\left(E2\right)$ calculations discussed in the text.

Figure 4

Cd-Sn isotonic shifts. The experimental results from [20] and [19] are compared to the Sv-min and $\mathrm{Fr}\left(\mathrm{\Delta }r\right)$ EDF calculations given in [20] and [19].

Figure 5

Summed $B(E2,\uparrow )$ strengths in ${}^{42–45}\mathrm{Ca}$ where ZBM2* results (in black) are compared with the experimental upper and low limits (in red). The experimental data are from [42] for ${}^{42}\mathrm{Ca}$, [43] for ${}^{43}\mathrm{Ca}$, and [44] for ${}^{44}\mathrm{Ca}$.