Ab Initio Computation of Charge Densities for Sn and Xe Isotopes

We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the ${\mathrm{NNLO}}_{\mathrm{sat}}$ chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for ${}^{100}\mathrm{Sn}$. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The present study closes the gap between the largest isotopes reachable by ab initio methods and the smallest exotic nuclei accessible to electron scattering experiments.

Figure 1

Model space dependence of the charge radius for ${}^{132}\mathrm{Xe}$ obtained from Gorkov SCGF calculations at ADC(2).

Figure 2

Charge density distribution for ${}^{132}\mathrm{Xe}$ obtained from Gorkov SCGF calculations at ADC(2). The dotted line with gray band corresponds to the two-point Fermi distribution with parameter and error bars extracted from Ref. [10].

Figure 3

Luminosity multiplied by the differential cross section for ${}^{132}\mathrm{Xe}$ obtained from Gorkov SCGF calculations at ADC(2). The values for the $NN+3N(\mathrm{lnl})$ interaction have been scaled by ${10}^2$ for clarity. The gray bands correspond to the two-point Fermi distribution with parameter and error bars extracted from Ref. [10]. Experimental values are taken from [10] and duplicated with a scaling of ${10}^2$ for comparison with $NN+3N(\mathrm{lnl})$ values, where error bars have been removed for clarity.

Figure 4

Charge density distributions for ${}^{100}\mathrm{Sn}$, ${}^{132}\mathrm{Sn}$, ${}^{132}\mathrm{Xe}$, ${}^{136}\mathrm{Xe}$, and ${}^{138}\mathrm{Xe}$ obtained from Gorkov SCGF calculations. The charge density is shifted upward by $0.025{\mathrm{fm}}^{-3}$ between each two nuclei, and the colored bands indicate the theoretical error associated with model space convergence.