Nuclear Structure corrections for Parity Non-conservation in Atomic Ba$^+$ and Ra$^+$

Abstract

We calculate the binding energy, charge radii in $^{126}$Ba--$^{140}$Ba and $^{214}$Ra--$^{228}$Ra using the relativistic mean field theory which includes scalar and vector mesons. We then evaluate the nuclear structure corrections to the weak charges for a series of isotopes of these atoms using different parameters and estimate their uncertainty in the framework of this model. Our results will have important implication for the ongoing and planned parity non-conservation experiments and atomic structure calculations on Ba$^+$ and Ra$^+$.