Parity Nonconservation in Rb and Sr${}^{+}$ due to Low-Mass Vector Boson

We calculate the parity non-conserving (PNC) electric-dipole ($E1$) transition amplitudes for the $5s-6s$ and $5s-4d_{3\mathrm{/}2}$ transitions in Rb and Sr${}^{+}$. Our results include both the nuclear-spin-independent and nuclear-spin-dependent contributions, with particular emphasis on the potential effects of a hypothetical additional $Z^{\mathrm{\prime }}$-boson. We highlight possible advantages of using light atoms in searches for such new interaction. The ratio of the contribution of a low mass $Z^{\mathrm{\prime }}$-boson to the contribution of the Standard model $Z$ -boson to PNC effects increases rapidly (faster than $1\mathrm{/}{Z}^2$) with decreasing nuclear charge $Z$. Another advantage is that theoretical interpretations of experiments in lighter systems may be carried out with a higher accuracy than that in Cs, Ba${}^{+}$, Fr and Ra${}^{+}$.