We calculate the parity nonconserving (PNC) electric-dipole ($E1$) transition amplitudes for the $5s\text{–}6s$ and $5s\text{–}4d_{3/2}$ transitions in Rb and ${\mathrm{Sr}}^{+}$. Our results include both the nuclear-spin-independent and nuclear-spin-dependent contributions, with particular emphasis on the potential effects of a hypothetical additional $Z^{\prime }$ boson. We highlight possible advantages of using light atoms in searches for such new interaction. The ratio of the contribution of a low-mass $Z^{\prime }$ boson to the contribution of the Standard Model $Z$ boson to PNC effects increases rapidly (faster than $1/Z^2$) 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, ${\mathrm{Ba}}^{+}$, Fr, and ${\mathrm{Ra}}^{+}$.

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• Electronic transitions
• Atomic Properties
• First-principles calculations
• Hartree-Fock methods