Effects of the long-range neutrino-mediated force in atomic phenomena

As known, electron vacuum polarization by nuclear Coulomb field produces Uehling potential with the range $\mathrm{\hslash }\mathrm{/}2m_{e}c$. Similarly, neutrino vacuum polarization by $Z$ boson field produces long range potential $\sim G_F^2\mathrm{/}{r}^5$ with a very large range $\mathrm{\hslash }\mathrm{/}2m_{\nu }c$. Measurements of macroscopic effects produced by potential $G_{\mathrm{e}\mathrm{f}\mathrm{f}}^2\mathrm{/}{r}^5$ give limits on the effective interaction constant $G_{\mathrm{e}\mathrm{f}\mathrm{f}}$ which exceed Fermi constant $G_F$ by many orders of magnitude, while limits from spectroscopy of simple atomic systems are approaching the Standard Model predictions. In the present paper we consider limits on $G_{\mathrm{e}\mathrm{f}\mathrm{f}}$ from hydrogen, muonium, positronium, deuteron, and molecular hydrogen. Constraints are also obtained on fifth force parameterised by Yukawa-type potential mediated by a scalar particle.