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 $\hbar/2m_e c$. Similarly, neutrino vacuum polarization by $Z$ boson field produces long range potential $\sim G_F^2/r^5$ with a very large range $\hbar/2m_{\nu}c$. Measurements of macroscopic effects produced by potential $G_{\rm{eff}}^2/r^5$ give limits on the effective interaction constant $G_{\rm{eff}}$ 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 $G_{\rm{eff}}$ 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.