Precision physics of simple atoms and constraints on a light boson with ultraweak coupling

Constraint on spin-dependent and spin-independent Yukawa potential at atomic scale is developed. That covers constraints on a coupling constant of an additional photon $\gamma^*$ and a pseudovector boson. The mass range considered is from $1\;{\rm eV}/c^2$ to $1\;{\rm MeV}/c^2$. The strongest constraint on a coupling constant $\alpha^\prime$ is at the level of a few parts in $10^{13}$ (for $\gamma^*$) and below one part in $10^{16}$ (for a pseudovector) corresponding to mass below $1\;{\rm keV}/c^2$. The constraints are derived from low-energy tests of quantum electrodynamics and are based on spectroscopic data on light hydrogen-like atoms and experiments with magnetic moments of leptons and light nuclei.