On the problem of proton radius puzzle

Abstract: This paper concerns the most intriguing question of modern atomic physics: determination of the proton root-mean-square (rms) charge radius ($r_p$). This problem was announced by the difference in $r_p$ values extracted from the experiments on measurement of transition frequencies in hydrogen ($H$) atom and measurement of Lamb shift in muonic hydrogen ($\mu H$) atom. The both experiments give the possibility for the very accurate comparison of values evaluated theoretically and experimentally. As a result of this analysis the value of proton charge radius extracted from the $\mu H$ experiment was found on $4\%$ smaller than the value given by the hydrogenic experiments. For a decade a lot of theoretical efforts were devoted to the search of 'new physics' on the basis of such deviation. In this paper we reproduce the analysis on determination of proton charge radius in the hydrogen atom.