  Reinforcement of the puzzle about the proton charge radius r, stimulated by
the recent experiments with muonic hydrogen induced news discussions on the
subject, and now some physicists are ready to adopt the exotic properties of
muon, lying beyond the Standard Model, in order to explain the difference
between the results of muonic hydrogen experiments (r=0.84087(39) fm) and
CODATA-2010 value r=0.8775(51) fm based on electron-proton scattering and H
spectroscopy. In the present contribution we suggest a way to achieve a
progress in the entire problem via paying attention on a logical inconsistency
of fundamental equations of atomic physics, constructed by analogy with
corresponding classical equations without, however, taking into account a
purely bound nature of electromagnetic field generated by electrically bound
particles in the stationary energy states. We suggest eliminating this
inconsistency via introducing some appropriate correcting factors into these
equations, which involve the requirement of total momentum conservation in the
system of bound particles in the absence of electromagnetic radiation. We
further show that this approach allows not only eliminating long-standing
discrepancies between theory and experiment in physics of simple atoms, but
also yields the same estimation for the proton size in the classic 2S-2P Lamb
shift in hydrogen, 1S Lamb shift in hydrogen, and 2S-2P Lamb shift in muonic
hydrogen, with the mean value r=0.841 fm. Finally, we suggest the crucial
experiment for verification of the validity of pure bound field corrections:
the measurement of lifetime of bound moun in meso-atoms with large Z, where the
standard calculations and our predictions essentially deviate from each other,
and some of the available experimental results (Yovanovitch, Phys. Rev. 117
(1960) 1580) strongly support our approach.
