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Reinforcement of the puzzle about the proton charge radius r, stimulated bythe recent experiments with muonic hydrogen induced news discussions on thesubject, and now some physicists are ready to adopt the exotic properties ofmuon, lying beyond the Standard Model, in order to explain the differencebetween the results of muonic hydrogen experiments (r=0.84087(39) fm) andCODATA-2010 value r=0.8775(51) fm based on electron-proton scattering and Hspectroscopy. In the present contribution we suggest a way to achieve aprogress in the entire problem via paying attention on a logical inconsistencyof fundamental equations of atomic physics, constructed by analogy withcorresponding classical equations without, however, taking into account apurely bound nature of electromagnetic field generated by electrically boundparticles in the stationary energy states. We suggest eliminating thisinconsistency via introducing some appropriate correcting factors into theseequations, which involve the requirement of total momentum conservation in thesystem of bound particles in the absence of electromagnetic radiation. Wefurther show that this approach allows not only eliminating long-standingdiscrepancies between theory and experiment in physics of simple atoms, butalso yields the same estimation for the proton size in the classic 2S-2P Lambshift in hydrogen, 1S Lamb shift in hydrogen, and 2S-2P Lamb shift in muonichydrogen, with the mean value r=0.841 fm. Finally, we suggest the crucialexperiment for verification of the validity of pure bound field corrections:the measurement of lifetime of bound moun in meso-atoms with large Z, where thestandard 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.

Pure bound field corrections to the atomic energy levels and the proton size puzzle