We continue the analysis of quantum two-particle bound systems we have started in (Kholmetskii, A.L., Missevitch, O.V. and Yarman, T. Phys. Scr., 82 (2010), 045301), where we re-postulated the Dirac equation for the bound electron in an external EM field based on the requirement of total momentum conservation, when its EM radiation is prohibited. It has been shown that the modified expression for the energy levels of hydrogenic atoms within such a pure bound field theory (PBFT) provides the same gross and fine structure of energy levels like the standard theory. Now we apply the PBFT to the analysis of hyperfine interactions and show the appearance of some important corrections to the energy levels (the 1S-2S interval and hyperfine spin-spin splitting in positronium, 1S and 2S-2P Lamb shift in hydrogen), which remedies considerably the discrepancy between theoretical predictions and experimental results. In particular, the corrected 1S-2S interval and the spin-spin splitting in positronium practically eliminate the available up to date deviation between theoretical and experimental data. The re-estimated classic 2S-2P Lamb shift as well as ground state Lamb shift in the hydrogen atom lead to the proton charge radius rp=0.837(8) fm (from 2S-2P Lamb shift), and rp=0.840(24) fm (from 1S Lamb shift), which corresponds to the latest estimation of proton size via the measurement of 2S-2P Lamb shift in muonic hydrogen, i.e. rp=0.84184(67) fm. We also emphasize the universal character of PBFT, which is applicable to heavy atoms, too, and analyze 2S-2P interval in Li-like uranium. We show that the corrections we introduced provide a better correspondence between the calculated and experimental data than that furnished by the standard approach. The results obtained support our principal idea of the enhancement of the bound EM field in the absence of EM radiation for quantum bound systems.
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