Abstract: Scientists are making attempts to solve proton radius puzzle. In this paper, the calculated value matches the experiment observation within 0.1%, compared to those obtained from CODATA, and muonic hydrogen scattering experiments of 4%. The calculation is made based on the assumption that the muonic hydrogen system has (Ep – Eµ) energy state (or frequency mix state of np –nµ), which interacts resonantly with the incoming photon of energy 206.2949(32) meV. A similar calculation is also made for muonic deuterium 2S-2P transition experiment with an accuracy of 1% from the experimental observation. The paper has also explored the theoretical as well as experimentation advancements that have led towards the development of results with lesser deviations.
Abstract: Recent progress in calculation of the one-loop selfenergy
of the electron bound in the Coulomb field is summarized.
The relativistic multipole expansion is introduced. This expansion
is based on a single assumption: except for the part of the time
component of the electron four-momentum corresponding to the
electron rest mass, the exchange of four-momentum between the
virtual electron and photon can be treated perturbatively. For non Sstates
and normalized difference n3En −E1 of the S-states this
itself yields very accurate results after taking the method to the third
order. For the ground state the perturbation treatment of the electron
virtual states with very high three-momentum is to be avoided. For
these states one can always rearrange the pertinent expression in such
a way that free-particle approximation is allowed. Combination of
the relativistic multipole expansion and free-particle approximation
yields very accurate result after taking the method to the ninth order.
These results are in very good agreement with the previous results
obtained by the partial wave expansion and definitely exclude the
possibility that the uncertainity in determination of the proton radius
comes from the uncertainity in the calculation of the one-loop selfenergy.