{"title":"The Self-Energy of an Ellectron Bound in a Coulomb Field","authors":"J. Zamastil, V. Patkos","volume":79,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":1171,"pagesEnd":1174,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/16481","abstract":"
Recent progress in calculation of the one-loop selfenergy
\r\nof the electron bound in the Coulomb field is summarized.
\r\nThe relativistic multipole expansion is introduced. This expansion
\r\nis based on a single assumption: except for the part of the time
\r\ncomponent of the electron four-momentum corresponding to the
\r\nelectron rest mass, the exchange of four-momentum between the
\r\nvirtual electron and photon can be treated perturbatively. For non Sstates
\r\nand normalized difference n3\u0001En −\u0001E1 of the S-states this
\r\nitself yields very accurate results after taking the method to the third
\r\norder. For the ground state the perturbation treatment of the electron
\r\nvirtual states with very high three-momentum is to be avoided. For
\r\nthese states one can always rearrange the pertinent expression in such
\r\na way that free-particle approximation is allowed. Combination of
\r\nthe relativistic multipole expansion and free-particle approximation
\r\nyields very accurate result after taking the method to the ninth order.
\r\nThese results are in very good agreement with the previous results
\r\nobtained by the partial wave expansion and definitely exclude the
\r\npossibility that the uncertainity in determination of the proton radius
\r\ncomes from the uncertainity in the calculation of the one-loop selfenergy.<\/p>\r\n","references":"
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