Fourth order magnetic moment of the electron

Abstract

Abstract A more complete account is given of an estimation, by rigourous upper and lower bounds, of the fourth order magnetic moment of the electron which has already been published by the author. The method is illustrated for one typical term. Then the results of a more elaborate estimation are given. In the terminology used by Karplus and Kroll, the term symbolized by the diagram IIc is found to satisfy μ(II) c =(−0.60±0.11) α 2 π 2 − 1 2 α 2 π 2 log λ 2 m 2 , in contradiction with the value −3.18 α 2 π 2 − 1 2 α 2 π 2 log λ 2 m 2 given by the previous authors. It has been found that the other terms are not in disagreement with Karplus and Kroll values. If one accepts them, then the total fourth order moment amounts to μ(4) = (−0.39±0.11) (α2/π2). One notes finally that this new value increases the Lamb shift by (0.82±0.03) Mc/s and brings the fine structure constant to 1/α = 137.0384.