A new value for the lamb shift

Abstract

The recent analytic value of the α 2 slope of the Dirac form factor of the free electron, from the crossed ladder diagram, is added to the contributions of the fourth order diagrams already evaluated by different workers. The sum is found to be F 1 ′(0) total = ( α 2 π 2 ) {− 4819 5184 − 49π 2 432 + 1 2 π 2 log 2 − 3 4 ζ(3)} = ( α 2 π 2 ) {0.4699}. This contributes to the Lamb shift in H: ( α 2 π 2 ) α 1 2 2mα 2 0.4699 = 0.444 MHz . The total Lamb shift in H is then: S H = (2 S 1 2 − 2 P 1 2 ) H = 1057.911 ± 0.011 MHz (s.d.), and the separation ΔE H − S H : (2 S 3 2 − 2 S 1 2 ) H = 9911.115 ± 0.031 MHz (s.d.).