arXiv subjects
Publications and source records attributed to A. S. Yelkhovsky.
In the recent paper by Zhang the order $α^4 R_{\infty}$ corrections to the positronium P levels were reconsidered. Those calculations confirm our corresponding results, except for the contribution due to the squared spin-orbit interaction. We present here a new derivation of our previous result for this last correction, this derivation being to our opinion both simple and convincing.
The order $α^4 (m/M) R_{\infty}$ shift of hydrogen P levels is found. The corrections are predominantly of relativistic origin. Our approach is a straightforward extension of that developed and applied by us previously to positronium P levels. The corrections to the Lamb shift in hydrogen constitute numerically δE(2 P_{1/2})=0.55 kHz, δE(2 P_{3/2}) =0.44 kHz.
The expression for the first recoil correction to the Dirac-Coulomb spectrum is obtained employing the gauge invariance.
The order $α^4 R_{\infty}$ corrections to positronium $P$ levels are found. The calculation is reduced to the ordinary perturbation theory for the nonrelativistic Schrödinger equation. The perturbation operators have the Breit-type structure and are obtained by calculating on-mass-shell diagrams. Found energy corrections constitute numerically $δE(2 ^1 P_1)=0.06$ MHz, $δE(2 ^3 P_2)=0.08$ MHz, $δE(2 ^3 P_1)=0.025$ MHz, $δE(2 ^3 P_2)=-0.58$ MHz.