The majority of this effect arises from mass renormalization diagrams; vacuum polarization enters with the opposite sign.  
Na?e computations of this give the unphysical value of infinity but, in 1947, Bethe (bet-uh) obtained approximately the correct value without resort to relativity.  The majority of this effect arises from mass renormalization diagrams; vacuum polarization enters with the opposite sign.  For n=2 hydrogen states, this induces a splitting of about 1.058 gigahertz.  It is very small except for L=0 states, and breaks the degeneracy in hydrogen between s and p states of the same principal quantum number and total angular momentum.  For 10 points - identify this effect, a change in the energy levels of hydrogen-like atoms due largely to electron self-interaction, predicted to a high degree of accuracy by quantum electrodynamics.
Na?e computations of this give the unphysical value of infinity but, in 1947, Bethe (bet-uh) obtained approximately the correct value without resort to relativity.  
Lamb shift