THE GENERALIZED BETHE LOGARITHM FOR TIGHTLY BOUND ELECTRONS

We derive a closed relativistic expression that makes it possible to c alculate the self-energy of multiply charged ions in an external Coulo mb field without resorting to a series expansion in powers of alpha Z. The expression contains the generalized Bethe logarithm for tightly b ound electrons. We do numerical calculations of the self-energy for th e 1s(1/2)-electrons of multiply charged hydrogenlike ions. The propose d method allows for self-energy calculations for any values of the nuc lear charge Z. (C) 1997 American Institute of Physics.