Negative-energy contributions to transition amplitudes in heliumlike ions

Abstract

We derive the leading term in an aZ expansion for the negative-energy ~virtual electron-positron pair! contributions to the transition amplitudes of heliumlike ions. The resulting expressions allow us to perform a general analysis of the negative-energy contributions to electric- and magnetic-multipole transition amplitudes. We observe a strong dependence on the choice of the zeroth-order Hamiltonian, which defines the negativeenergy spectrum. We show that for transitions between states with different values of total spin, the negativeenergy contributions calculated in a Coulomb basis vanish in the leading order while they remain finite in a Hartree basis. The ratio of negative-energy contributions to the total transition amplitudes for some of nonrelativistically forbidden transitions is shown to be of order 1/ Z. In the particular case of the magnetic-dipole transition 3 3 S1!2 3 S1 , we demonstrate that the neglect of negative-energy contributions, in an otherwise exact no-pair calculation, would lead one to underestimate the decay rate in helium by a factor of 1.5 in calculations using a Hartree basis and by a factor of 2.9 using a Coulomb basis. Finally, we tabulate revised values of the line strength S for the magnetic-quadrupole ( M 2) transition 2 3 P2!1 1 S0 . These values include negative-energy contributions from higher partial waves, which were neglected in our previous calculations. @S1050-2947~98!03512-4#