Negative-energy contributions to transition amplitudes in heliumlike ions

We derive the leading term in an alpha Z 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 negative-energy spectrum. We show that for transitions between states with different values of total spin, the negative energy 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 S-3(1) --> 2 S-3(1), 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 P-3(2) --> 1 S-1(0). These values include negative-energy contributions from higher partial waves, which were neglected in our previous calculations. [S1050-2947(98)03512-4].