Negativeenergy contributions to transition amplitudes in heliumlike ions
Abstract
We derive the leading term in an αZ expansion for the negativeenergy (virtual electronpositron pair) contributions to the transition amplitudes of heliumlike ions. The resulting expressions allow us to perform a general analysis of the negativeenergy contributions to electric and magneticmultipole transition amplitudes. We observe a strong dependence on the choice of the zerothorder 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 negativeenergy 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 magneticdipole transition 3 ^{3}S_{1}>2 ^{3}S_{1}, we demonstrate that the neglect of negativeenergy contributions, in an otherwise exact nopair 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 magneticquadrupole (M_{2}) transition 2 ^{3}P_{2}>1 ^{1}S_{0}. These values include negativeenergy contributions from higher partial waves, which were neglected in our previous calculations.
 Publication:

Physical Review A
 Pub Date:
 December 1998
 DOI:
 10.1103/PhysRevA.58.4453
 Bibcode:
 1998PhRvA..58.4453D
 Keywords:

 31.30.Jv;
 31.15.Md;
 32.70.Cs;
 Relativistic and quantum electrodynamic effects in atoms and molecules;
 Perturbation theory;
 Oscillator strengths lifetimes transition moments