Negative-energy contributions to transition amplitudes in heliumlike ions
Abstract
We derive the leading term in an αZ 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 3S1-->2 3S1, 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 (M2) transition 2 3P2-->1 1S0. These values include negative-energy 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