Energy levels and transition amplitudes for alkali-metal atoms in the Brueckner approximation

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Abstract
We use the B-spline approximation to solve the Brueckner equation. The Brueckner equation is obtained from Dyson equation for the one-particle propagator by cutting the kernel at second order in the electron-electron interaction. Thus the Brueckner approximation is a straightforward extension of the frozen-core Dirac-Fock approximation to include second-order correlations in a self-consistent way. We also give the explicit expression for the gauge-invariant transition in the Brueckner approximation. The numerical results of energies and transition amplitudes for alkali-metal atoms in the Brueckner approximation differ from experimental values by percentages ranging from 0.1% to 2%, increasing from Li to Cs. These results are comparable to existing accurate theoretical values.