Numerical approach to transit probabilities in the Coulomb approximation: Be II and Mg II Rydberg series

Abstract

An entirely numerical approach to the Coulomb approximation for atomic dipole transition probabilities Ajj(j=n, l) is investigated. The wavefunction divergency at the origin and the resulting normalization problem are taken care of by introducing a numerically determined cut-off radius (a function of j) inside which the wavefunction is chosen equal to zero. The method has been applied to the Rydberg states nmin<or=n<or=10, 0<or=l<or=5 of Be II (nmin= 3), and Mg II (nmin=3), and the stability with respect to cut-off radius is examined for transition probabilities, lifetimes and branching ratios.