With a view to testing the adequacy of the perturbation theory as applied to radiationless transitions in light atoms, the probability of such a transition in the Be atom from the 1s22p3s3P state to the continuum 1s22s + ejected p electron has been calculated. The wave functions employed for the discrete states are obtained by the variational method and the wave function for the continuous state by numerical integration of the Schrodinger equation. The transition probability obtained is 5 × 1013 per second, leading to a width of ~ 290 cm.−1 for the level 1s22p3s3P. This is at least 103 times larger than what is indicated by the observed widths of the spectral lines. Thus the present calculation, together with similar earlier calculations for the He atom, shows that the perturbation theory is inadequate for the light atoms.It is also pointed out that there is an inconsistency in the use of the perturbation theory in these calculations and those on the Auger effect in the literature since the use of variational or "screened" wave functions implies that a part of the electron–electron interaction has already been included in the initial approximation, and it is hence incorrect to treat this whole interaction as the perturbation causing the transition.
Cosmological perturbation theory for baryons and dark matter: One-loop corrections in the renormalized perturbation theory framework
