Energy levels and oscillator strengths for the exponential-cosine screened Coulomb potential in the shifted large-dimension expansion theory

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Abstract
The method of shifted large-N expansion, where N is the number of spatial dimensions, is applied to the study of energy levels and oscillator strengths for the exponential-cosine screened Coulomb potential, V(r)=-exp(- delta r) cos delta r/r. The analytic expressions for the energy eigenvalues. E/sub /n,l yield very accurate results in general for a wide range of n, l even when the screening parameter delta is large and quite close to its critical value delta c for which the quantum state becomes just bound. However, for the 1s state, accuracy of the results falls off rapidly at delta approximately=0.8 delta c. This is because the effective large-N potential becomes quite shallow in comparison with the true potential and the expansion parameter is not sufficiently small to guarantee the convergence of the expansion series for the energy levels. The normalised wavefunctions are used to calculate the oscillator strengths for the 1s to 2p transition for some values of the screening parameter. In spite of the simplicity of this approach, the predicted oscillator strengths compare fairly well with those obtained numerically. The success of the calculation prompts us to make further applications of the shifted large-N technique to other areas of atomic physics.