Calculation of the Energy of Excited States with Zero Electron Orbital Angular Momenta

Abstract

Within the framework of the variational method, as the result of a numerical calculation we have found the energy of the excited state and the screening constant of the helium atom in the electron configuration 1s 2s, which is metastable with respect to the single-photon transition to the 1s² state, and also in the 1s 3s configuration. The results of numerical calculation of the energy are in approximate agreement with other values given for these states in the literature which are available to us. For the first time, numerical calculations have also been carried out for 1s ns configurations in the range of values n = 4, …, 9, in which the corresponding values of the energy E_n and the screening constant σ_n were obtained. It was found, in particular, that σ_n and |E_n| for the excited states in the range n = 2, 3, …, 9 fall monotonically with increasing n, where σ_n → 0 in the formal limit n → ∞, and E_n tends to the energy of a hydrogenlike atom with nuclear charge (2e), as it should be in accordance with the physical meaning of these quantities. The results of the calculations are illustrated graphically. The present study has important methodological significance in terms of the development and application of the basic principles of quantum mechanics to the helium atom.