Question of calculation of energy of excited helium states with zero orbital electron moments

In the framework of the variational method, as a result of a numerical calculation, the energy of the excited state and the screening constant of the helium atom in the electronic configuration 1 s 2 s were found. This state is metastable with respect to the single-photon transition to the ground state of 1 s ², as well as in the configuration of 1 s 3 s . The results of the numerical calculation of energy approximately coincided with other values given for these states in the modern literature. For the first time, numerical calculations were also carried out for 1 s ns configurations in the range of values n = 4, ..., 9 with obtaining the corresponding values of energy E_n and screening constant σ _n . In particular, it was obtained that for excited states in the range n = 2, 3, ..., 9, the values σ _n and E_n monotonously decrease with increasing n , and in the formal limit n → ∞ σ _n → 0, and | E_n | tends to the energy of a hydrogen-like atom with a nuclear charge (2 e ). Such a character of the change of the specified parameters is consistent with the general physical concepts related to the quantum system under consideration. 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.

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