On the basis of the variational method we study the energy levels of pionic helium (π-e-He) and kaonic helium (K-e-He) with an electron in the ground state and a meson in the excited state with principal and orbital quantum numbers n~l+1~20. Variational wave functions are taken in the Gaussian form. Matrix elements of the basic Hamiltonian and corrections to vacuum polarization and relativism are calculated analytically in a closed form. We calculate some bound-state energies and transition frequencies which can be studied in the experiment.
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Korobov et al. (2024) studied this question.
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