Energy levels of mesonic helium in quantum electrodynamics

In the variational method we study energy levels of pionic helium $(\pi-e-He)$ and kaonic helium $(K-e-He)$ with the electron in ground state and a meson in 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 experiment.