Distortion of the Electron Wave Function in $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ Atoms

An investigation is made of the extent to which the binding energies and wave functions for some states of the $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ atoms are affected by the dipole and higher multipole interactions of the electron with the meson or the antiproton. The meson or antiproton is treated as a classical point charge. Perturbation theory is employed to determine the admixture of discrete excited states of the unperturbed electron Hamiltonian. The unperturbed electron Hamiltonian takes into account only the monopole interaction of the electron with the meson. A variational method is employed to determine approximately the change in the binding energy as well as some of the more important features of the distortion of the electron wave function. It is found, in particular, that the binding energies of those states of the $\alpha K^{-}{e}^{-}$ atom in which the meson is in a circular orbit with principal quantum number $n=27, 28, or 29$ are lowered by slightly less than 1 eV. The maximum relative change in the amplitude of the electron wave function for one of these states is found to be roughly 20%.