On the bosonic atoms

We investigate the ground state properties of atoms, in which substitute fermions—electrons by bosons, namely, $\pi^-$-mesons. We perform some calculations in the frame of modified Hartree–Fock (HF) equation. The modification takes into account symmetry, instead of antisymmetry of the pair identical bosons wavefunction. The modified HF approach thus enhances (doubles) the effect of self-action for the boson case. Therefore, we accordingly modify the HF equations by eliminating the self-action terms “by hand.” The contribution of meson–meson and meson–nucleon non-Coulomb interaction is inessential at least for atoms with low and intermediate nuclear charge, which is our main subject. We found that the binding energy of pion negative ions $A_\pi^-$, pion atoms $A_\pi$, and the number of extra bound pions $\Delta N_\pi$ increases with the nuclear charge $Z$. In particular, for Xe $\Delta N_\pi=4$. As an example of a simple process with a pion atom, we consider photoionization that differs essentially from that for electron atoms. Namely, it is not monotonic decreasing from the threshold but has instead a prominent maximum above threshold. We study also elastic scattering of pions by pion atoms.