Self-localized state of an electron in a dense helium vapor. Successive approximations in a self-consistent approach

The problem of a self-localized electron state in dense helium vapor is theoretically considered by the successive approximation method using a small parameter ɛ proportional to the ratio of the electron mass to the helium atom mass. The wave equation for an electron was solved self-consistently jointly with the mechanical equilibrium equation. It is shown that such a method allows one to satisfy not only the normalization condition for an electron wave function but also the condition of conservation of the helium vapor particle total number. Both the wave function and vapor density profile are calculated as a function of a radial coordinate. The energy of the localized electron ground state is estimated for some analytical approximations for the equilibrium helium vapor density. The results are compared with those previously obtained within a variational approach and in zero approximation ɛ when the helium atom mass was treated as infinite in comparison with the electron mass.