Electron tunneling theory through atoms and molecules

A variation method for calculating the amplitude of electron subbarrier scattering on electron-containing systems (atoms and molecules) is suggested. The method is reduced to finding the asymptotic value of electron wave function in the range of scattering system. A general expression for scattering amplitude T through the asymptotics was obtained. Amplitudes of subbarrier scattering by H and He atoms were calculated. The obtained limiting (at low binding energies) values of the amplitudes are close to slow electrons scattering amplitudes. Dependence of T on energy and on angle was found. The way, in which electron tunnel transition amplitude can be found using T, allowance made for the scattering system influence, is shown