Energy barrier for electron penetration into helium

The Galitskii approach to the calculation of self-energies is used to find the energy barrierΔE opposing the penetration of electrons into He, Ne, and Ar. To second order in thes-wave scattering lengtha, it is found that $$\Delta {\text{E = (2}}\pi \hbar ^2 {\text{na/m)}}\left\{ {{\text{1 + 2a}}\pi ^{{\text{ - 1}}} \int_0^\infty {{\text{dk1 - S(k)]}}} } \right\}$$ wheren is the fluid number density,m is the electron mass, andS(k) is the fluid static structure factor. Typical barrier energies for⁴He and³He are 0.97 and 0.67 eV.