The Electron Capture Cross Sections for Protons in Helium

The impact parameter formulation of the method of perturbed stationary states is used to calculate the cross section for electron capture by protons in helium. The σ-σ transition from ground state to ground state is investigated. A one-body formulation is used in which the captured electron moves initially in the combined field of the other electron, the helium nucleus and the incident proton. The presence of the passive electron is allowed for by using as the initial wave function before the collision, an approximation to that calculated from the self-consistent field for the helium atom. During the collision this initial wave function is modified by the introduction of a variational parameter which is determined by a minimization condition for the energy. The possibility of using the one-body formulation for more complex systems is demonstrated by calculations of the electron-capture cross section for protons in argon and neon.