Quantum-mechanical four-body versus semi-classical three-body theories for double charge exchange in collisions of fast alpha particles with helium targets

Within the two-channel distorted wave second-order perturbative theoretical formalism, we study capture of both electrons from helium-like targets by heavy nuclei as projectiles at intermediate and high impact energies. The emphasis is on the four-body single-double scattering (SDS-4B) method and the three-body continuum distorted wave impact parameter method (CDW-3B-IPM). The SDS-4B method deals with the full quantum-mechanical correlative dynamics of all the four interactively participating particles (two electrons, two nuclei). The CDW-3B-IPM is a semi-classical three-body independent particle model (one electron, two nuclei), using a combinatorial calculus to describe double capture by a product of two uncorrelated probabilities, integrated over impact parameters. Both theories share a common feature in having altogether two electronic full Coulomb continuum wave functions. One such function is centered on the projectile nucleus in the entrance channel, whereas the other is centered on the target nucleus in the exit channel. These two methods satisfy the correct initial and final Coulomb boundary conditions in the asymptotic region of scattering, at infinitely large inter-particle separations. Yet, it is presently demonstrated that most of the available experimental data on total cross sections for the double capture from helium by alpha particles distinctly favor the SDS-4B method. This is especially true at intermediate energies. Such energies are critically important in versatile applications under the general umbrella of ion transport in matter, including thermonuclear fusion (plasma physics) and ion therapy (medicine).