Cross section sensitivity to perturbation strengths in distorted waves for double electron capture by alpha particles from helium targets

Computer experiments are performed on total cross sections for capture of both electrons from helium targets at 100-10000 keV. Employed are four quantum-mechanical perturbative four-body distorted wave methods (one of the first and three of the second order). The goal is to determine the cross section sensitivity to the perturbation strengths in distorted waves from the second-order methods. The perturbation strength is parametrized by the Sommerfeld factor (the quotient of the nuclear charge and the relative velocity of the colliding particles). At each fixed impact energy, the sought sensitivity is monitored by gradually modifying the nuclear charges in the Sommerfeld factors. These factors reside in the Coulomb distortions of the unperturbed channels states. The focus is on the electronic distortions through the eikonal Coulomb logarithmic phases and the full Coulomb waves. The logarithmic phases are the constituents of the compound phases for the net charges of the two heavy scattering aggregates in relative motions. A striking perturbation strength sensitivity of the obtained total cross sections is recorded.