Abstract
Inelastic transitions in slow ion-atom collisions are described using an adiabatic representation of the collision system, where the transition probabilities are determined by the branch points of the potential energy curves in the complex plane of internuclear separation $R$. As an example, the ${\mathrm{HeH}}^{2+}$ system is treated, in which the evolution of the branch points related to hidden, avoided, and ${L}_{3}$ crossings in the dynamical adiabatic basis of three-body Coulomb problem as functions of parameter $\ensuremath{\omega}=\ensuremath{\rho}v$ ($\ensuremath{\rho}$ is the impact parameter and $v$ the impact velocity) is studied. Rearrangement of hidden couplings due to the passage of ${L}_{3}$ branch points with the increase of $\ensuremath{\omega}$ is discussed.
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