Two-state model for top-of-barrier processes

Wei–Norman–Kolokolov dual approach for arbitrary spinSin a time-dependent magnetic field

“…Consider an  -level model with a V R R 1 ( ) µ diabatic potential where R is the internuclear distance. The model with R=vt (where v is the constant sweep velocity of the driving field) is treated in [25][26][27][28][29]. Such models are today known as Coulomb models [27][28][29].…”

“…Such models are today known as Coulomb models [27][28][29]. The twostate Coulomb model with one neutral and one ionized state describes top-of-barrier processes in ion-atom collisions at low velocity [26,27]. It was extended to a multi-level in [28] with limitation on diabatic dissociation of channels i.e.…”

“…This is possible for t  ¥ when the diabatic levels come very close forming a multichannel band. Such transitions are called 'underbarrier' [26]. Our multichannel Coulomb model describes 'underbarrier' transitions between S 2 1 ( ) + ionized (without any limitation) coupled states of arbitrary spin S. This can be applied to strongly ionized large spin systems such as plasma [31].…”

Application of the Second Born Approximation to Excitation of Hydrogen Atoms by Protons and Antiprotons Impact

“…A two-state model applicable to topof-barrier processes in ion-atom collisions at low velocity is investigated in Ref. [7]. An expression for the Massey parameter of the transition n → n + 1 was derived and used it to compute ionization, capture, and excitation from states of high principal quantum number in proton-hydrogen atom collisions.…”

“…In general, the second Born approximation in the case of the 2s−3s excitation plays a different rule than in the 2s−2s one. The second Born approximation allows for two-stage processes of the form i−n−f where n denotes an arbitrary intermediate state, and it involves an infinite summation over n. According to the calculations of Tantawi [7] and the classical trajectory Monte Carlo calculations of Olson, [24] capture from an initial excited state occurs to the resonant state is much greater than to other states. Also Olson [24] reported that the electron capture can be neglected at energies above 30 keV.…”