Transitions of electrons from a bound state into the continuous spectrum. Quadratic approximation in a model of a short-range potential

The destruction of negative ions in slow collisions with atoms: Taking into account the quantum-mechanical character of nuclear motions

“…(5) and (7), we should select those that, in combination with a certain contour selection, pro vide the fulfillment of condition (3). An analysis similar to that performed in [4,5] shows that the conditions specified are satisfied by solutions f 3 , F 3 to Eqs. (5), (7), which decrease in sector 3 (Fig.…”

“…An analysis shows that only terms with f 2 F 1 for the L 1 contour and terms with f 1 F 2 for the L 2 contour have the t 0 = -ax saddle point. Calculations according to the The amplitude of electron transition into the continu ous spectrum state with momentum k is calculated in the x → +∞ limit as in [3][4][5]; it is (9) and the wave function describing the motion of nuclei is…”

“…tron volt fractions. However, at such energies, it can not be assumed (as is done in [2][3][4][5]) that atoms move along a given trajectory at a certain rate, and changes in electron energy do not influence the motion of atoms. It follows that the development of a model under consideration should be related to the necessity of jointly considering atom and electron motions, especially if the abstraction reaction is considered close to the reaction threshold.…”

“…The transition probabil ity is then described by the Landau-Zener equation [1]. Transition probability equations for the interac tion of one discrete level with a continuous spectrum were obtained in [2][3][4][5], where this problem was con sidered for the example of the destruction of a negative ion in collisions with an atom A + В -→ A + B + е (A and B are atoms of different elements). The analysis was based on the assumption of discrete level crossing with a continuous spectrum at a critical distance R ≈ R 0 .…”

“…Electron abstraction is therefore only related to the radial motion of atoms. As in [2][3][4][5], the wave function of the additional electron is assumed to be spherically symmetrical, and electron-atom inter actions are described using the delta function model. The logarithmic derivative of the wave function at r = 0 (r is the coordinate of the electron) is then a function of interatomic distance, f(R 0 -R), rather than time.…”