Research

 

Collinear inelastic collisions of an atom and a diatomic molecule using operator methods

 

T. Wendler^a, J. Récamier^b, and M. Berrondo^a

 

^a Dept. Physics and Astronomy, Brigham Young University, Provo, UT84602 USA.

^b Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, Cuernavaca, Morelos 62251, México.

 

Received 21 January 2013
Accepted 21 February 2013

 

Abstract

We calculate transition probabilities between vibrational levels of a diatomic molecule induced by an incident atom. Our prototype model is constructed treating the relative translation of the colliding species as a classical variable. The vibrational states of the diatomic molecule are treated quantum mechanically in terms of the evolution operator without involving wave functions. The corresponding equations of motion are coupled quasi-classically. For illustration purposes we present applications to the time dependence of transition probabilities for different initial and final states as well as a canonical ensemble of initial conditions.

Keywords: Inelastic; collisions; Lie; algebraic; harmonic; oscillator.

 

Resumen

Calculamos probabilidades de transición entre estados vibracionales de una molécula diatómica inducidas por un átomo incidente. El modelo prototipo trata el movimiento de traslación relativo como una variable clásica. Los estados vibracionales de la molecula diatómica se tratan cuánticamente en términos del operador de evolucián, sin involucrar funciones de onda. Las ecuaciones de movimiento correspondientes se acoplan cuasi-clásicamente. A manera de ilustración presentamos aplicaciones a la dependencia temporal de probabilidades de transición para diferentes estados inicial y final así como para un ensamble canónico de condiciones iniciales.

Descriptores: Colisiones; inelásticas; álgebras; Lie; oscilador; armónico.

 

PACS: 03.65.Fd; 02.30.Tb; 42.50

 

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