Rotation-vibration excitation using the infinite order sudden approximation for rotational transitions: Li+–N2

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Abstract
The rotational transitions in a collision of Li+ with N2 at 4.23 eV (center of mass) have been treated in the infinite order sudden approximation while treating the vibrational transitions in close coupling. A number of new problems were encountered and solved. The solution of the close coupling equations for the long range ion–molecule interaction was facilitated by use of an asymptotic ending technique. Due to the high energy of the collision and the extent of the potential, as many as 10 000 relative angular momentum states were required. Solutions for the high angular momentum states were obtained by means of a Born‐like approximation. Intermediate angular momentum states were treated in the WKB approximation. Many low angular momentum states were obtained by solving the vibrationally close coupled equations, and a technique was developed by which it was possible to interpolate the magnitude and phase of the S‐matrix elements between relative angular momentum states, permitting the solution of the close coupling equations for far fewer angular momentum states than would otherwise be required. Since the phase of the S matrix varies rapidly with diatom orientation, the integration of the S matrix over molecular orientation requires a large number of Gauss integration points. To avoid this problem we used Filon quadrature which allows integration over several periods of the phase with just a few integration points. A fit to an a priori interaction potential for Li+–N2 was made. The calculations of integral and differential cross sections were made over a range of angles which covered the experimentally measured cross sections. The results of the calculation do not agree with the experiment.