CALCULATION OF VIBRATIONAL EXCITATION OF DIATOMIC MOLECULES BELOW DISSOCIATIVE ATTACHMENT THRESHOLD

Abstract

The problem of vibrational excitation (VE) of diatomic molecules by low-energy electrons below the threshold of dissociative attachment (DA) is a difficult and interesting problem. One of the interesting features is the unusual series of oscillations in VE cross section converging to the DA threshold, sometimes called the boomerang oscillations [1,2] see Figure 1. These oscillations are very sensitive to minor changes of underlying forces and represent a very stringent test of the theory used for the calculation of the VE cross section. The calculation of the VE cross section in this case is difficult because for energies below the DA threshold we have to solve scattering integral equations describing the motion of the nuclei in the resonance state at a negative energy. Scattering equations are always solved for positive energies since at these energies the particles may escape the scattering region completing the process of scattering. In such a case the leading term and the integral kernel are bounded functions provided the interaction potential is bounded. If the energy is negative the particles cannot escape. The leading term in scattering integral equation represents usually the free particle wave function which at negative energies diverges at large internuclear distances. We are therefore faced with the problem to solve integral equation with diverging leading term and diverging kernel. Since the underlying forces always decay at large distances we can restrict the integration to a finite range (0,R) where however R might be large for long range forces of polarization type. To our knowledge such problem has never been discussed in the literature. To tackle this problem we make use of the R-matrix representation of scattering Green's function recently proposed by the authors [3, 4] and perform detailed numerical study of convergence of the VE cross section in dependence of all parameters involved.