Semiclassical description of collisionally induced rainbow satellites: a model study

Abstract

We apply the uniform Airy approximation (Beuc and Horvatic 1992 J. Phys. B: At. Mol. Opt. Phys. 25 1497) to the analytical model proposed by Devdariani et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 2469. The model describes asymptotically forbidden quasimolecular optical transitions within the frame of the semiclassical approach. Our results support conclusions that the uniform Airy approximation, originally developed for the asymptotically allowed transitions, is applicable to a broad class of asymptotically forbidden but collisionally assisted optical transitions as well. In addition, we present a new transitional formula and discuss some further approximations.

On the Approximate Evaluation of Some Oscillatory Integrals

“…For simplicity, we take ( ) 1 gu = in all the examples. The dependence of the integral (6) on the variable transition dipole moment was discussed by Beuc et al in [5]. Peer-reviewed version available at Atoms 2019, 7, 47; doi:10.3390/atoms7020047…”

“…In some range of the parameter a the stationary points are real and The leading-order uniform approximation in the case of the fold catastrophe is given by [4] ( aa ) and enables analytical continuation from the region of real stationary points into the region of complex ones. The transitional approximation is given by [5] ( )…”

“…The motivation to study these types of integrals originates from the investigation of optical spectra of diatomic molecules [5]. For example, in the semiclassical approximation the matrix element of the dipole moment () DR for the optical transition is proportional to the integral [12] ( )…”

On the Approximate Evaluation of Some Oscillatory Integrals

“…The transitional approximation I tr F (a) reproduces the uniform approximation I F (a) on the neighbourhood of a ≈ a e (I tr F (a e ) = I F (a e )) and enables analytical continuation from the region of real stationary points into the region of complex ones. The transitional approximation is given by [9],…”

“…The motivation to study these types of integrals originates from the investigation of optical spectra of diatomic molecules [9]. For example, in the semiclassical approximation the matrix element of the dipole moment D(R) for the optical transition is proportional to the integral [11]…”