Perturbation analysis of anharmonic relaxation and dissociation

✍ Scribed by John H. Kiefer

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 350 KB
• Volume: 24
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(74)85430-8

✦ Synopsis

A generalized perturbation analysis for anhzmonic population distriiutions during both relaxation and dissociation is developed. The method encompasses previous perturbation treatments of this problem and is applicable with or without V-V transfer. The resulting solution is also in general accord with the long-time solution of the simple harmonic oseiflator.

The differential equations which describe the time evolution of vibrational state populations are "stiff" equations [I] which can cause some difficulty in numerical integration [2,3]. However, this feature of the equations suggests an amenability to perturbation methods and such have been applied to specific examples of this problem (4,S]. Here we offer a more general perturbation solution for the long-time behaviour of the anharmonic oscillator distribution which encompasses these previous analyses and is valid whether V-V transfer processes are present or not. An important feature of the soIution is a general correspondence with the famifiar long-time solution of the simpte harmonic oscillator [6,7].

To exemplify the method-consider a homonuclear diatomic-oscillakr with d + 1 vibrational states. We formulate the goveining equations with the familiar assumptions: (i) only-transitions to adjacert states are allowed; and (ii)

the translatiorial and rotational states have their equilibrium distribution at temperature T. This somewhat unrealistic but usual model is chosen for simplicity in presentation. The perturbation method itself may be readily applied