Recursion analysis of the configurationalhyphen;coordinate model for equal force constants

摘要

For transitions between two offset oscillators with equal force constants, the optical band shapes are described by the distributionWpugiving the probability that the optical transition is accompanied by the generation ofpuphonons. For the Condon approximation and for thermal equilibrium among the initialhyphen;oscillator vibrational levels,Wpuis shown through the Manneback recursion formulas for the overlap integrals to satisfy the recursion formulaS0mvWpuplus;1plus;puWpuminus;S01plus;mvWpuminus;1equals;0.S0and mvare offset and temperature parameters, respectively. From thisWpurecursion formula, the moments of theWpudistribution, its approximate forms, its exact expression, and numerical values are obtained in simple ways.