Numerical Calculation of Vibrational Transition Probability for the Forced Morse Oscillator by Use of the Anharmonic Boson Operators

摘要

The vibrational transition probability expressions for the forced Morse oscillator have been derived using the commutation relations of the anharmonic Boson operators. The formulation is based on the collinear collision model with the exponential repulsive potential in the framework of semiclassical collision dynamics. The sample calculation results for H₂+ He collision system, where the anharmonicity is large, are in excellent agreement with those from an exact, numerical quantum mechanical study by Clark and Dickinson, using the reactance matrix. Our results, however, are markedly different from those of Ree, Kim and Shin`s in which they approximate the commutation operator I。 as unity, the harmonic oscillator limit. We have concluded that the quantum number dependence in I。 must be retained to get accurate vibrational transition probabilities for the Morse oscillator.