Sudden Approximation Theory of Vibrational Excitation

The time-independent quantal sudden theory of vibrational excitation is presented for a collinear system. A new semiclassical sudden theory is also obtained directly from the quantal theory by simply replacing quantal oscillator wavefunctions by their JWKB approximations. For the atom-harmonic oscillator system with the Jackson-Matt interaction potential, closed-form expressions are obtained for the quantal and semiclassical scattering matrices. The unitarity of the quantal and semiclassical S matrices and the conditions for the validity of the sudden approximation are discussed.