Hemiquantal mechanics. I. Vibrational predissociation of van der Waals molecules

The ‘‘hemiquantal’’ equations (HQE), which pertain to a system consisting of a quantally-behaving (‘‘light’’) subsystem coupled to a classically-behaving (‘‘heavy’’) one, result from a partial classical limit of Heisenberg’s equations of motion. In effect, all heavy particles are required to follow precisely their classical trajectories. The HQE are applied to vibrational predissociation in a collinear model of the van der Waals molecule He ⋅ ⋅ ⋅I2(B). Here, the vibration of I2 is the classical subsystem and the motion of He relative to the center of mass of I2 is the quantal subsystem. In this case, the HQE comprise a partial differential equation (Schrödinger’s equation for the He motion) coupled to two ordinary differential equations (Hamilton’s equations for the I2 vibration). These were solved numerically on the CYBER 205 supercomputer by means of an algorithm that uses a second-order predictor–corrector for Hamilton’s equations and second-order time differencing for Schrödinger’s equation. A scheme based on the fast Fourier transform was used to evaluate the spatial derivative of the wave function. The computed rates of vibrational predissociation are compared with the results of previous quasiclassical and fully quantal calculations and with experimental results.