Time dependent nucleation. II. A semiclassical approach

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Abstract
The continuum approximation of the Becker-Doring birth and death equations [B. Shizgal and J. C. Barrett, J. Chem. Phys. 91, 6505 (1989)] leads to a Fokker-Planck equation for the continuous cluster distribution. This linear Fokker-Planck equation is solved with the expansion of the cluster distribution function in the eigenfunctions of the Fokker-Planck operator. The Fokker-Planck eigenvalue problem can be transformed into an equivalent Schrodinger equation. In this paper, the semiclassical Wentzel-Kramers-Brillouin (WKB) method and the corresponding supersymmetric WKB method are employed in the determination of the eigenvalues and eigenfunctions of the equivalent Schrodinger equation. We compare the approximate results with those obtained with a standard discretization scheme. We obtain eigenvalues and eigenfunctions of the Fokker-Planck operator which are in good agreement with the exact ones. The nucleation fluxes and associated time lags are also considered.