Application of a theory of large amplitude collective motion to a generalized landscape model

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Abstract
The classical theory of large amplitude collective motion described in a previous paper is applied to a model with three degrees of freedom, in which the potential energy function has landscape features such as a valley which provides the easiest means, both classically and quantum mechanically, for a ‘‘particle’’ to escape from the center of the potential, a local minimum, to the ‘‘outside world.’’ We analyze exhaustively the problem of decoupling two collective degrees of freedom from the original three coordinates. We compute the two-dimensional surface to which the collective motion is (approximately) confined. This function in turn determines the collective Hamiltonian. We suggest and apply various criteria for measuring the goodness of the decoupling, and achieve a clear understanding of the domain of applicability of the analysis.