Effective one-dimensional equation of motion for nuclear fission

An approach for describing the dynamics of nuclear fission in the framework of generalized quantum mechanics is discussed. The collective kinetic energy is assumed to be two dimensional, and the reduced mass is allowed to vary with the coordinates. The generalized calculus of variation is employed for minimizing the action after being properly quantized as required by Hamilton's principle, employing a curvilinear coordinate system. The corresponding Euler Lagrange equation is identified as the required generalized equation of motion. The proposed generalized two-dimensional equation of motion is separated into a vibrational eigenvalue equation and a set of coupled-channel one-dimensional equations which describe the translational motion, by exploiting the completeness of the vibrational eigenfunctions. Such a system of coupled equations can be decoupled by replacing the coupling matrix elements by a nonlocal interaction, which can be rendered local after employing the effective mass approximation. As a consequence this differential equation is provided with an effective mass, an effective potential barrier, and a differential boundary term which is responsible for restoring the self-adjointness of the kinetic energy differential operator.