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Analytically soluble model for fusion time.

We derive an analytical expression for the essential parameters (viz., positions, heights, and curvatures) characterizing the extrema of the effective potential between two heavy ions. These parameters together with the energy are used to calculate, in closed form, the times for complete fusion above the Coulomb barrier. The method is found to work well for nuclear (and/or Coulomb) trajectories of zero or small orbital angular momentum when friction is absent. The inclusion of dissipation is shown to reduce the fusion time substantially for typical heavy-ion systems provided the energy satisfies certain kinematic constraints.