We investigate here the origin of nuclear levelwidth as an effect of the coupling of particle mode and the surface vibration mode of the nucleus. This interaction is taken to be stochastic in nature, characterized by a single correlation timet₀, the random nature of the interaction originating from the partition of the total hamiltonian into those of the two modes. The Redfield equation of motion for the density matrix for the particle mode is solved. The solution of the Redfield equation shows that the occupation number in any particle state decays with a time constant depending on the correlation timet₀ and the quantum-mechanical matrix elements of the interaction hamiltonian. The inverse of this decay time will give the width of this level. Numerical calculations have been done for₈₂²⁰⁷Pb₁₂₅.