[en] Particle motion in a slowly modulated wave as studied. Recent results for the change in the adiabatic invariant due to separatrix crossing are used to calculate the diffusion coefficient for the adiabatic invariant of a particle moving in an amplitude modulated wave. It is argued that the calculated scaling also holds for the case of a narrow spectrum wave field. The present scaling law due to adiabatic invariant jumps, D/sub J approx. k/sub O/Δv/sub phi/³, differs substantially from the resonance broadening theory result D/sub RB/ approx. W/sub O/sup 3/4//k/sub O/sup 1/2/, where Δv/sub phi/ is the spectral width of the phase velocity, and W/sub O/ is the energy density of the wave field