Crank-Nicholson solutions are obtained to the time-dependent Fokker-Planck equation for propagation in the interplanetary medium following a point in time injection of energetic solar particles and including the acceleration terms $$\frac{\partial }{{\partial T}}\left( {D_{TT} \frac{{\partial U}}{{\partial T}}} \right) - \frac{\partial }{{\partial T}}\left( {\frac{{D_{TT} U}}{{2T}}} \right)$$ . The diffusion coefficient in kinetic energyDTT is allowed to be either independent of radial distance,R(AU), or follow the lawDTT=D0T2R02/(A2+R2) in either case with the 1 AU value ofDTT at 10 MeV ranging between 10−4 (MeV)2 s−1 and zero. The spatial diffusion mean free path at the Earth's orbit is fixed at λ‖ AU at 10 MeV according to numerical estimates made by Moussas and Quenby. However, a variety ofR dependences are allowed. Reasonable agreement with experimental data out to 4 AU is obtained with the above values ofDTT and the spatial diffusion coefficientKr=K0R−2 forR«1 andKr=K0R0.4 forR»1 AU. It is only in the decay phases of prompt events as seen at 2–4 AU that significant differences in the temporal behaviour of the events can be distinguished, depending on the value ofDTT chosen within the above range. Experimental determination of the decay constant is difficult.