It is well known that cometary pickup ions (e.g., H2O+, OH+, O+, CO+, H+) initially form a ring-beam distribution in the solar wind reference frame, which is highly unstable to the growth of MHD waves (such as ion-cyclotron waves). The low-frequency magnetic fluctuations (or waves), which were observed upstream of comet Halley, cannot only pitch angle scatter the pickup ions so that the distribution becomes at least partially isotropized, but also stochastically accelerate the ions, resulting in the energetic ion populations observed in the vicinity of comet Halley. We have used numerical solutions of the quasi-linear diffusion equation to investigate the cometary ion pickup process at comet Halley. Both pitch angle and energy diffusion are taken into account. Many quasi-linear models of cometary pickup ions exist which involve one type of diffusion or the other but not both types at once. We find that the pitch angle scattering occurs faster than the energy diffusion, as expected, Moreover, our results demonstrate that the distribution of accelerated energetic ions is more isotropic than that of ions which have just been picked up. In fact, the ion distribution function on the initial pickup shell is quite anisotropic, even close to the comet Halley bow shock. ¿ American Geophysical Union 1991