The process of the slowing down of 3.5 MeV fusion alpha particles in dense thermonuclear plasmas, characterizing the inertial confinement fusion (ICF) scheme, is investigated on the basis of a full dielectric theory that describes both the electron response and the ion response. It is shown that, with increasing plasma density, the collective behaviour of the plasma becomes more and more important in determining the alpha particle energy losses. The electrostatic potential and the stopping power of alpha particles are computed for different particle velocities and temperature ratios, Te/Ti. In addition, the fuel-areal density, ρR, is calculated and compared with the results of recent theories. It is demonstrated that individual particle models overestimate ρR values of ICF alphas by almost 20%