Helium at pressures ranging from 0.5 to 8 bar is excited by an intense e-beam. The absolute population densities of the He(2 ¹P), He(2 ³P) and He₂^*(a,v), v=0, 1, 2 states are determined by measuring the transient absorption of probe light delivered by a dye laser. The experimental data are readily described by a kinetic model taking into account the excitation and the de-excitation processes. The recombination of He₂⁺ by a termolecular reaction with e+He to He(2 ³P) as proposed by Bates (1984) is confirmed quantitatively. The rate constants for the termolecular reactions of He(2 ¹P) and He(2 ³P) were deduced to be (1.8+or-0.4)*10^-31 cm⁶ s^-1 and (1.6+or-0.4)*10^-32 cm⁶ s^-1 respectively. The rotational and vibrational relaxation of He₂(a) by helium is investigated.