We have measured the total ionisation cross section Qion(g) and the large angle differential cross section s(¿, g) for the system He(21S, 23S)+ Ar, N2 at energies 0.05 <Ec.m. (eV) <6. This energy range is covered by applying two different discharge sources for the production of metastable atoms. In the atomic beam the He(23S) level is most abundant with relative populations C = 0.91±0.01 and C = 0.96±0.01 for thermal energy range and the superthermal energy range, respectively. A quench lamp is used for the quenching of the (21S) level population. In the thermal energy range, s(¿, g) and Qion(g) are in fair agreement with experimental results of other authors and with calculated cross sections based on the optical potential given by Siska. In the superthermal energy range, the He(23S)+Ar optical potential is modified to describe our experimental data. The slope of the repulsive branch of the real potential is increased for r <2.85 Å; in the imaginary potential a saturation to a constant (or even decreasing) value for internuclear distances less than 2.5 Å is introduced.