The impact-parameter dependence of the total L-shell ionisation and of the L_alpha, L_beta, L_gamma and L_l X-ray production probabilities of Au by alpha -particles with energies of 12, 30, 40 and 50.8 MeV have been measured in the alpha -angle region 0.3 degrees -3 degrees . The experimental values are compared with the theoretical predictions of the semiclassical approximation, the binary encounter approximation and the plane-wave Born approximation ('low-energy SCA'). Serious deviations are found for projectile energies E>30 MeV. All three theories underestimate the recorded data. The discrepancy increases with increasing projectile energy, reaching a factor of about five at an energy of 50.8 MeV.