We present theoretical H alpha and HI infrared recombination line calc
ulations for low-density discs around B stars. Such a disc shows no vi
sible emission in H alpha, while the HI IR recombination lines are in
emission. This phenomenon has been found in the spectrum of the B0.2V
star, tau Sco and could be simulated with a simple disc model. As an e
xtension of that particular case we calculate the entire IR HI line sp
ectrum of a normal B star surrounded by a low-density disc with a theo
retical curve of growth for HI IR line fluxes, which we introduce as a
tool for studying low-density discs. We find that IR emission lines m
ay be detectable for densities up to about 10(-14) gcm(-3) which is a
factor 10(2) - 10(3) lower than typically found in Be stars. For diffe
rent spectral types, B0, B2, B5 and B8 we determined the density range
for which emission is prominent in the IR recombination lines but not
in Ha alpha.