Dating geological samples by the 40Ar/39Ar method involves an irradiation in a reactor during which interfering nuclear reactions also occur that require corrections to be made to the observed data. The (39Ar/37Ar)Ca and (36Ar/37Ar)Ca correction factors for HIFAR reactor agree with those reported for other reactors, whereas the (40Ar/39Ar)K correction factor (about 0.3) is more than an order of magnitude greater than that found for most other reactors. A positive correlation found between reported thermal/fast neutron flux ratios and the (40Ar/39Ar)K correction factors for different reactors leads to the inference that significant 40Ar can be produced by the 40K(n,p40Ar reaction through interaction with thermal neutrons. This effect of thermal neutrons also causes substantial variation (40Ar/39Ar)K as a function of position in the reactor. Cadmium shielding has been used to modulate these effects over about 2 orders of magnitude and thereby to reproduce artifically the entire range of (40Ar/39Ar)K values reported for other reactors. Elimination of the thermal neutron interference (via Cd shielding ?0.5 mm) can increase the range of useful neutron fluencies by about an order of magnitude and also reduce corrections in young samples, where it can be relatively large.