The behaviour of reactive scattering at ultracold temperatures is explored by calculating the real and imaginary parts of the scattering length for the reaction of F with a molecule composed of a pair of pseudo-hydrogen atoms of arbitrary mass. The origin of a low energy feature in the cross section for the reaction of F with H₂ and its absence for the reaction with D₂ is investigated. Close-coupling calculations of the scattering matrix show that the F–H₂ feature arises from the presence of a virtual state associated with the van der Waals well in the entrance channel and that the virtual state is responsible for the enhanced zero temperature rate coefficient of the F–H₂ reaction. For a mass of about 1.12 hydrogen masses the virtual state turns into a zero energy resonance and the corresponding zero temperature rate coefficient is 1 × 10⁻⁹ cm³ s⁻¹ despite an energy barrier of 300 K. Evidence in support of the virtual state is also provided by the detection of a deep Ramsauer–Townsend minimum in the elastic component of the total cross section for F–H₂ which the present calculations predict to occur at low energies.