The low-energy np elastic-scattering parameters, including the zero-energy free-proton cross section σ 0 , are determined with a substantially improved precision over previous values, using available np-scattering data below 3 MeV. The method includes a careful handling of a correlation between the singlet and triplet effective ranges which does not seem to have been previously treated. This correlation is responsible for a large systematic error in the singlet effective range and spoils a model-independent determination of the zero-energy triplet effective range. It is shown that improved cross section measurements between 20 and 600 keV (laboratory neutron energy) are needed to overcome the degrading effect of this correlation. The values obtained for the zero-energy cross section and the scattering lengths and effective ranges for the singlet and triplet are: σ 0 = 20.4278(78) b, a t = 5.4112(15) fm, a s = −23.7148(43) fm, r t = 1.7436(19) fm, r s = 2.750(18) fm (systematic error: −0.059 fm). The widely used measurement of the zero-energy free-proton elastic cross section from W. Dilg, Phys. Rev. C 11, 103 (1975), appears to be in error.This article presents a model-independent method for determining the zero-energy cross section σ 0 and effectiverange theory (ERT) parameters for np elastic scattering from low-energy data. The method is similar to that presented in Ref.[1] but contains some improvements that permit the zero-energy triplet effective range to be obtained from data. It is demonstrated that there is a range of energy most sensitive to a determination of this quantity and that better measurements are needed in that range, if it is to be obtained with sufficient precision to be of any use in comparing predictions from NN potential models.NN potential models [2][3][4][5] can determine the ERT parameters, but small errors are introduced if low-energy data are not included (or are inaccurate) in the partial-wave analyses used to fit the model parameters [3]. Because NN potential models are often used in low-energy applications [6][7][8], it is important that they incorporate accurate low-energy data. Some NN potential models [5,9,10] use the Dilg measurement of σ 0 , some models [2][3][4]8,11,12] use an average of the Dilg and Houk values, but none seem to use the more precise Koester et al. value (Table I).The Dilg determination of σ 0 is the only one that required molecular corrections but did not obtain them as part of the experiment. That experiment performed measurements on water and three hydrocarbons at a single energy, 132 eV, where the molecular corrections are small but not negligible. There was, therefore, no way of determining the molecular corrections, which require measurements at two or more energies for each target. The corrections used were asymptotic extrapolations to 132 eV from values taken from the literature, which described scattering on water and benzene at energies from about 1 to 15 eV. Prior to the Koester et al. σ 0 , the Dilg σ 0 was not quite significantly deviant from th...