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A completely model-independent effective range theory fit to available, unpolarized, np scattering data below 3 MeV determines the zero-energy free proton cross section {sigma}{sub 0} = 20.4287 {+-} 0.0078 b, the singlet apparent effective range r{sub s} = 2.754 {+-} 0.018{sub stat} {+-} 0.056{sub syst} fm, and improves the error slightly on the parahydrogen coherent scattering length, a{sub c} = -3.7406 {+-} 0.0010 fm. The triplet and singlet scattering lengths and the triplet mixed effective range are calculated to be a{sub t} = 5.4114 {+-} 0.0015 fm, a{sub s} = -23.7153 {+-} 0.0043 fm, and {rho}{sub t}(0,-{epsilon}{sub t}) = 1.7468 {+-} 0.0019 fm. The model-independent analysis also determines the zero-energy effective ranges by treating them as separate fit parameters without the constraint from the deuteron binding energy {epsilon}{sub t}. These are determined to be {rho}{sub t}(0,0) = 1.705 {+-} 0.023 fm and {rho}{sub s}(0,0) = 2.665 {+-} 0.056 fm. This determination of {rho}{sub t}(0,0) and {rho}{sub s}(0,0) is most sensitive to the sparse data between about 20 and 600 keV, where the correlation between the determined values of {rho}{sub t}(0,0) and {rho}{sub s}(0,0) is at a minimum. This correlation is responsible for the large systematic error in r{sub s}. Moremore » precise data in this range are needed. The present data do not event determine (with confidence) that {rho}{sub t}(0,0) {ne} {rho}{sub t}(0, -{epsilon}{sub t}), referred to here as ''zero-energy shape dependence''. The widely used measurement of {sigma}{sub 0} = 20.491 {+-} 0.014 b from W. Dilg, Phys. Rev. C 11, 103 (1975), is argued to be in error.« less

Neutron-proton effective range parameters and zero-energy shape dependence