NEUTRON-PROTON EFFECTIVE RANGE PARAMETERS AND ZERO-ENERGY SHAPE DEPENDENCE

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 σ0 = 20.4287 ± 0.0078 b, the singlet apparent effective range rs = 2.754 ± 0.018stat ± 0.056syst fm, and improves the error slightly on the parahydrogen coherent scattering length, ac = -3.7406 ± 0.0010 fm. The triplet and singlet scattering lengths and the triplet mixed effective range are calculated to be at = 5.4114 ± 0.0015 fm, as = -23.7153 ± 0.0043 fm, and ρt(0,-εt) = 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 εt. These are determined to be ρt(0,0) = 1.705 ± 0.023 fm and ρs(0,0) = 2.665 ± 0.056 fm. This determination of ρt(0,0) and ρs(0,0) is most sensitive to the sparse data between about 20 and 600 keV, where the correlation between the determined values of ρt(0,0) and ρs(0,0) is at a minimum. This correlation is responsible for the large systematic error in rs. More precise data in this range are needed. The present data do not event determine (with confidence) that ρt(0,0) ≠ ρt(0, -εt), referred to here as ''zero-energy shape dependence''. The widely used measurement of σ0 = 20.491 ± 0.014 b from W. Dilg, Phys. Rev. C 11, 103 (1975), is argued to be in error