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

The low-energy np elastic-scattering parameters, including the zero-energy free-proton cross section ${\sigma }_0$, 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: ${\sigma }_0=20.4278(78)$ 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.

Figure 1

The effect on the calculated cross section of the correlation between ${\rho }_t(0,0)$ and ${\rho }_s(0,0)$. (line at zero) $r_t={\rho }_t(0,0),r_s={\rho }_s(0,0)$ from (10); (upper curve) $r_t={\rho }_t(0,0)+0.025$ fm, $r_s={\rho }_s(0,0)$; (middle curve) $r_t={\rho }_t(0,0)+0.025$ fm, $r_s={\rho }_s(0,0)+0.059$ fm; and (lower curve) $r_t={\rho }_t(0,0),r_s={\rho }_s(0,0)+0.059$ fm.

Figure 2

Cross-section differences. The cross section calculated with the parameters from Eq. (9) is subtracted from data and calculations made with other choices of parameters. The curves form the one-standard-deviation envelope for the cross section calculated with ${\rho }_t(0,0)$ and ${\rho }_s(0,0)$ from Eq. (10); (line at zero) Shape-independent parameters from Eq. (9); (upper curve) $r_t={\rho }_t(0,0)-0.025$ fm, $r_s={\rho }_s(0,0)-0.059$ fm; and (lower curve) $r_t={\rho }_t(0,0)+0.025$ fm, $r_s={\rho }_s(0,0)+0.059$ fm. The lower curve is below and barely separated from the line. Data: [16] (Koester), [28] (Fujita), [17] (Engelke), [31] (Poenitz), [27] (Kirilyuk), and [32] (Lampi). Off-scale data are omitted; these have error bars that would span the entire vertical range of the plot.