Review of Indirect Methods Used to Determine the ${}^1{S}_0$ Neutron-Neutron Scattering Length

Abstract

We have determined a value for the ${}^1{S}_0$ neutron-neutron scattering length ($a_{nn}$) from high-precision measurements of time-of-flight spectra of neutrons from the ${}^{2}H(\ddot{I}{€}^{-},n{\hat{I}}^3)n$ capture reaction. The measurements were done at the Los Alamos Meson Physics Facility by the E1286 collaboration. The high spatial resolution of our gamma-ray detector enabled us to make a detailed assessment of the systematic uncertainties in our techniques. The value obtained in the present work is $a_{nn}=-18$.63 $\pm$0.10 (statistical) $\pm$ 0.44 (systematic) $\pm$ 0.30 (theoretical) fm. This result is consistent with previous determinations of $a_{nn}$ from the $\ddot{I}{€}^{-}d$ capture reaction. We found that the analysis of the data with calculations that use a relativistic phase-space factor gives a more negative value for $a_{nn}$ by 0.33 fm over the analysis done using a nonrelativistic phase-space factor. Combining the present result with the previous ones from $\ddot{I}{€}^{-}d$ capture gives: $a_{nn}=-18$.63 $\pm$ 0.27 (expt) $\pm$ 0.30 fm (theory). For the first time the combined statistical and systematic experimental uncertainty in $a_{nn}$ is smaller than the theoretical uncertainty and comparable to the uncertainty in the proton-proton ${}^1{S}_0$ scattering length ($a_{pp}$). This average value of $a_{nn}$ when corrected for the magnetic-moment interaction of the two neutrons becomes -18.9 $\pm$ 0.4 fm which is 1.6 $\pm$ 0.5 fm different from the recommended value of $a_{pp}$, thereby confirming charge symmetry breaking at the 1% confidence level.

8 pages, 1 figure and 3 tables