Measurement of the neutron-neutron scattering length using theπ−dcapture reaction

Abstract

We have determined a value for the ${}^{1}{S}_{0}$ neutron-neutron scattering length (${a}_{\mathit{nn}}$) from high-precision measurements of time-of-flight spectra of neutrons from the $^{2}\mathrm{H}$$({\ensuremath{\pi}}^{\ensuremath{-}},n \ensuremath{\gamma}) n$ capture reaction. The measurements were done at the Los Alamos Meson Physics Facility by the E1286 Collaboration. The high spatial resolution of our \ensuremath{\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 ${a}_{\mathit{nn}}=\ensuremath{-}18.63\ifmmode\pm\else\textpm\fi{}0.10$ (statistical) \ifmmode\pm\else\textpm\fi{} 0.44 (systematic) \ifmmode\pm\else\textpm\fi{} 0.30 (theoretical) fm. This result is consistent with previous determinations of ${a}_{\mathit{nn}}$ from the ${\ensuremath{\pi}}^{\ensuremath{-}}d$ 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 ${a}_{\mathit{nn}}$ by 0.33 fm over the analysis done using a nonrelativistic phase-space factor. Combining the present result with the previous ones from ${\ensuremath{\pi}}^{\ensuremath{-}}d$ capture gives ${a}_{\mathit{nn}}=\ensuremath{-}18.63\ifmmode\pm\else\textpm\fi{}0.27(\mathrm{expt})\ifmmode\pm\else\textpm\fi{}0.30$ fm (theory). For the first time the combined statistical and systematic experimental uncertainty in ${a}_{\mathit{nn}}$ is smaller than the theoretical uncertainty and comparable to the uncertainty in the proton-proton ${}^{1}{S}_{0}$ scattering length (${a}_{\mathit{pp}}$). This average value of ${a}_{\mathit{nn}}$ when corrected for the magnetic-moment interaction of the two neutrons becomes \ensuremath{-}18.9 \ifmmode\pm\else\textpm\fi{} 0.4 fm, which is 1.6 \ifmmode\pm\else\textpm\fi{} 0.5 fm different from the recommended value of ${a}_{\mathit{pp}}$, thereby confirming charge symmetry breaking at the 1% confidence level.