Proton-Proton Final-State Interaction in theH2(p,n)2pReaction

Neutron spectra from the ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(p,n)2p$ reaction have been measured at nine proton energies between 16 and 26 MeV. The high-energy portions of the neutron spectra taken at a laboratory angle of 3.5° have been analyzed with impulse approximation calculations of the proton-proton final-state interaction to extract the proton-proton scattering length. The average value of the scattering length determined from these measurements is within approximately 1 fm of the - 7.8-fm result of $pp$ scattering but is not independent of the details of the comparison of experimental and calculated spectra. Experimental requirements for a determination of the neutron-neutron scattering length from the ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(n,p)2n$ reaction are discussed.