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A measurement is reported of the spectrum of y rays from the reaction iT+d^n+n+y (1) for r\~ mesons stopped in liquid deuterium. A 180-deg-focusing y-ray pair spectrometer 1 with an energy resolution of 1% was used as the detector. The measured spectrum was compared with theoretical spectra yielding a value for the neutron-neutron singlet S-state scattering length a. It is well known from existing experimental results that for the nucleon-nucleon interaction the np and pp singlet state scattering lengths differ considerably. The apparent violation of charge independence has stimulated considerable work in attempts at a reasonable explanation. 2-6 One of the desirable pieces of information to help clarify the situation is the nn scattering length.One of the cleanest ways of measuring a is by means of Reaction (1), since in the final state only the two neutrons interact strongly. Phillips and Crowe 7 have measured the y-ray spectrum from this reaction and obtained a value for a of -15.9 F with probable errors of -<*> F and +7.4 F. A recent measurement by Cerineo et al. 8 of the proton spectrum from the d(n,p)2n reaction yields a value for a of -21.7 ± 1 F. Although the statistical accuracy of this latter experiment is quite good, there seems to be considerable uncertainty in the assumptions used in the theoretical analysis.A detailed description of the experimental setup for the present measurement is given in reference 1. 7r~ mesons from the Berkeley 184-in. synchrocyclotron were stopped in liquid hydrogen and also in liquid deuterium. The spectrum of y rays from the radiative reaction in hydrogen, 77 +p-~n+y,and Reaction (1) in deuterium were both measured. Identical spectrometer settings were employed for the two measurements. The measured deuterium spectrum was compared with theory in a manner identical to that employed by Phillips and Crowe. 7 In this analysis the energy resolution function for the spectrometer is folded into theoretical spectra evaluated for different values of the nn scattering length. The scattering length is then determined by the best fit of the measured spectrum with the folded theoretical spectra.A theoretical calculation of the spectra has been made by Watson and Stuart 9 who employ the impulse approximation and consider the two finalstate neutrons to interact only in the singlet S state. The nn wave function is approximated by a square well with the correct scattering length and effective range r 0 . For the deuteron S state the Hulthe'n wave function (e~a r -e~@ r )/r is employed. The validity of the approximations made in the calculation are discussed by Watson and Stuart and also by McVoy. 10 Calculations made by McVoy of the integrals which occur in the formula for the spectra were used by us in the numerical calculation. An IBM 7074 computer was employed. For this calculation the following constants were used: r 0 = 2.65 F, /x = 139.58 MeV, M W /JLL = 6.7310, a/\i = 0.3274, /3/JLL = 1.54, [M ~(M n -Mp) -Bo]/M n = 0.9141 /x. Here, /x is the TTmeson mass, M n the neutron mass, Mp...

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