The Scattering of Slow Neutrons by Bound Protons. I. Methods of Calculation

The mathematical problem of the scattering of slow neutrons by chemically bound protons is stated in terms of a boundary condition and its equivalent integral equation. By means of the latter it is possible to calculate corrections to the results of Fermi which can be considered as the first approximation to the more accurate equations. The method is applied to free protons, and it is shown how the well-known results for this case are obtained from the more general equations. This special case allows also an estimate (${10}^{-3\mathrm{}}$) of the order of the corrections in the case of chemically bound protons in agreement with general estimates in connection with Eq. (8.4) of Section 7 of the present paper and the application to harmonic oscillator binding made in the succeeding paper jointly with P. R. Zilsel. The corrections discussed are greater than the inaccuracies of the boundary condition formulation which are of the order ${10}^{-5\mathrm{}}$.