A LEAST-SQUARES METHOD FOR THE ANALYSIS OF PROTON-PROTON SCATTERING DATA,
Abstract
A detailed method is developed for the analysis of low-energy proton-proton scattering experiments. Convenient formulas for the differential scattering cross section and for the polarization are derived from the scattering amplitudes, and a completely analytic leastsquares method is derived for fitting the theoretical expression to the experimental data. Contributions to the cross section from scattering in the S, P, and D states are included; contributions from tensor and spin-orbit forces are included in addition to those from central forces. The effects of vacuum polarization, of scattering in states of higher angular momentum, and of coupling between states of same J but different L are not computed by inclusion in the scattering amplitudes, but provision has been made to include these effects when calculated separately. The treatment is relativistically correct, but does not include dynamic relativistic effects which are negligible at low energy. Two Fortran-language computer programs are presented; the first makes the least-squares analysis to derive phase shifts from the experimental scattering data, while the second evaluates the theoretical expressions for the cross section and polarization for given values of the phase shifts. The estimation of uncertainties in the derived phase shifts is discussed in some detail. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1964
- Accession Number
- AD0610004
Entities
People
- David J. Knecht
Organizations
- Air Force Research Laboratory