Dispersion Theoretic Treatment for Nucleon-Nucleon Scattering at Large Impact Parameter

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Abstract
Chew-Mandelstam type integral equation for the nucleon-nucleon scattering is derived by assuming the analyticity properties of the scattering amplitude in the type of the Mandelstam representation, and the uncoupled equations are solved under the one-pion-exchange approximation provided that it is valid in the special region where the impact parameter is large enough. Comparison with semi-empirical phase shift given by Hamada and by Breit et al. shows that the impact parameter may be a useful measure of the reliability in the dispersion theoretic approach as well as in the potential theoretic one. The results of the comparison in the 3P-states are summarized as follows. (i) The one-pion-exchange contribution dominates the behavior of phase shift in the region where impact parameter is larger than 1.5 ∼2 pion Compton wavelengths. (ii) In the same region, the two pion and more massive states contributions can be approximated to a rather simple form which is absorbed in slight modification of the corresponding scattering length. (iii) The result of the pole approximation for the one-pion-exchange cut is very close to the exact one in the same region. The comparison in the 1S-states shows that there is no region where the behavior of 1S-phase shift is dominated by the one-pion-exchange contribution. It is also shown that partial wave expansion may be inappropriate for the evaluation of higher partial wave (l ≥2), unless we use a further suitable approximation.

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