Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering

Abstract

The two-pion-exchange contribution to nucleon-nucleon scattering is calculated, following the method of Goldberger, Grisaru, MacDowell, and Wong. The results are shown for two cases. In the first case, the input $\pi \pi \to \overline{N}N$ amplitude is approximated by a nucleon pole term only; in the second case it is approximated by a nucleon pole term plus a $\Delta \mathrm{}\left(1236\right)\mathrm{}$ pole term. It is found that for the physical value of the $\Delta \mathrm{}\left(1236\right)\mathrm{}$ width, ${\Gamma }_{\Delta }=120\mathrm{}$ MeV, there is very little difference for the two cases in the resulting effect on nucleon-nucleon scattering below 400 MeV. The model is mathematically equivalent to the Amati-Leader-Vitale approach for all but ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ $\mathrm{NN}$ partial waves. The results are found to be sensitive to the value of ${\Gamma }_{\Delta }$.