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 $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\overline{N}N$ amplitude is approximated by a nucleon pole term only; in the second case it is approximated by a nucleon pole term plus a $\ensuremath{\Delta}(1236)$ pole term. It is found that for the physical value of the $\ensuremath{\Delta}(1236)$ width, ${\ensuremath{\Gamma}}_{\ensuremath{\Delta}}=120$ 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 ${\ensuremath{\Gamma}}_{\ensuremath{\Delta}}$.
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