Nucleon-nucleon inelasticities below 1000 MeV

NN inelasticities are determined from a helicity partial-wave decomposition of a peripheral model for $\mathrm{NN}\to \mathrm{NN}\pi$. The helicity partial-wave formalism is presented for the reaction $\mathrm{NN}\to \mathrm{NN}\pi$ and the relation between partial-wave helicity amplitudes and NN partial-wave reaction cross sections is derived. Partial-wave cross sections are projected out of the pion- and rho-exchange diagrams with NN and $\mathrm{N}\Delta$ intermediate states. Below 1000 MeV one obtains significant contributions to the total cross section from many isospin one partial waves while isospin zero inelasticities are non-negligible only for $J=1\mathrm{}$. Large ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}F_3^{}{}_{}{}^{}$ inelasticities originate in these first-order Born-approximation terms for $\mathrm{NN}\to \mathrm{NN}\pi$ which have no resonance behavior in the NN system. The effects of omitting rho exchange and form factors from the model are studied and determined to be small for $L\gtrsim 3$. Comparisons are made with other calculations of NN inelasticities and show qualitative agreement.