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Using a number of nonlocal, two-term, separable, nucleon–nucleon interactions and their phase-equivalent transforms, it is shown that the production of s-wave pions near the threshold in the reaction p + p → π+ + d is sensitive, not only to the D-state probability of the deuteron and the nonlocality of the interaction, but also to the off-shell behavior of the interaction. The reaction, therefore, cannot serve, in the context of simple two-term separable potentials, as an effective criterion to constrain the value of the D-state probability of the deuteron to better than the present range of 3–8%. Results are presented also for Reid soft-core local interaction where we find that the off-shell effects are constrained by the deuteron form factor.

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