Impulse approximation in nuclear pion production reactions: Absence of a one-body operator

The impulse approximation of pion production reactions is studied by developing a relativistic formalism, consistent with that used to define the nucleon-nucleon potential. For plane wave initial states we find that the usual one-body (1B) expression O-1B is replaced by O-2B = -iK(m(pi)/2)O-1B/m(pi), where K(m(pi)/2) is the sum of all irreducible contributions to nucleon-nucleon scattering with energy transfer of m(pi)/2. We show that O-2B approximate to O-1B for plane wave initial states. For distorted waves, we find that the usual operator is replaced with a sum of two-body operators that are well approximated by the operator O-2B. Our new formalism solves the (previously ignored) problem of energy transfer forbidding a one-body impulse operator. Using a purely one pion exchange deuteron, the net result is that the impulse amplitude for np -> d pi(0) at threshold is enhanced by a factor of approximately two. This amplitude is added to the larger "rescattering" amplitude and, although experimental data remain in disagreement, the theoretical prediction of the threshold cross section is brought closer to (and in agreement with) the data.