  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 is approximately
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.
