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

Abstract

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.

arXiv comment31 pages, 14 figures, final published version

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Cited by in corpus (4)

• Effective Field Theory calculations of $NN\to NN\pi$
• Pion production in nucleon-nucleon collisions in chiral effective field theory: next-to-next-to-leading order contributions
• Pion production in nucleon-nucleon collisions in chiral effective field theory with Delta(1232)-degrees of freedom
• Charge Symmetry Breaking and Nuclear Pion Production Reactions