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

TL;DR

This paper develops a relativistic formalism for pion production reactions, showing that the traditional one-body operator is replaced by a two-body operator, which improves theoretical predictions of the threshold cross section.

Contribution

The paper introduces a new formalism that replaces the one-body operator with a two-body operator in pion production, addressing energy transfer issues and improving agreement with experimental data.

Findings

The one-body operator is replaced by a two-body operator in the formalism.

The impulse amplitude for np --> d pi^0 at threshold is approximately doubled.

The new approach brings theoretical predictions closer to experimental data.

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.