Theory of elastic π3He scattering

The pion-three-nucleon system is investigated using coupled Schrödinger equations. The coupling between the four-body (πNNN) and three-body (NNN) systems is explicitly implemented by operators for emission and absorption of the pion by each nucleon. The only simplifying assumption is the separable form for amplitudes pertaining to pure potential scattering. A set of Amado-Lovelace type equations is derived, from which the amplitude for the reaction π + ³He→ π + ³He can be evaluated. The integral equations involve intermediate integration over single relative momenta so that subsequent numerical solution is within reach.