Resonances in three-body systems

Abstract: Three particles interacting via Coulomb forces represents a fundamental problem in quantum mechanics whose approximate solution provides some insight into the more complex analysis associated with few-body problems. We have investigated resonance states composed of three particles interacting via Coulombic and more general potentials in non-relativistic quantum mechanics, using the complex scaling method. My calculations have been applied to two different physical systems: (i) an investigation of the possibility of resonances in the $p e \mu$ system, which has been suggested as a possible reason for unexpected results from a recent measurement of the proton radius in muonic hydrogen (ii) a calculation of resonances in positron-hydrogen scattering, which shows that we can represent this system with the accuracy needed for future scattering calculations. The basis set used is built from Gaussians in Jacobi coordinates, thus automatically including mass-polarisation effects which cannot be neglected in muonic systems.