The Faddeev-Merkuriev Differential Equations (MFE) and Multichannel 3-Body Scattering Systems

Numerical implementation of the modified Faddeev Equation (MFE) is presented in some detail. The Faddeev channel wave function displays unique properties of each and every open channel, respectively. In particular, near resonant energies, the structures of the resonances are beautifully displayed, from which, the life-time of the resonances can be determined by simply using the uncertainty principle. The phase shift matrix, or the K-matrix, provides unique information for each and every resonance. This information enables the identification of the physical formation mechanism of the Gailitis resonances. A few of these resonances, previously known as the mysterious shape resonances, have occurred in a number of different collision systems. The Gailitis resonances are actually produced by a quantized Stark-effect within the various collision systems. Since the Stark-effect is a universal phenomenon, the Gailitis resonances are expected to occur in much broader classes of collision systems. We will present the results of a precision calculation using the MFE method in sufficient detail for interested students who wish to explore the mysteries of nature with a powerful theoretical tool.