SINGLE QUANTUM PAIR ANNIHILATION OF A BOUND PARTICLE-PARTICLE-ANTIPARTICLE SYSTEM

A relativistic coupled channel formalism is presented for the descript ion of a quasi-bound three-body state. The annihilation of a particle- particle-antiparticle system into a particle and a single quantum is s tudied in the scalar Yukawa model, in which scalar ''nucleons'' (phi) and ''antinucleons'' (<(phi)over bar>) interact via scalar ''meson'' ( chi) exchange. A three-Fock-slate trial state is used to derive variat ional equations that describe the quasi-bound <phi phi(phi)over bar> s ystem as a resonance in the chi phi collision channel. These equations are solved approximately to yield the <phi phi(phi)over bar> decay wi dth. This width is found to be negligible compared with the two-quantu m pair annihilation width if the coupling is weak (alpha much less tha n 1), but is found to be of comparable magnitude for strong coupling ( alpha similar or equal to 1). Relativistic effects on the width are pr onounced and cannot be neglected at strong coupling. Order of magnitud e comparison is made with the Ps(-) system for the massless-chi case, and to nuclear NN(N) over bar systems for the massive-chi case.