Practical theory of three particle states. 1. Nonrelativistic
Apr, 1964Published in:
- Phys.Rev. 135 (1964) B1225-B1249
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Abstract: (APS)
We use Faddeev's mathematical work on nonrelativistic three-particle systems to obtain a practical theory of three-particle states. Each of the two-particle subsystems is assumed to be dominated by a finite number of bound states and resonances. We then obtain two sets of equations. One expresses processes with three final particles in terms of unstable-particle scattering. It generalizes and justifies the isobar model. The other is a set of coupled Lippmann-Schwinger equations for the scattering of bound states and unstable particles. The potentials in these scattering equations for composite particles are nonlocal and energy-dependent, and become complex above the three-particle threshold. They are expressed in terms of the wave functions of the two-particle bound states and resonances—there are no new arbitrary constants. The solution satisfies three-particle unitarity. Unstable particles are not approximated by stable ones. The theory applies especially to "overlapping" final-state interactions. The equations are given in detail for the 3N and Nππ systems in the static limit. In the latter case, the nucleon is treated as an Nπ bound state. The Nππ equations are solved approximately in closed form, giving analogs of the Chew-Low effective-range formula, for the coupled Nπ and N*π systems. This predicts large inelasticity in the P11 state, in agreement with experiment. Detailed solutions will be given in subsequent papers. If all elementary particles are treated as bound states of themselves, our approach gives the basis of a complete dynamical theory of strong interactions.References(89)
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