IMPROVED BOUNDS ON MANY-BODY HAMILTONIANS .2. BARYONS FROM MESONS IN THE QUARK-MODEL

We derive an improved lower limit on the binding energy of a three-body system in terms of the binding energies of two-body systems with a fictitious mass. This represents a considerable improvement with respect to the previous lower limit and gives results very close to high accuracy calculations in the hyperspherical formalism for pairwise potentials rβ, 0≤β≤3. For β = 2, the inequality becomes an equality, and this is also true for its N-body generalization. This is clarified in an appendix by T.T. Wu. It is also possible to make model-independent predictions on the masses of the baryons by using the known dependence of the masses of the mesons on the masses of the quarks. Possible generalizations and other applications are discussed, in particular in atomic physics. © 1990.