Critical stability of three-body relativistic bound states with zero-range interaction

Abstract

For zero-range interaction providing a given mass M_2 of the two-body bound state, the mass M_3 of the relativistic three-body bound state is calculated. We have found that the three-body system exists only when M_2 is greater than a critical value M_c (approx. 1.43m for bosons and approx. 1.35m for fermions, m is the constituent mass). For M_2=M_c the mass M_3 turns into zero and for M_2<M_c there is no solution with real value of M_3.

Comments: 6 pages, 3 figures. Contribution to the workshop "Critical Stability-III", 1-6 Sept. 2003, Trento, Italy. To be published in "Few-Body Systems"