Critical Stability of Three-Body Relativistic Bound States with Zero-Range Interaction

Abstract

For the zero-range interaction providing a given mass M2 of the two-body bound state, the mass M3 of the relativistic three-body system is calculated. We have found that the three-body system exists only when M2 is greater than a critical value M c (≈ 1.43 m for bosons and ≈ 1.35 m for fermions, m being the constituent mass). For M2=M c the mass M3 turns into zero and for M2 < M c there is no solution with real value of M3.