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

摘要

For the zero-range interaction providing a given mass M_2 of the two-body bound state, the mass M_3 of the relativistic three-body system is calculated. We have found that the three-body system exists only when M_2 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 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.