A New Feature of the Efimov-Like Structure in the Hadron System: Long-Range Force as a Recoil Effect

Abstract

On the three-body kinematics, we investigate the threshold behavior which appears not only at the three-body break-up threshold (3BT), but also at the quasi two-body threshold (Q2T) for the reactions: A+(BC)rightarrow A+B+C, and (ABC)rightarrow A+(BC), respectively. Recently, the author proposed a generalparticle {transfer} (GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a 1/r^n-type potential for long range. The long range part of the GPT potential for n=1 indicates an attractive Coulomb-like or a gravitation-like potential. While, n=2 indicates the Efimov-like potential between A and (BC). The three-body binding energy: E_n=epsilon +zeta _n with the two-body binding energy epsilon , and the separation energy zeta _n for (ABC)rightarrow A+(BC) satisfies E_n/E_{n+1}=zeta _n/zeta _{n+1}=const for epsilon =0 or the two-body scattering length: arightarrow infty (i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of E_n/E_{n+1}=(zeta _n+epsilon )/(zeta _{n+1}+epsilon )rightarrow 1 (const) for nrightarrow infty (with zeta _nrightarrow 0) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.