Few-Body Systems

, 59:51 | Cite as

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

  • Shinsho Oryu
Open Access
Part of the following topical collections:
  1. Critical Stability 2017


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 general particle \( {transfer}\) (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: \(a\rightarrow \infty \) (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 \(n\rightarrow \infty \) (with \(\zeta _n\rightarrow 0\)) 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.


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Authors and Affiliations

  1. 1.Department of PhysicsTokyo University of ScienceNodaJapan

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