Three-Body Potentials in {\varvec{\alpha }}-Particle Model of Light Nuclei

In three-body model calculations of atomic nuclei, e.g., the ({}^{12})C nucleus as (alpha )-(alpha )-(alpha ) system and the ({}^{9})Be nucleus as (alpha )-(alpha )-n system, the Hamiltonians of the systems consisting of two- and three-body potentials are important inputs. However, our knowledge of three-body potentials is quite restricted. In this paper, I will examine a relation between (alpha )-(alpha )-(alpha ) and (alpha )-(alpha )-n three-body potentials that is obtained in a simple cluster model picture, which gives a phenomenological constraint condition on the three-body potential models to be used.