Effective mass concept for few-body nuclear systems*

We consider the possibility of utilizing the effective mass concept initially proposed in many-body and solid-state physics to study nuclear systems like 3N and 3alpha-cluster systems. Our consideration is based on a property of a three-body nuclear Hamiltonian for bound states. We describe the property as mass-energy compensation (MEC). The MEC reflects the general physical relation between mass and energy. For bound nuclear states, this relation appears as the mass defect formula. Recently, we investigated the mass-energy compensation for the three-nucleon Hamiltonian in relation to the three-body force acting in 3N systems. To avoid a sophisticated constrict for three-body force, we propose a phenomenological model in which the nucleon effective mass is defined so that to compensate the effect of the three-body force [1].   Another nuclear system constituted of identical particles is the system of three alpha particles (the cluster model for the ¹²C nucleus). The initial phenomenological model includes pair and three-body potentials. However, instead of using a three-body potential, we adjust the mass of the alpha particle in the system and define the alpha-particle effective mass that reproduces experimental data. The MEC property of the 3alpha Hamiltonian justifies the procedure. The MEC effect is modeled numerically and explained in the presented work. The effective masses of alpha particles for the 3alpha 0⁺ ground and excited states are evaluated. The coupling of these levels is shown.