Effective Mass of $α$-Cluster in $^{12}$C Nucleus

Abstract

Based on the effective-mass concept, we perform the Faddeev calculations for a lowlying spectrum of 3α states in 12 C nucleus. A three-body potential is used to describe the known breaking of the 3α-cluster structure in the nucleus. We show that the contribution of the three-body potential to the Hamiltonian can be compensated by increasing/decreasing the α-particle free mass. The effective-mass values are adjusted so that to reproduce the experimental data for the 12 C nucleus. The energy dependence of the effective mass and the correlation to a three-body potential are discussed. We show that the coupling between the 0 + (2 + ) levels forms a specific picture of anti-crossing on the energy/effective-mass plane.

Mass-Energy Equivalence in Bound Three-Nucleon Systems

“…Finelly, we can note that the method of effective mass can also be applied for the three-body cluster models like the 3α-particle model of 12 C, in which a three-body force are required [53][54][55].…”