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

Abstract

Based on the effective-mass concept, we perform the Faddeev calculations for a low-lying spectrum of 3$\alpha$ states in ${}^{12}$C nucleus. A three-body potential is used to describe the known breaking of the 3$\alpha$-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 $\alpha$-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.

Comments: 13 pages, 6 figures