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

TL;DR

This paper investigates the effective mass of alpha particles within the $^{12}$C nucleus using Faddeev calculations, revealing how three-body potentials influence the mass and energy levels, and discussing the anti-crossing phenomena.

Contribution

It introduces a method to adjust the alpha particle effective mass to account for three-body potential effects in $^{12}$C, linking mass variations to experimental data.

Findings

Effective mass adjustments reproduce experimental spectra.

Three-body potential effects can be compensated by mass changes.

Anti-crossing behavior observed in energy/effective-mass plane.

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.