Article révisé par les pairs
Résumé : We develop a method for calculating the bound and continuum energy spectrum of three particles interacting through both short-range and Coulomb potentials. Our method combines hyperspherical coordinates with the slow variable discretization approach. A complex absorbing potential is employed to describe accurately the continuum wave functions. The method is well known in atomic and molecular physics. It is extended here to nuclear physics, with a special emphasis on the long-range Coulomb interaction. The method is applied to compute the energy spectrum of C12 in a 3α-particle model, focusing on an accurate calculation of the Hoyle resonance width of the narrow near-threshold Jnπ=02+ state, which plays an important role in stellar nucleosynthesis. We employ an effective α-α interaction potential which reproduces both the energy and width of Be8, while a three-body force is added in order to fix the C12 energy levels at the experimental values. We also analyze the structure of the bound and resonance states by calculating the wave functions and one-dimensional distribution functions.