Triple−αcontinuum structure and Hoyle resonance ofC12using the hyperspherical slow variable discretization

Abstract

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 $^{12}\mathrm{C}$ in a $3\ensuremath{\alpha}$-particle model, focusing on an accurate calculation of the Hoyle resonance width of the narrow near-threshold ${J}_{n}^{\ensuremath{\pi}}={0}_{2}^{+}$ state, which plays an important role in stellar nucleosynthesis. We employ an effective $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ interaction potential which reproduces both the energy and width of $^{8}\mathrm{Be}$, while a three-body force is added in order to fix the $^{12}\mathrm{C}$ 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.