Integral equations for three-body Coulombic resonances

We propose a novel method for calculating resonances in three-body Coulombic systems. The method is based on the solution of the set of Faddeev and Lippmann-Schwinger integral equations, which are designed for solving the three-body Coulomb problem. The resonances of the three-body system are defined as the complex-energy solutions of the homogeneous Faddeev integral equations. We show how the kernels of the integral equations should be continued analytically in order that we get resonances. As a numerical illustration a toy model for the three-$\alpha$ system is solved.Comment: 9 pages, 1 EPS figur

Three-alpha-cluster structure of the 0^+ states in ^{12}C and the effective alpha-alpha interactions

The $0^{+}$ states of $^{12}\mathrm{C}$ are considered within the framework of the microscopic three-$\alpha$-cluster model. The main attention is paid to accurate calculation of the width of the extremely narrow near-threshold $0^+_2$ state which plays a key role in stellar nucleosynthesis. It is shown that the $0^{+}_2$-state decays by means of the sequential mechanism ${^{12}\mathrm{C}} \to \alpha+{^8\mathrm{Be}} \to 3\alpha$. Calculations are performed for a number of effective $\alpha - \alpha$ potentials which are chosen to reproduce both energy and width of $^8\mathrm{Be}$. The parameters of the additional three-body potential are chosen to fix both the ground and excited state energies at the experimental values. The dependence of the width on the parameters of the effective $\alpha - \alpha$ potential is studied in order to impose restrictions on the potentials