The Three-Body Continuum Coulomb Problem and the 3$\alpha$ Structure of ${}^{12}$C

Abstract

We introduce an approach, based on the coordinate space Faddeev equations, to solve the quantum mechanical three-body Coulomb problem in the continuum. We apply the approach to compute measured properties of the first two $0^{+}$ levels in ${}^{12}$C, including the width of the excited level, in a 3$\alpha$-particle model. We use the two-body interaction which reproduces the low energy $\alpha$-$\alpha$ scattering data and add a three-body force to account for the compound state admixture.

Comments: LaTeX, 8 pages, 3 postscript figures, revised version, to be published in Phys.Let.B