Studying the 3 alpha reaction in hyperspherical harmonic approach

In this work, the 3 alpha reaction is studied by using the Faddeev hyper-spherical harmonic (HH) method [1]. Starting from a three body model, we derive the analytical formulas for the quadrupole strength function B(E2) as well as the reaction rate which is well known for the two particles but not for three particle system. The 2+ state and the 0+ resonance are well reproduced but we consider the contributions of the nonresonant continuum states to the reaction rate in a consistent manner. Considering only Coulomb interaction for the three alpha scattering problem we can obtain analytical continuum wave functions for the 0+ states. At low temperature our calculations agree very well with NACRE and there is an expected increase in the reaction rate at high temperature due to the nuclear contribution (resonant process). A full calculation with the R-matrix method in hyper-spherical coordinate space is being done to include nuclear and coulomb in equal footing. Final results and a detail physical analysis of the reaction mechanism will be presented and compared with [2,3]. [1] I. J. Thompson, F. M. Nunes, B. V. Danilin, Comput.Phys.Comm. 161, 87-107 (2004). [2] K.Ogata, M.Kan, M.Kamimura, Prog. Theor. Phys. 122, 1055 (2009). [3] R. de Diego, E. Garrido, D.V. Fedorov, A.S. Jensen, EPL. 90, 52001(2010).