Speaker
Description
Three-body break-up channels play an important role in light nuclear systems even at low incident energies. In standard two-body R-matrix theory these processes can only be treated approximatively for instance by using sequential decay models. We will present a novel three-body R-matrix formalism that is based on a proposal by Glöckle [1]. In this framework the Faddeev equations are solved by dividing the space of Jacobi-coordinates into interior regions with strong local interactions and an asymptotic exterior region. Using the asymptotic form of the three-body wave functions one obtains a system of linear equations which includes the boundary conditions at the division of the Jacobi-coordinates. Its solution directly yields the elastic and the break-up transition amplitudes and thus the elastic and the breakup cross sections. The form of these equations resembles a similar one in the standard R-matrix theory and justifies its denomination.
In a first step we generalized the proposal of Glöckle to three spinless particles with different masses. A first numerical implementation indicated severe shortcomings as well as ill-posedness of the algorithm. Significant changes especially with regard to the conditions and the choice of basis functions as well as the normalization of bound states were required leading to a novel formalism of Glöckle type. The ill-posedness of the equations has been cured by regularization. The novel formalism was first applied to the neutron-deuteron system. Systematic studies of different sets of basis functions and regularization parameters were performed and stable results were achieved. The calculated break-up cross section and the elastic cross section are in fair agreement to the experimental data up to 10 MeV since we include s-waves only. Furthermore, we present an outlook and first results regarding the n+9Be system.
Acknowledgement: The work has been carried out within the framework of the EUROfusion Consortium and has received funding from the European research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
[1] W. Glöckle, Z. Phys. 271, 31 (1974)