Speaker
Description
R-matrix theory is a unique tool to provide quantitatively reliable descriptions of resonant scattering and reaction processes in nuclear systems. Albeit it is not a microscopic theory and lacks predictive power the method is widely used for analyses of experimental reaction data because it satisfies major conservation rules thus leading to consistent descriptions of collision processes. However, the application of standard R-matrix theory is limited to two-body channels and requires the inclusion of all energetically open reaction channels. Consequently breakup channels with three or more outgoing particles can only be treated within approximations. With increasing collision energy the number of channels is increasing and due to the lack of experimental data and the high number of parameters a complete analysis becomes difficult. These features are particularly limiting for the analysis of reactions in light nuclear systems which show resonant behaviour up to rather high collision energy. In addition light nuclear systems may exhibit dominant breakup channels at rather low energy (e.g. in the n + $^9$Be system).
Based on this observation Lane and Thomas [1] introduced the so-called Reduced R-Matrix formalism for analyses of incomplete nuclear systems. In this formalism only a subsystem of channels is explicitly included in the R-matrix analysis leading to a complex-valued R-matrix taking into account the remaining channels in a global way. Although the formalism was introduced more than fifty years ago, no standard parametrisation for analyses with the Reduced R-matrix has been established. Starting from the basics of R-matrix theory we developed for several realistic assumptions parametrisations for Reduced R-matrix analyses. All parametrisations account for the thresholds of the globally treated channels, a quantity which is usually well known for reaction systems. Thus a proper transition from real to complex R-matrices is obtained with increasing energy. If open channels are not included in the Reduced R-matrix analysis, the associated collision submatrix is not unitary. Thus exploiting the unitarity of the complete collision matrix the missing flux and the associated cross section were determined. This feature allowed a comparison with the Reich-Moore [2] parametrisation at low energies.
The developed parametrisations of the Reduced R-matrix based on different model assumptions are implemented in the R-matrix module of our code GECCCOS. A first Reduced R-matrix analysis of the n+$^9$Be system using a simple one-pole parametrisation yields satisfactory result. In the presentation an overview on the developed parametrisations will be given and discussed with regard to their applicability and their limitations in actual Reduced R-matrix analyses. In addition first Reduced R-matrix analyses of reaction data will be presented.
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] A.M. Lane and R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958).
[2] C.W. Reich and M.S. Moore, Phys. Rev. 111, 929 (1958).