Calculation of nuclear reaction rates in astrophysical processes
A dissertation submitted to the Department of Physics of the University of Lisbon in partial fulfillment of the requirements for the Degree of Doctor of Philosophy
Bruno Marques Braizinha
Professor Ana Maria Eiró (University of Lisbon)
Professor Filipe Duarte Santos (University of Lisbon)
Professor Ian J. Thompson (University of Surrey)
The field of Nuclear Astrophysics is concerned with the study of nuclear reactions involved in the nucleosynthesis process inside stars (stellar nucleosynthesis) and in the early universe (primordial nucleosynthesis). This field flourished from the early work of Burbidge, Burbidge, Fowler and Hoyle, which postulated a series of energy generating processes in stars.
In recent years, this field has seen a remarkable expansion and exciting developments, with the introduction of more sophisticated stellar models, and increased precision in the experimental determination of stellar reaction rates. However, it is still rare to find experimental values of nuclear reaction rates at the energies needed as inputs to stellar models, as these energies are almost always bellow the Coulomb barrier. Therefore, this field continues to be marked by the need of theoretical models that extrapolate, in a reliable way, the experimental data to the astrophysical relevant energies.
This work focuses precisely on this aspect of the Nuclear Astrophysics field, the theoretical analysis of nuclear reaction data, particularly in the low energy region. We propose and implement a framework for the systematic study of nuclear reactions, and attempt to address fundamental issues regarding the modeling of low energy nuclear reactions, namely the interplay between direct and resonant contributions to the reaction mechanism, and the accurate extrapolation of experimental data.
We focus on applications that involve transfer or photonuclear processes, and study a set of reactions, namely the 14N(p,g)15O, the 3He(d,p)4He, the 12C(a,g)16O and the 7Li(p,)8Be reactions, that involve several types of processes (transfer and photonuclear processes, direct and resonant mechanisms, effects of tensor forces, etc), that are the object of much interest as modern topics of research.
We start with the introduction of the theoretical framework, where we focus on the coupled channels model and the R-matrix theory of nuclear reactions, both as a method of solving the coupled equations and in the pure phenomenological approach, and explore the possibility of including R-matrix poles in a coupled channels analysis, which we call the hybrid framework.
The first application of the theoretical framework is in the analysis of the 3He(d,p)4He transfer reaction. We study the available experimental low energy data (total and differential reaction cross section data, vector and tensor analyzing powers and polarization transfer observables) with DWBA, coupled channels and phenomenological R-matrix models. In this analysis we also include new experimental measurements of the Ayy and cross section observables at zero degrees, performed in the context of this work at TUNL (Triangle Universities Nuclear Laboratory), USA.
The study described in the last paragraph leads to the introduction of the hybrid R-matrix + potential analysis where the negative parity contributions, essentially arising from a direct reaction mechanism, are taken in consideration through a potential description, while the resonant contributions to the reaction mechanism are treated in the R-matrix framework. With this model we are able to describe the measured observables, fitting the potential and R-matrix parameters to the experimental data, and to disentangle the direct and resonant contributions to the reaction mechanism.
The range of applications of the theoretical framework developed is then expanded to include radiative capture processes. The analysis of these processes in the hybrid framework requires the introduction of photonuclear couplings in the coupled channels formalism, a development that has important application in the Nuclear Astrophysics field since many nuclear reactions important in Astrophysics involve photonuclear processes. We use the 12C(a,g)16O and 7Li(p,g)8Be reactions as a testing ground for the formalism, before studying the 14N(p,g)15O reaction.
Finally, the 14N(p,g)15O radiative capture reaction is studied with a phenomenological R-matrix model, showing the strengths and weaknesses of this approach, and with the hybrid framework. Both these models allow the correct description of the available experimental data, however, they yield different parameters for the set of 15O resonances used in the analysis, and different values for the astrophysical S-factor. These differences can be attributed to a high degree of uncertainty in the low energy experimental data available, with large error bars affecting the data in this energy range.
We conclude that the hybrid framework developed has important applications in the analysis of low energy nuclear reaction data. With this model we are able to obtain information on the properties of the states that dominate the resonant contribution to the reaction mechanism, as well as on the strength of the direct process contributions. Furthermore, we are able to accurately extrapolate the theoretical curves to the energy region relevant for the astrophysical processes.