**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

by

Bruno Marques Braizinha

SUPERVISORS:

Professor Ana Maria Eiró (University of Lisbon)

Professor Filipe Duarte Santos (University of Lisbon)

Professor Ian J. Thompson (University of Surrey)

Lisbon, 2004

Abstract

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 ^{14}N(p,g)^{15}O,
the ^{3}He(d,p)^{4}He, the ^{12}C(a,g)^{16}O
and the ^{7}Li(p,)^{8}Be 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
^{3}He(d,p)^{4}He 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 A_{yy}
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 ^{12}C(a,g)^{16}O
and ^{7}Li(p,g)^{8}Be reactions as a
testing ground for the formalism, before studying the ^{14}N(p,g)^{15}O
reaction.

Finally, the ^{14}N(p,g)^{15}O
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 ^{
15}O 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.