The paper describes a multilevel, multichannel R-matrix code, AZURE, for applications in nuclear astrophysics. The code allows simultaneous analysis and extrapolation of low-energy particle scattering, capture, and reaction cross sections of relevance to stellar hydrogen, helium, and carbon burning. The paper presents a summary of R-matrix theory, code description, and a number of applications to demonstrate the applicability and versatility of AZURE.

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An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and no boundary-condition constants which allows the positions and partial widths of an arbitrary number of levels to be easily fixed in an analysis. These alternative parameters can be converted to standard R-matrix parameters by a straightforward matrix diagonalization procedure. In addition it is possible to express the collision matrix directly in terms of the alternative parameters.

The creation of carbon and oxygen in our universe is one of the forefront questions in nuclear astrophysics. The determination of the abundance of these elements is key to both our understanding of the formation of life on earth and to the life cycles of stars. While nearly all models of different nucleosynthesis environments are affected by the production of carbon and oxygen, a key ingredient, the precise determination of the reaction rate of 12 C(α, γ) 16 O, has long remained elusive. This is owed to the reaction's inaccessibility, both experimentally and theoretically. Nuclear theory has struggled to calculate this reaction rate because the cross section is produced through different underlying nuclear mechanisms. Isospin selection rules suppress the E1 component of the ground state cross section, creating a unique situation where the E1 and E2 contributions are of nearly equal amplitudes. Experimentally there have also been great challenges. Measurements have been pushed to the limits of state of the art techniques, often developed for just these measurements. The data have been plagued by uncharacterized uncertainties, often the result of the novel measurement techniques, that have made the different results challenging to reconcile. However, the situation has markedly improved in recent years, and the desired level of uncertainty, ≈10%, may be in sight. In this review the current understanding of this critical reaction is summarized. The emphasis is placed primarily on the experimental work and interpretation of the reaction data, but discussions of the theory and astrophysics are also pursued. The main goal is to summarize and clarify the current understanding of the reaction and then point the way forward to an improved determination of the reaction rate.

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