Phenomenological R-matrix analysis of reactions populating the ¹⁶O compound nucleus

The phenomenological R-matrix technique has proved to be very successful in describing the cross sections for low energy, low level density compound nucleus reactions. It is then an ideal tool for the field of nuclear astrophysics where one of the primary interests is obtaining charged particle cross sections, usually capture and (p, α), at energies close to the particle threshold (often few keV). This technique has been used mainly for reactions of interest in Big Bang nucleosynthesis, CNO and Carbon burning as well as some higher mass cases (usually A < 40). The technique is most useful for cross sections that cover an excitation energy range that is dominated by short lived states that manifest as broad energy resonances in the excitation curve measurements. Because of the Coulomb penetrability, the low energy cross sections are often too small to measure directly. Instead higher energy (higher cross section) measurements are made and then extrapolated to the low energies of interest with the aid of a model. The phenomenological R-matrix technique describes the cross section in terms of individual nuclear levels. This is a double edged sword. It has the advantage that a more fundamental model is not necessary, but means that the accuracy of the extrapolation is very data dependent and that ambiguities in the analysis can develop. The R-matrix technique also has the advantage that it enforces unitarity. While this means that a proper analysis must include all allowed reaction channels (with significant branching ratios), it provides a consistent mathematical framework to compare the different reactions that populate the same compound nucleus (something that is often neglected). Layered on top of the reaction theory are corrections for target effects and extended detector geometry. Further, the free parameters of the theory must be fit to the experimental data and uncertainties extracted. To illustrate, I will describe an R-matrix analysis of the reactions that populate the ¹⁶O compound nucleus above both the α and proton separation energies. This combines the astrophysically important reactions ¹²C(α,γ)¹⁶O, ¹⁵N(p, γ)¹⁶O, and ¹⁵N(p,α₀)¹²C, with other reactions like ¹²C(α,α₀)¹²C,¹²C(α,α₁)¹²C,¹²C(α,p)¹²,¹⁵N(p,p)¹⁵N,¹⁵N(p,α₁)¹²C, and ¹⁶N(βα)¹²C.