R-matrix analysis of elastic scattering, phase shift and radiative capture reaction cross sections in the $\alpha + \alpha$ system

TL;DR

This paper performs a comprehensive R-matrix analysis of elastic scattering, phase shifts, and radiative capture reactions in the alpha-alpha system, providing insights into the structure and reactions of $^8$Be relevant to stellar nucleosynthesis.

Contribution

It introduces a simultaneous phenomenological R-matrix analysis of multiple reaction channels in the alpha-alpha system, comparing results with experimental data and theoretical models.

Findings

Reduced transition strength matches experimental estimates.

R-matrix B(E2) value aligns with cluster model predictions.

Results inform understanding of $^8$Be structure and astrophysical reactions.

Abstract

The unstable nucleus $^8$Be, with its two $\alpha$-cluster configuration, is the doorway to the formation of heavier $\alpha$-cluster nuclei. Most importantly, its the precursor of the production of $^{12}$C through the Hoyle state, a resonance state of three $\alpha$ clusters, in the helium burning phase of a massive star. The nucleus exhibits a ground state band of rotational states established through $\alpha-\alpha$ scattering experiments. A subsequent precision particle-$\gamma$ coincidence measurement of the electromagnetic transition between the 4$^+\rightarrow$ 2$^+$ excited states also corroborated the evidence for a highly deformed dumb-bell shaped structure of $^8$Be. A simultaneous phenomenological R-matrix analysis of the measured capture reaction cross sections along with the elastic excitation function and phase shift data has been performed. The resulting reduced transition strength of 21.96$\pm$3.86 $e^2 fm^4$ compares well with the estimated experimental value of 21.0$\pm$2.3 e$^2$ fm$^4$. The R-matrix yield of the B($E2$) value is closer to the prediction of cluster model but about 19$\%$ less than the {\it ab initio} result.