A Boson exchange approach for Helium Burning Stars

TL;DR

This paper introduces a novel N-body scattering approach to analyze helium burning stars, focusing on the 3α reaction and resonances, with implications for astrophysical reaction rates and decay mechanisms.

Contribution

It develops a new N-body scattering method to describe both sequential and direct 3α reactions, addressing Coulomb complications and low-temperature behavior.

Findings

Reproduces known resonance structures like the Hoyle state.

Provides reaction rates consistent with astrophysical constraints.

Offers a new framework for low-temperature helium burning analysis.

Abstract

Helium burning plays a key role in the hierarchy of stellar nucleosynthesis and evolution, as the archetype of a bosonic 3-body system. Here, we examine the kinetic and nuclear aspects of the 3$\alpha$ reaction, under the auspices of the Thomas-Efimov theorem. Due to the 92.08 keV ground state of $^8$Be, multiple $\alpha$-cluster resonances appear especially at the lowest temperature (Thomas State), while with increasing temperature the system is dominated by the Hoyle/Efimov state. We extend our previous methodology for the sequential channel to describe the direct mechanism, that results in an equilateral geometry similar to the Thomas state. This is accomplished by developing a general approach to the N-body scattering, via successive particle-exchanging 2-body collisions, which eliminates long range Coulomb complications, in a similar manner to the Thomas-Efimov mechanism. We furthermore, discuss the e$^+$e$^-$ decay of the compound state with a perturbation based methodology. Due to the symmetry of the system and the resulting reaction rates, we favor the E0 decay scheme over the E2. The E0 reaction rates obey all the available astrophysical and nuclear constraints and are compared to theoretical data from the literature, whose limitations are discussed. Our extended methodology provides a physically sound description of the debated low temperature region.