Quantum three-body calculation of the nonresonant triple-\alpha reaction rate at low temperatures

TL;DR

This paper presents a quantum three-body calculation of the triple-alpha reaction rate at low temperatures, revealing significantly higher rates than previous estimates due to nonresonant continuum contributions.

Contribution

It introduces a direct quantum three-body approach treating resonant and nonresonant processes uniformly, improving accuracy over traditional methods.

Findings

Reaction rate is about 20 orders of magnitude higher at 10^7 K than previous estimates.

Nonresonant continuum states below 92.04 keV resonance significantly enhance the reaction rate.

Nomoto's approximation is shown to be a crude estimate compared to the quantum model.

Abstract

The triple-\alpha reaction rate is re-evaluated by directly solving the three-body Schr\"odinger equation. The resonant and nonresonant processes are treated on the same footing using the continuum-discretized coupled-channels method for three-body scattering. Accurate description of the \alpha-\alpha nonresonant states significantly quenches the Coulomb barrier between the two-\alpha's and the third \alpha particle. Consequently, the \alpha-\alpha nonresonant continuum states below the resonance at 92.04 keV, i.e., the ground state of 8Be, give markedly larger contribution at low temperatures than in foregoing studies. We show that Nomoto's method for three-body nonresonant capture processes, which is adopted in the NACRE compilation and many other studies, is a crude approximation of the accurate quantum three-body model calculation. We find about 20 orders-of-magnitude enhancement of the triple-\alpha reaction rate around 10^7 K compared to the rate of NACRE.