Direct triple-$\alpha$ process in non-adiabatic approach

TL;DR

This paper estimates the direct triple-alpha process contribution using a non-adiabatic approach, revealing significantly lower reaction rates than adiabatic models but consistent with NACRE data at helium burning temperatures.

Contribution

It introduces a non-adiabatic method to evaluate the direct triple-alpha process, providing new estimates that differ from previous adiabatic models.

Findings

Direct triple-alpha contribution is 10^{-15}--10^{-3} pb in certain energy ranges.

Results are much lower than recent adiabatic model predictions.

Reaction rates align with NACRE data at helium burning temperatures.

Abstract

Triple-$\alpha$ reaction rates have been determined well with the sequential process via the narrow resonances. However, the direct triple-$\alpha$ process at off-resonant energies still remains in unsolved problems. In the present report, the direct triple-$\alpha$ contribution is estimated with a non-adiabatic method, and it is found to be 10$^{-15}$--10$^{-3}$ pb order in photodisintegration cross sections of $^{12}$C(2$^+_1 \rightarrow$ 0$^+$) for $0.15 < E < 0.35$ MeV. This is far below the values predicted by the recent adiabatic models. In spite of the large difference, the derived rates are found to be concordant with NACRE at the helium burning temperatures.