Abstract
Abstract The triple-alpha reaction is key to $^{12}$C production and is expected to occur in weakly coupled thermal plasmas as encountered in normal stars. We investigate how Coulomb screening affects the structure of a system of three alpha particles in such a plasma environment by precise three-body calculations within the Debye–Hückel approximation. A three-alpha model that has the Coulomb interaction modified in the Yukawa form is employed. Precise three-body wave functions are obtained by a superposition of correlated Gaussian basis with the aid of the stochastic variational method. The energy shifts of the Hoyle state due to the Coulomb screening are obtained as a function of the Debye screening length. The results, which automatically incorporate the finite-size effect of the Hoyle state, are consistent with the conventional result based on the Coulomb correction to the chemical potentials of ions that are regarded as point charges in a weakly coupled thermal plasma. We have given a theoretical basis to the conventional point-charge approach to the Coulomb screening problem relevant for nuclear reactions in normal stars by providing the first evaluation of the Coulomb corrections to the $Q$ value of the triple-alpha process that produces a finite-size Hoyle state.
Highlights
Properties of NucleusDiscovery of NucleusThe central core of an atom that contains all the atom’s positive charges is called the atomic nucleus
We find that our results are consistent with the conventional results based on the Coulomb correction to the chemical potentials of ions that are regarded as point charges in a weakly-coupled, thermal plasma
Three-alpha particles in plasma environment is formed from the radiative
Summary
Properties of NucleusDiscovery of NucleusThe central core of an atom that contains all the atom’s positive charges is called the atomic nucleus. If Thomson’s plum pudding model was true, Rutherford reasoned, the positively charged alpha particles would pass through the gold foil with very little deviation in their paths. They discovered that many alpha particles were deflected at very large angles. It was concluded that an atom has a highly dense central part where practically all of the mass and all of the atom’s positive charges are concentrated in a very small region. This central part of the atom is known as the nucleus
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