Coulomb screening correction to the Q value of the triple-alpha process in thermal plasmas

Abstract

The triple-alpha reaction is key to 12C 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 threebody calculations within the Debye-Hückel approximation. A three-alpha model that has the Coulomb interaction modified in theYukawa 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 pointcharge 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.