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

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.

A time-dependent Hartree-Fock study of triple-alpha dynamics

Time-dependent Hartree-Fock calculations have been performed for fusion reactions of ^44He + ^44He \rightarrow→^88Be^**, followed by ^44He + ^88Be^**. Depending on the orientation of the initial state, a linear chain vibrational state or a triangular vibration is found in ^{12}12C, with transitions between these states observed. The vibrations of the linear chain state and the triangular state occur at \simeq≃9 and 4 MeV respectively.