Coulomb screening effect on the Hoyle state energy in thermal plasmas

Abstract

The first excited $J^{\ddot{I}}€=0^{+}$ state of ${}^{12}$C, the so-called Hoyle state, plays an essential role in a triple-$\hat{I}\pm$ (${}^4$He) reaction, which is a main contributor to the synthesis of ${}^{12}$C in a burning star. We investigate the Coulomb screening effects on the energy shift of the Hoyle state in a thermal plasma environment using precise three-$\hat{I}\pm$ model calculations. The Coulomb screening effect between $\hat{I}\pm$ clusters are taken into account within the Debye-Hückel approximation. To generalize our study, we utilize two standard $\hat{I}\pm$-cluster models, which treat the Pauli principle between the $\hat{I}\pm$ particles differently. We find that the energy shifts do not depend on these models and follow a simple estimation in the zero-size limit of the Hoyle state when the Coulomb screening length is as large as a value typical of such a plasma consisting of electrons and $\hat{I}\pm$ particles.

6 pages, 2 figures, contribution to the 8th Asia-Pacific Conference on Few-Body Problems in Physics (APFB2020), 1-5 March 2021, Kanazawa, Japan