Coulomb Screening Effect on the Hoyle State Energy in Thermal Plasmas

Abstract

The first excited $$J^{\\pi }=0^+$$ J π = 0 + state of $$^{12}$$ 12 C, the so-called Hoyle state, plays an essential role in a triple- $$\\alpha $$ α ( $$^{4}$$ 4 He) reaction, which is a main contributor to the synthesis of $$^{12}$$ 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- $$\\alpha $$ α model calculations. The Coulomb screening effect between $$\\alpha $$ α clusters is taken into account within the Debye-Hückel approximation. To generalize our study, we utilize two standard $$\\alpha $$ α -cluster models, which treat the Pauli principle between the $$\\alpha $$ α particles differently. We find that the energy shift does not depend on these models and follows 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 $$\\alpha $$ α particles.