Abstract
The first excited \(J^{\pi }=0^+\) state of \(^{12}\)C, the so-called Hoyle state, plays an essential role in a triple-\(\alpha \) (\(^{4}\)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-\(\alpha \) model calculations. The Coulomb screening effect between \(\alpha \) clusters is taken into account within the Debye-Hückel approximation. To generalize our study, we utilize two standard \(\alpha \)-cluster models, which treat the Pauli principle between the \(\alpha \) 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 \(\alpha \) particles.
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References
E.-E. Salpeter, Astrophys. J. 115, 326 (1952)
F. Hoyle, Astrophys. J. Suppl. Ser. 1, 12 (1954)
W.H.G. Lewin, J. van Paradijs, R.E. Taam, Space Sci. Rev. 62, 223 (1993)
E.-E. Salpeter, Aust. J. Phys. 7, 373 (1954)
L.H. Phyu, H. Moriya, W. Horiuchi, K. Iida, K. Noda, M.T. Yamashita, Prog. Theor. Exp. Phys. 2020, 093D01 (2020)
H. Suno, Y. Suzuki, P. Descouvemont, Phys. Rev. C 91, 014004 (2015)
S. Ali, A.R. Bodmer, Nucl. Phys. 80, 99 (1966)
D.V. Fedorov, A.S. Jensen, Phys. Lett. B 389, 631 (1996)
S. Saito, Prog. Theor. Phys. 40, 893 (1968); 41, 705 (1969); Suppl. 62, 11 (1977)
E.C. Pinilla, D. Baye, P. Descouvemont, W. Horiuchi, Y. Suzuki, Nucl. Phys. A 865, 43 (2011)
T. Arai, W. Horiuchi, D. Baye, Nucl. Phys. A 977, 82 (2018)
C. Kurokawa, K. Katō, Phys. Rev. C 71, 021301 (2005)
C. Kurokawa, K. Katō, Nucl. Phys. A 792, 87 (2007)
V.I. Kukulin, V.N. Pomenertsev, Ann. Phys. 111, 330 (1978)
K. Varga, Y. Suzuki, Phys. Rev. C 52, 2885 (1995)
Y. Suzuki, K. Varga, Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems, Lect. Notes in Phys., Vol. m54 (Springer, Berlin, 1998)
Y. Suzuki, W. Horiuchi, M. Orabi, K. Arai, Few-Body Syst. 42, 33 (2008)
J. Mitroy, S. Bubin, W. Horiuchi, Y. Suzuki, L. Adamowicz, W. Cencek, K. Szalewicz, J. Komasa, D. Blume, K. Varga, Rev. Mod. Phys. 85, 693 (2013)
Y. Suzuki, W. Horiuchi, Emergent phenomena in atomic nuclei from large-scale modeling: a symmetry-guided perspective (world scientific, Singapore. Chap. 7, 199–227 (2017)
E. Nakano, K. Iida, W. Horiuchi, Phys. Rev. C 102, 055802 (2020)
H. Moriya, H. Tajima, W. Horiuchi, K. Iida, E. Nakano, arXiv:2106.14469
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This work was in part supported by JSPS KAKENHI Grant Nos. 18K03635, 18H01211, 18H05406, and 19H05140, and the Collaborative Research Program 2021, Information Initiative Center, Hokkaido University. MTY thanks the Brazilian agencies Fundação de Amparo à Pesquisa do Estado de São Paulo-FAPESP Grant No. 2019/00153-8 and Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq Grant No. 303579/2019-6.
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Phyu, L.H., Moriya, H., Horiuchi, W. et al. Coulomb Screening Effect on the Hoyle State Energy in Thermal Plasmas. Few-Body Syst 62, 44 (2021). https://doi.org/10.1007/s00601-021-01633-0
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DOI: https://doi.org/10.1007/s00601-021-01633-0