Nuclear fusion in dense matter: Reaction rate and carbon burning

L. R. Gasques, A. V. Afanasjev, E. F. Aguilera, M. Beard, L. C. Chamon, P. Ring, M. Wiescher, and D. G. Yakovlev
Phys. Rev. C 72, 025806 – Published 29 August 2005

Abstract

In this paper we analyze the nuclear fusion rates among equal nuclei for all five different nuclear burning regimes in dense matter (two thermonuclear regimes, two pycnonuclear ones, and the intermediate regime). The rate is determined by Coulomb barrier penetration in dense environments and by the astrophysical S factor at low energies. We evaluate previous studies of the Coulomb barrier problem and propose a simple phenomenological formula for the reaction rate that covers all cases. The parameters of this formula can be varied to take into account current theoretical uncertainties in the reaction rate. The results are illustrated for the example of the C12+C12 fusion reaction. This reaction is important for the understanding of nuclear burning in evolved stars, in exploding white dwarfs producing type Ia supernovas, and in accreting neutron stars. The S factor at stellar energies depends on a reliable fit and extrapolation of the experimental data. We calculate the energy dependence of the S factor by using a recently developed parameter-free model for the nuclear interaction, taking into account the effects of the Pauli nonlocality. For illustration, we analyze the efficiency of carbon burning in a wide range of densities and temperatures of stellar matter with the emphasis on carbon ignition at densities ρ109 g cm3.

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  • Received 21 February 2005

DOI:https://doi.org/10.1103/PhysRevC.72.025806

©2005 American Physical Society

Authors & Affiliations

L. R. Gasques1, A. V. Afanasjev1, E. F. Aguilera2, M. Beard1, L. C. Chamon3, P. Ring4, M. Wiescher1, and D. G. Yakovlev5

  • 1Department of Physics & The Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556 USA
  • 2Departamento del Accelerador, Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, C.P. 11801, Destrito Federal, Mexico
  • 3Departamento de Física Nuclear, Instituto de Física da Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, SP, Brazil
  • 4Physik-Department, Technische Universitat München, D-85747, Garching, Germany
  • 5Ioffe Physical Technical Institute, Poliekhnicheskaya 26, RU-194021 St. Petersburg, Russia

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Vol. 72, Iss. 2 — August 2005

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