Plasma screening enhancement of nuclear fusion reactions and detailed balance principle

A. I. Chugunov

Ioffe Institute, Politekhnicheskaya 26, Saint Petersburg 194021, Russia

In compact stars (white dwarfs and envelopes of neutron stars) nuclear fusion reaction rates are enhanced for many orders of magnitude by plasma screening [1]. The screening enhancement factors F was extensively studied for the first stage of the reaction - formation of the compound nucleus (A+B→C*). However, naive usage of these results as enhancement factors for reaction rate at certain exit channel (e.g. A+B→C→ D+E) can lead to violation of the detailed balance principle [2,3]. To solve this problem in reaction network codes, Ref. [2] suggests to select a 'preferred' direction of the reaction and calculate the rate of reverse reaction according to the detailed balance. Here I suggest a more accurate approach based on the more detailed treatment of the mechanism of the plasma screening enhancement of reaction rate. Namely, the screening enhancement factor for compound nucleus formation F is known to be factorized as F=Fcl Fq [4]. Here Fcl is classical enhancement factor, it is associated with increase of the number density of closely separated nuclei in classically allowed region and can be calculated on the base of thermodynamics [5]. Fq is quantum part of the screening factor, it is associated with screening effect on the internuclear potential in classically forbidden zone, i.e. on course of the tunneling [4]. If Fq∼1, which takes place if the tunneling length for Gamow peak ions is much smaller than typical separation of nuclei in plasma, the total screening enhancement factor is equal to Fcl. As far as Fcl is associated with enhancement of number density for closely separated ions, and does not deal with details of nuclear reaction as it is, the branching ratios for decay of the compound nucleus are unaffected by screening and Fcl can be directly applied as enhancement factor for certain exit channel. It can be shown that this description agrees with the detailed balance principle [3]. In opposite case, than Fq significantly differs from 1, the plasma screening affects the tunneling probability, which is crucial part of nuclear reaction. As a result, the partial width for decay of compound nucleus to initial nuclei (C*→A+B) is affected by screening, thus the branching ratios for decay of compound nucleus are reweighted. This effect should be included to get accurate enhancement factor for rate of reaction at certain exit channel (e.g. A+B→C*→D+E) and correspondent procedure is described in this presentation.

  1. E.E. Salpeter // Australian Journal of Physics 1954. V.7. P.373.
  2. A.C. Calder et al. // Astrophysical Journal 2007. V.656. P.313.
  3. D. Kushnir, E. Waxman, A.I. Chugunov // Monthly Notices of the Royal Astronomical Society, accepted
  4. D.G. Yakovlev et al. // Phys. Rev. C. 2006. V 74. 035803
  5. H.E. Dewitt, H.C. Graboske, M.S. Cooper // Astrophysical Journal 1973. V.181 P.439.

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