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Author(s):
V.N. Tsytovich
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Title:
Collective Plasma Corrections to Thermonuclear Reactions Rates in Dense Plasmas
Date of publication:
Jan. 2002
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Key words:
nuclear reactions, dense plasmas, solar interior, solar neutrino
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Abstract:
General kinetic equations for nuclear reaction in dense plasmas are obtaincd. They take into account the first order collective plasma effects. Together wit,h previously known corrections proportional to ZiZj, the product of the charges Zi and Zj of two interacting nuclei, it is shown tha there exist corrections proportional to the squares Z_i^2 and Z_j^2 of the charges. It is shown that the Salpeter's [l] corrcction due to the plasma screening of the interaction potential is at least r/d smaller(r is the nuclei size and d is Debye screening length) than previously thought and is zero in the approximation when the terms of the order r/d are neglectcd. But the correlation effects in the first approximation in the paramter 1/N_d (where N_d is the number of particle in the Debye sphere) give corrections which often coincide with the first order Salpeter's corrections (found by expansion in another small parameter, the ratio of thermal energy to Gamov's energy). The correlation corrections are propto Z_iZ_j, have a different physical meaning than the correctious [l], can have a different sign and are present for reactions where the Salpeter's corrections are zero. Previously in astrophysical applications it was widely used the interpolation formulas between weak and strong Salpeter's screening corrections. Since the correlation correction take placc the previously known Salpeter's corrections and the strong correlation corrections is difficult to describe analytica1ly, the interpolation formulas between the weak and strong correlations cannot be yet found. A new type of corrections are found here which are proportional to the sequare of the charges. They are due to collective change in electrostatic self-encrgy of the plasma system during the nuclear reactions. The latter corrections are found by taking into account the changes of plasma particle fluctuatious by the nuclear reactions. Numerical evaluation of the plasma corrections for the nuclear reactions of thc hydrogen cycle, using the parameters of the present, temperature, density and abundance in the solar interior, are performcd.
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