Bahcall, John N. and Chen, Xuelei and Kamionkowski, Marc (1998) Electron-screening correction for the proton-proton reaction. Physical Review C, 57 (5). pp. 2756-2759. ISSN 0556-2813. http://resolver.caltech.edu/CaltechAUTHORS:BAHprc98a
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We test the Salpeter formalism for the electron screening of the solar proton-proton fusion reaction by solving numerically the relevant Schrödinger equation. We evaluate exactly the square of the overlap integral of the two-proton wave function and the deuteron wave function and compare with the usual analytic approximation. The usual WKB solution agrees with the numerical result to O(10^-4). The WKB approximation should be even more precise for the other nuclear fusion reactions in the pp chain and CNO cycles.
|Additional Information:||©1998 The American Physical Society Received 23 December 1996; revised 13 January 1998 This work was supported by U.S. DOE Contract No. DEFG02-92-ER 40699, NASA NAG5-3091, and the Alfred P. Sloan Foundation at Columbia. J.N.B. was supported at the Institute for Advanced Study by NSF Grant No. PHY95-13835. M.K. thanks J. Applegate for useful conversations and J.N.B. thanks A. Gruzinov for valuable discussions. This work was initiated in response to a conjecture by A. Dar that the standard treatment of screening could cause an error of order 5% in the proton-proton reaction rate in the sun. We are grateful to A. Dar for this stimulating discussion.|
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