Beyond the mean-potential approximation in the calculation of thermonuclear reaction rates in dense stars

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Dense Matter - Nuclear Reactions - Stars: Interiors - White Dwarfs

Scientific paper

In dense matter the thermonuclear reaction rate is significantly affected by neighbouring ions to a reacting pair. The rigorous theory of Alastuey & Jancovici shows that, if small quantum-mechanical effects associated with the neighbouring ions are neglected, the correct way to estimate thermonuclear reaction rates in dense matter is first to calculate the rate for a fixed configuration of neighbours to the fusing pair, and then to thermally average over positions of the neighbours. The standard assumption made in most calculations of rates is that the processes of thermodynamic averaging and the evaluation of the tunneling amplitude may be reversed. This is equivalent to assuming that the fusing pair of ions move in the average potential produced by the other ions. We make quantitative estimates of the reaction rate for a simple, physically motivated, three-dimensional model, and show that under some circumstances the standard approximation can give reaction rates that are too high by a factor 2.

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