Enhancement of Thermonuclear Reaction Rate due to Strong Screening release_cuxbm5ryxvfdlho4lbafvlavae

Abstract

The enhancement factor for the rate of thermonuclear reactions which involve two kinds of nuclei with charges Z<jats:sub>i</jats:sub>and Z<jats:sub>j</jats:sub>in the strong-screening regime is given for general cases of surrounding nuclear plasmas by the formula, exp[1.25Γ<jats:sub>ij</jats:sub>−0.095τ<jats:sub>ij</jats:sub>(3Γ<jats:sub>ij</jats:sub>/τ<jats:sub>ij</jats:sub>)<jats:sup>2</jats:sup>]. Here, Γ<jats:sub>ij</jats:sub>= 2Z<jats:sub>i</jats:sub>Z<jats:sub>j</jats:sub>e<jats:sup>2</jats:sup>/(a<jats:sub>i</jats:sub>+a<jats:sub>j</jats:sub>)T; a<jats:sub>i</jats:sub>= [3Z<jats:sub>i</jats:sub>/4πΣ<jats:sub>k</jats:sub>Z<jats:sub>k</jats:sub>n<jats:sub>k</jats:sub>]<jats:sup>1/3</jats:sup>; τ<jats:sub>ij</jats:sub>= [(27π<jats:sup>2</jats:sup>/4)(2μ<jats:sub>ij</jats:sub>Z<jats:sub>i</jats:sub><jats:sup>2</jats:sup>Z<jats:sub>j</jats:sub><jats:sup>2</jats:sup>e<jats:sup>4</jats:sup>Th<jats:sup>2</jats:sup>)]<jats:sup>1/3</jats:sup>; μ<jats:sub>ij</jats:sub>is the reduced mass for the two reacting nuclei Z<jats:sub>i</jats:sub>and Z<jats:sub>j</jats:sub>; and n<jats:sub>k</jats:sub>is the number density of nuclei Z<jats:sub>k</jats:sub>. The calculation is based on the recent results of Monte Carlo computations for binary ion mixtures, which have shown that the screening functions h<jats:sub>ij</jats:sub>(r) at intermediate distances [0.5 ≤ r/[(a<jats:sub>i</jats:sub>+a<jats:sub>j</jats:sub>)/2] ≤ 1.6] can be expressed to a good degree of accuracy by<jats:disp-formula id="S007418090007412X_eqnU1"><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:href="S007418090007412X_eqnU1" xlink:type="simple" /></jats:disp-formula>Application to the calculation of carbon ignition in the carbon-oxygen core of a highly evolved star is discussed. The carbon ignition temperature is found to be single-valued as a function of the density in contrast to the work of Graboske.
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