Abstract
In the hope of uncovering additional Urca-active nuclei that might appear during carbon burning in the electron-degenerate carbon-oxygen core of an asymptotic-branch star and avert a thermonuclear runaway, a nuclear-reaction matrix connecting 244 nuclear species has been constructed. Analytic expressions for rates of all relevant ..beta..-transitions are also presented and used. It is shown that in matter which is composed initially of elements in a solar-system distribution and which has undergone first complete hydrogen burning and then complete helium burning, neutrino-loss rates due to 11 Urca pairs either rival or exceed neutrino losses predicted by the charge- and neutral-current theories of weak interactions. Most remarkably, no new Urca pairs of any consequence appear as a result of several thousand reactions that are allowed to occur during carbon burning. The dominant Urca-loss rates are still due to the pairs /sup 21/F-/sup 21/Ne, /sup 23/Ne-/sup 23/Na, /sup 25/Na-/sup 25/Mg, and /sup 25/Ne-/sup 25/Na, as in matter containing a solar-system distribution of elements that has undergone prior processing during hydrogen- and helium-burning phases. The abundances of these Urca-active pairs are enhanced by one to three orders of magnitude as a consequence of carbon-burning reactions.
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