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12 Nuclear Astrophysics > 12.8 Red Giants - Pg. 360

360 | Chapter 12 where µ is the reduced mass of the reactants 8 Be and -particle. This further reduces by the above argument to r 3 12 C = 3 N 3/2 3 2 - 2h 2 M kT 3 f - h exp - Q kT . (12.59) The Q -value of the reaction is the sum of E R ( 8 Be + ) = 287 keV and E R ( + ) = |Q | = 92 keV and turns out to be Q 3 = (M 12 C - 3M )c 2 = 379.38 ± 0.20 keV. Numerically, the energy generation rate for the triple- reaction is 3 = 2 X 3 r 3 Q 3 = 3.9 × 10 11 3 f exp ( - 42.94/T 8 ) erg gm -1 s -1 . T 8 (12.60) The triple- reaction has a very strong temperature dependence near a value of temper- ature T 0 , and one can show that the energy generation rate is (T ) = (T 0 ) T T 0 n , (12.61) where n = 42.9/T 8 - 3. Thus at a sufficiently high temperature and density, the helium gas is very highly explosive, so that a small temperature rise gives rise to greatly accelerated reaction rate and energy liberation. When helium thermonuclear burning is ignited in the stellar core under degenerate conditions, an unstable and sometimes explosive condition develops.