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potential well (Figure 14-05a). Thus fusion occurs only at high temperature when the charged particles have acquired enough energy to overcome the Coulomb repulsion. The stellar interior is the only place where fusion occurs naturally via the proton-proton reaction and the carbon cycle (Figure 14-13a). The amount of energy released is about an order of magnitude lower than fission and many of the reactions takes a long time to occur. Nevertheless, since there are so many charged particles inside the stars, they keep on generating energy |
Figure 14-13a Stellar Fusion |
for a long time especially when the key (initial) step of proton-proton reaction takes an average of 14 billion years to occur (this is lucky for the evolution of life, otherwise the Sun may cease to shine long time ago). |
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Figure 14-13b shows the dependence of temperature for the p-p reaction and carbon cycle (CNO). The p-p reaction is the dominant process in lower temperature (in million degree K) for most of the main sequence stars. Whereas at higher temperature, the CNO process is important for massive stars with mass greater than 1.5 Msun and in the later stage of all stars. Careful examination of Figure 14-13a reveals that two protons in the p-p chain and one carbon in the CNO cycle act like a catalyze to produce a nucleus of He-4. The time scale in Figure 14-13a is the "mean reaction time per particle", which is proportional to T2/3/ (and other constants) where T is the temperature and is the density of the proton (and He-3 in one of the steps). The entities with no label in the diagrams of Figure 14-13a are the compound nuclei, which exist for a very short time of about 10-16 sec.
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Figure 14-13b Temp. & Reaction Rate |