Stellar Helium Burning
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Exercise:
The half-life of isotopeBe is only .s. Explain qualitatively why the triplalpha process upalpha to isotopeC nevertheless occurs in stars.
Solution:
Although isotopeBe is unstable as shown in part~a its decay is slow enough that at sufficiently high densities and temperatures a small but non-zero uilibrium concentration of isotopeBe builds up: isotopeHe + isotopeHe rightleftharpoons isotopeBe A fraction of these isotopeBe nuclei is then captured by a third upalpha particle before decaying: isotopeBe + isotopeHe longrightarrow isotopeC + gamma This second step is enormously enhanced by a resonance: isotopeC has an excited state at E^* .MeV the Hoyle state which lies almost exactly at the combined energy of isotopeBe and an upalpha particle under typical stellar conditions. The resonance increases the reaction cross-section by many orders of magnitude making carbon synthesis possible despite the fleeting existence of isotopeBe. The process only occurs at the extreme conditions found in red giant cores: temperatures of T approx eK and densities of rho approx egpcmk.
The half-life of isotopeBe is only .s. Explain qualitatively why the triplalpha process upalpha to isotopeC nevertheless occurs in stars.
Solution:
Although isotopeBe is unstable as shown in part~a its decay is slow enough that at sufficiently high densities and temperatures a small but non-zero uilibrium concentration of isotopeBe builds up: isotopeHe + isotopeHe rightleftharpoons isotopeBe A fraction of these isotopeBe nuclei is then captured by a third upalpha particle before decaying: isotopeBe + isotopeHe longrightarrow isotopeC + gamma This second step is enormously enhanced by a resonance: isotopeC has an excited state at E^* .MeV the Hoyle state which lies almost exactly at the combined energy of isotopeBe and an upalpha particle under typical stellar conditions. The resonance increases the reaction cross-section by many orders of magnitude making carbon synthesis possible despite the fleeting existence of isotopeBe. The process only occurs at the extreme conditions found in red giant cores: temperatures of T approx eK and densities of rho approx egpcmk.