$\ce{^{4}He} + \ce{^{4}He} + \ce{^{4}He} \longrightarrow \ce{^{12}C} + \gamma$ After enough $\ce{^{4}He}$ accumulates in the core of the star, it can immediately fuse to $\ce{^{12}C}$ if the conditions allow the reaction. It requires: - helium density $\gtrsim 105 \; {\rm g/cm^{3}}$ - temperature $\gtrsim 10^{8} \; {\rm K}$ When these conditions are met, then the three $\alpha$ particles ($\ce{^{4}He}$) can overcome the beryllium-8 ($\ce{^{8}Be}$) barrier to fuse to create a stable carbon-12 nuclei ($\ce{^{12}C}$). In massive stars, this process of creating stable $\ce{^{12}C}$ can directly feed into the [[Alpha Process|alpha process]] to produce heavier elements. **More Details:** - Two helium-4 nuclei can fuse and produce beryllium-8 ($\ce{^{8}Be}$); however, it is highly unstable with a half-life $= 8.19 \times 10^{−17} \; {\rm s}$. - Very quickly decays back into smaller nuclei (i.e. two $\alpha$ particles, see [[Proton-Proton Chain#PP III]]) - If a third $\alpha$ particle can overcome the Coulomb barrier and fuse with the $\ce{^{8}Be}$ nuclei before it decays, then it can create an excited resonance state of carbon-12 *(**the Hoyle state**)*. - Typically, the Hoyle state will still decays into 3 $\alpha$ particles - $1/2421.3$ times, the Hoyle state relaxes to it stable, ground-state configuration of carbon-12, giving off the extra energy through [[Gamma Decay|gamma decay]] > [!temperature] Extremely Temperature Sensitive > > Helium-4 is explosive at high temperatures. With the ignition temperature of the triple-$\alpha$ process being $T \sim 10^{8} \; {\rm K}$ and the significantly high densities, a small rise in temperature can result in a enormous increase in [[Nuclear Energy Generation Rate|energy output]]. > > $\text{Energy Generation Rate: }\hspace{1cm} \epsilon \propto T^{40}$ > > This is particularly true in stars with electron-degenerate cores. Within the core, the temperature and density can rise above the necessary thresholds; however, helium fusion is restricted until the core reaches a critical mass ($M \sim 0.45 \; {\rm M_{\odot}}$) and a lot of helium fusion occurs at once, resulting in a [[Hertzsprung-Russell Diagram#Helium Flash|helium flash]]. > [!note] > This is one of the two major nuclear fusion reactions that convert helium into heavier elements in stars. *(also see [[Alpha Process]])*