How is carbon produced inside stars through helium burning?

Inside stars, carbon is produced through a process known as the triple-alpha process. This reaction occurs in the dense cores of evolved stars when temperatures reach approximately 100,000,000 to 200,000,000 K.12

The synthesis of carbon proceeds in the following manner:

• Beryllium formation: Two helium nuclei (${}^4\text{He}$) collide to form an isotope of beryllium (${}^8\text{Be}$).21
• Instability: The resulting ${}^8\text{Be}$ nucleus is highly unstable and typically decays back into two helium nuclei almost immediately.21
• Carbon synthesis: If the temperature and density are sufficiently high, a third helium nucleus collides with the short-lived ${}^8\text{Be}$ nucleus before it can decay, resulting in the formation of a stable carbon-12 nucleus (${}^{12}\text{C}$).21

In some stars, this process begins with a sudden event called the "helium flash," while in others, it starts more gradually. Once carbon is formed, it may subsequently capture another helium nucleus to produce oxygen.12