Nuclear and Quantum Physics - Fusion and stars

Nuclear fusion is the process in which two light nuclei combine to form a more massive nucleus. For fusion to occur, the nuclei must have sufficient kinetic energy to overcome the electrostatic repulsion (the Coulomb barrier). This requires extremely high temperatures (around $10^7 \text{ K}$) and high pressures, typically found in stellar cores.

The energy released in fusion is due to the mass defect $\Delta m$. The mass of the resulting nucleus is less than the sum of the masses of the individual reactant nuclei. This 'lost' mass is converted into energy according to Einstein's mass-energy equivalence principle $E = \Delta mc^2$.

Binding energy per nucleon is a measure of nuclear stability. In the binding energy curve, fusion occurs for light elements (where mass number $A < 62$) because the product nucleus has a higher binding energy per nucleon than the reactants, resulting in a more stable state and the release of energy.

Main sequence stars, like our Sun, primarily generate energy through the proton-proton (p-p) chain. The net reaction involves four hydrogen nuclei (protons) fusing to form one helium-4 nucleus, two positrons, and two neutrinos: $4^1_1H \rightarrow ^4_2He + 2^0_{+1}e + 2\nu + \gamma$.

A star maintains its size through hydrostatic equilibrium, which is the balance between the inward pull of gravity and the outward radiation pressure generated by nuclear fusion in the core.

The Hertzsprung-Russell (H-R) diagram plots stars according to their luminosity ($L$) on the y-axis and surface temperature ($T$) on the x-axis (with temperature increasing to the left). Most stars fall along the Main Sequence, where they fuse hydrogen into helium.

Stellar evolution depends on the initial mass of the star. Low-mass stars (like the Sun) evolve into Red Giants and eventually shed their outer layers to leave a White Dwarf. High-mass stars evolve into Red Supergiants and end their lives in a Supernova, leaving behind a Neutron Star or a Black Hole.