23.5 Nuclear Stability, Binding-Energy Trends, and Nuclear Energy Levels

Light stable nuclei tend to have $N\approx Z$, while heavier stable nuclei require neutron excess. Extra neutrons increase strong-force bonding without adding Coulomb repulsion, helping counter proton-proton electrostatic repulsion in large nuclei. This is why stable heavy nuclides sit above the $N=Z$ line on an $N$-vs-$Z$ plot.

Nuclides above the stability band are often neutron-rich and tend toward beta minus decay (neutron to proton). Nuclides below the band are proton-rich and tend toward beta plus decay or electron capture (proton to neutron). Very heavy nuclei additionally show increased alpha-decay tendency because shedding a helium nucleus can reduce Coulomb strain while remaining energetically favorable.

For medium and large nuclei, each nucleon mainly interacts with nearby neighbors because strong force is short-range. Adding more distant nucleons does not proportionally increase strong binding for any one nucleon, so $E_b/A$ saturates instead of growing indefinitely. This near-constancy is a core clue that nuclear binding is not long-range additive in the way gravity is.

After alpha or beta decay, daughter nuclei are frequently left in excited states. A subsequent gamma transition can remove excess energy without changing $A$ or $Z$. This allows experiments to separate composition-changing decays from de-excitation photons and is one reason decay chains often include both particle emissions and gamma lines.