Neutron–proton ratio

Semi-empirical description

For stable nuclei, the neutron-proton ratio is such that the

From the liquid drop model, this bonding energy is approximated by empirical

${\displaystyle E_{B}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z^{2}}{A^{1/3}}}-a_{A}{\frac {(A-2Z)^{2}}{A}}\pm \delta (A,Z).}$

Given a value of ${\displaystyle A}$ and ignoring the contributions of nucleon spin pairing (i.e. ignoring the ${\displaystyle \pm \delta (A,Z)}$ term), the binding energy is a quadratic expression in ${\displaystyle Z}$ that is minimized when the neutron-proton ratio is ${\displaystyle N/Z\approx 1+{\frac {a_{C}}{2a_{A}}}A^{2/3}}$.