AcademyNuclear Physics
Academy
Nuclear Structure
Level 1 - Physics topic page in Nuclear Physics.
Principle
Nuclear structure follows from short-range attraction, electrostatic repulsion, quantum shells, and nucleon pairing.
Notation
\(F_{\mathrm s}\)
strong nuclear force
\(\mathrm{N}\)
\(F_{\mathrm C}\)
Coulomb repulsion
\(\mathrm{N}\)
\(r\)
nucleon separation
\(\mathrm{m}\)
\(\ell\)
orbital angular-momentum quantum number
1
\(j\)
total angular-momentum quantum number
1
\(I\)
nuclear spin
1
Method
Derivation 1: Competing interactions
The nucleus is held by attraction that saturates and opposed by proton-proton repulsion.
Short-range binding
\[F_{\mathrm s}\approx0\quad\text{for}\quad r\gtrsim\text{few fm}\]
Longer-range repulsion
\[U_C\sim\frac{1}{4\pi\epsilon_0}\frac{Z(Z-1)e^2}{R}\]
Derivation 2: Saturation
Each nucleon interacts strongly with nearby nucleons, not all nucleons equally.
Volume term
\[B_{\mathrm{volume}}\propto A\]
Surface correction
\[B_{\mathrm{surface}}\propto -A^{2/3}\]
Derivation 3: Shell and pairing effects
Quantum levels and pairing explain extra stability beyond a liquid-drop picture.
Closed shells
\[N,Z=2,8,20,28,50,82,126\]
Pairing trend
\[\text{even-even nuclei are usually most tightly paired}\]
Rules
Coulomb scale
\[U_C\sim\frac{1}{4\pi\epsilon_0}\frac{Z(Z-1)e^2}{R}\]
Radius scale
\[R=R_0A^{1/3}\]
Shell closures
\[N,Z=2,8,20,28,50,82,126\]
Examples
Question
Why does the strong force not make binding energy scale as \(A^2\)?
Answer
The strong force is short-range and saturates, so each nucleon mainly binds to nearby nucleons.
Checks
- Strong nuclear attraction is short-range and approximately charge-independent.
- Coulomb repulsion acts only between protons.
- Shell closures give extra stability at magic numbers.
- Pairing favors even \(Z\) and even \(N\) nuclei.