Strong Spin–Orbit Coupling in Nuclear Physics

In nuclear physics, strong spin–orbit coupling is the crucial interaction that makes the nuclear shell model work and explains the observed magic numbers. Below is a clear, step-by-step explanation of what it is, why it is “strong,” and what it does.

1. What “Spin–Orbit” Means

Every nucleon (proton or neutron) has:

• Orbital angular momentum — due to its motion inside the nucleus
• Intrinsic spin

The spin–orbit interaction couples these two:

This term shifts the energy depending on whether the spin is:

• Aligned with →
• Anti-aligned with →

2. Why Spin–Orbit Is “Strong” in Nuclei

In atoms:

• Spin–orbit coupling comes from relativistic corrections to the Coulomb interaction
• It is relatively weak

In nuclei:

• The interaction arises from the strong nuclear force, not electromagnetism
• The potential is deep (~50 MeV)
• Nucleons move at fast (relativistic) speeds
• The nuclear force has a strong tensor component

Result: Spin–orbit splitting in nuclei is an order of magnitude larger than in atoms.

3. Mathematical Form (Qualitative)

A typical nuclear shell-model Hamiltonian includes:

Where:

Key point: The nuclear potential has a sharp surface → is large near the surface → is very strong.

4. Energy Level Splitting

For each orbital , spin–orbit coupling splits levels into two:

Orbital	Levels
(p)	,
(d)	,
(f)	,

Crucially: The level is much lower in energy.

This downward shift of the higher- state creates large energy gaps and rearranges shell closures.

5. Creation of Magic Numbers

Without spin–orbit:

With strong spin–orbit:

Example: The large downward shift of the level creates the shell closure at 28. Similar effects produce 50, 82, and 126.

No strong spin–orbit → no correct magic numbers!

6. Physical Intuition

A useful picture:

• A nucleon moves through a strong, rapidly changing nuclear potential
• In its rest frame, motion through the nuclear field produces an effective magnetic field
• This field couples strongly to the nucleon’s spin
• Alignment lowers energy; anti-alignment raises it

Though this analogy borrows from electromagnetism, the force is the strong interaction, so the effect is much larger.

7. Experimental Evidence

Strong spin–orbit coupling is confirmed by:

• Large splittings between levels
• Correct prediction of magic numbers
• Nuclear spectroscopy
• Scattering experiments
• Binding energy systematics

8. Why This Was a Big Deal

Before 1949: The shell model failed beyond 20.

After Mayer & Jensen added strong spin–orbit coupling:

• Magic numbers explained
• Nuclear structure made sense
• Nobel Prize in Physics (1963)

This is considered one of the great breakthroughs of 20th-century nuclear physics.

9. Key Differences from Atomic Spin–Orbit

One-Sentence Summary
Strong spin–orbit coupling in nuclei arises from the strong nuclear force acting in a steep, short-range potential, producing large energy splittings between states and creating the observed nuclear magic numbers.