Strong nuclear force is largest in.....?

Question

Strong nuclear force (also called strong force or colour force) is largest between :

A. proton-proton

B. proton-neutron

C. neutron-neutron

D. all have approximately same.

Answer 1

D

Answer 2

That's a tricky one and there isn't a good general answer there, but B is probably the best answer.

Let's just restrict ourselves to looking at two nucleons.

The residual strong force is repulsive to isospin triplets (combinations of nucleons that are symmetric under neutron/proton exchange) and attractive to singlets (anti-symmetric combinations).

So two protons (pp), two neutrons(nn), or a symmetric combination of proton/neutron(pn + np) can not be bound.  This is why we don't see a bound state of two neutrons or Helium-2 in nature.

An anti-symmetric combination of proton-neutron (pn - np) can be bound--deuterium.

When people say the residual strong force is invariant under isospin flip (ie, the protons go to neutrons and vice-versa), that means it can't tell the difference between a single proton and a single neutron.  Or it can't tell the general difference between H-3 (pnn) and He-3 (npp).  Or it can't tell the difference between triplet pairs (pp, nn, and pn+np).  But it does know the difference between those and the singlet pair (pn - np).

How does it do this?  The dominant component of the nuclear potential has a spin/space parity flip operator.  So it is attractive if spin and space have the same parity.  And it is repulsive if spin and space have opposite parity.  But any fermions must have totally anti-symmetric wave functions.  So spin*space*isospin parities must be anti-symmetric.  Therefore, if isospin is anti-symmetric (np-pn), space and spin are symmetric and the force is attractive.  If isospin is symmetric (pp,nn,pn+np), then space and spin are anti-symmetric and the force is repulsive.

Now nuclear forces are complicated.  The potential also has a component that is generally attractive.  So the attraction of the singlets is greater than the repulsion of the triplets, which is why a nucleus is generally  stable and I'd answer B.

All this (along with the Pauli exclusion principle which allows protons and neutrons to stack in their energy levels separately) is the reason that smaller nuclei tend to have equal numbers of protons and neutrons.  With larger nuclei, the EM force starts to kick in and push the ratio towards a greater number of neutrons, because that minimizes the electrostatic repulsion between protons.