Is the Strong nuclear force experienced by two protons the same as two neutrons?

Question

My textbook says it doesn't depend on the charge and that they are the same, but shouldn't the repulsion between protons effect the total force they experience? Can we say the total force experienced by two neutrons is more than two protons? (Because of the similar charges)

Answer 1

The strong forces between neutrons and between protons are slightly different (after adjustment for electromagnetic effects). See, e. g., empirical values for the singlet scattering length (-18.9 vs -17.3 fm) and range (2.75 vs 2.85 fm) in PHYSICAL REVIEW C, VOLUME 63, 024001, eqs. 3.1 and 3.2.

Let me also note that strong forces between two neutrons and between a neutron and a proton are also different due to the Pauli exclusion principle. That is why the deuteron is stable, unlike the dineutron.

Answer 2

The strong force does not care but the total force includes electric repulsion. This is why nuclei tend to have more neutrons than protons (as this is energetically cheaper, the transition between them being beta-decay).

Answer 3

Even if we could turn off the electromagnetic force and consider only the strong force, a proton interacting with a proton would have a slightly different force than a neutron interacting with a neutron. These forces are approximately the same because of isosopin symmetry, but isosopin symmetry is not a perfect symmetry of nature. The up and down quarks that make up protons and neutrons have slightly different masses. This makes protons (made of two up quarks and a down quark) and neutrons (made of two down quarks and an up quark) slightly different from each other even ignoring the electric charges.

Answer 4

QCD is the theory of the strong nuclear force while QED is the theory of electromagnetic interactions. I assume that your textbook is not concerned with discussing QED here.

Moreover, at the length scales which you talk about, i.e. nucleonic distances, roughly around 1 fm $= 10^{-15} m$, the strong nuclear force is far too strong than the electromagnetic force (which you may have intuition for from everyday life). Therefore, ignoring the minuscule contribution from the electromagnetic force, the strong nuclear force should be the same between two protons when compared to the one between two neutrons.

I will let you think yourself about why gravity, i.e. the effects arising from the mass differences between the two scenarios, can also be ignored!