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the spectrum of quarkonium and the comparison with positronium potential for the strong force is:

$V(r) = - \frac{4}{3} \frac{\alpha_s(r) \hbar c}{r} + kr$

(where the constant $k$ determines the field energy per unit length and is called string tension. )

in other hand, one can talk about a Yukawa potential of the form

$$ V(r) = - \frac{g^2}{4 \pi c^2} \frac{e^{-mr}}{r} $$

where $m$ is roughly the pion mass and $g$ is an effective coupling constant.

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up vote 1 down vote accepted

The two formulae are dissimilar so the difference is mathematically evident.

If you are asking: why are we calling the nuclear force a strong force, the Wiki article has the answer in a nuttshell:, calling it a residual strong force:

The residual strong force is thus a minor residuum of the strong force which binds quarks together into protons and neutrons. This same force is much weaker between neutrons and protons, because it is mostly neutralized within them, in the same way that electromagnetic forces between neutral atoms (van der Waals forces) are much weaker than the electromagnetic forces that hold the atoms internally together.

Qualitatively: the proton and neutron as bound colorless states of three quarks each, to first order are neutral in the strong force, in the same way that a molecule is neutral to the electromagnetic force. First order, because at higher orders there are moments/distortions of the collective many body potential that extend outside the neutral region and create the Wan der Waals electromagnetic forces for the molecules and the nuclear force for the nuclei.

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