An estimate of the range of the strong force can be made by assuming that it is an exchange force involving neutral pions. This would be considering the pion involved in the exchange to be a "virtual particle", limited in lifetime by the uncertainty principle. When the range expression
is used with a pion mass of
π0 mass = 264 me = 135.0 MeV/c2 the range obtained isThis range is in the neighborhood of one fermi. When Hideki Yukawa was working on a theory of the strong force, he judged that the range of the nuclear force was about a fermi, and calculated that the exchange particle should be in the neighborhood of 100 MeV in mass equivalent. This triggered the search which led to the discovery of the pion. When the nuclear particles are very close together, other heavier particles must also be included in this type of model of the strong force. The current view is that the strong force is fundamentally an interaction between quarks, called the "color force" and that the "strong force" between nucleons which are colorless is really a residual color force.
Inside a proton or neutron (or any hadron), the force between quarks does not decrease with distance, leading to the confinement of quarks. But outside a proton or neutron, the strong force between them drops off precipitously within about a fermi of distance. The pion range is a reasonable predictor of this precipitous drop and gives further insight into the paradoxical nature of the strong nuclear force. For a proton to attract a neighboring proton, it must exchange something with it, but an isolated quark cannot be exchanged because of quark confinement. However, it can exchange a quark-antiquark pair (a meson) and the pion is the lightest of the mesons. Lighter exchange particle implies longer range, so the pion range gives you an upper bound for an exchange force involving quark-antiquark pairs.
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