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What meson influences the nucleon-nucleon interaction at a far range and why?

Nucleon-Nucleon (NN) interaction is divided up into three parts

a) long range (>2fm)

b) medium range (1 to 2fm)

c) short range (<1fm)

From my understanding, the pion is a lighter exchange particle, which implies longer range. What is the relationship between mass of the exchange particle and range?

Would the pion influence NN interaction at a far range more than ρ-mesons (rho mesons)?

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The range of a force mediated by a particle of mass $m$ is of order $\hbar\over mc$. For a pion, that turns out to be around 1-2 femtometers.

The pion is the lightest meson, and so at longer ranges nucleons interact primarily via electromagnetic forces. Rho mesons are much heavier and thus have a shorter range.

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