QFT — Michael Luke Lectures · Problem 3

Example (continued): Perturbation Theory for nonrelativistic quantum mechanics — Michael Luke

Physics — QFT · yukawa-potential-meson-exchange

Problem

Returning now to relativistic quantum mechanics, consider the amplitude for the scattering of two distinguishable ``nucleons''

\psi_a

and

\psi_b

with identical masses and couplings to the

\phi

field. In the non-relativistic limit, we can consider this as the scattering of two ``nuclei'' due to an effective nucleon-nucleon potential induced via meson exchange. In analogy with your answer to part (2), show that the effective nucleon-nucleon potential has the Yukawa form

V(r) \sim g^2 \frac{e^{-\mu r}}{r}.

Is the force attractive or repulsive?

Related theory

Electric Potential And Potential Difference

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