The relativistic correction for the Yukawa potential needs to be considered in self-interacting dark matter, neutron star binaries and non-static quark pairs. To avoid tedious calculations in non-relativistic effective field theory, we propose a new classicization scenario focusing on the correspondence between quantum states and classical observables, which both describe the evolution of their own systems. We classicize the Yukawa interaction through this method and expand the potential to the

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... next-to-leading order of the relativistic correction, which reproduces the same results in effective Yukawa field theory.