Yukawa potential

A central potential proportional to \(e^{-r/a}/r\), combining inverse-distance decay with exponential screening. Its finite range models interactions mediated by massive particles.

Klein–Gordon equation: A relativistic wave equation describing scalar fields and particles with spin zero. Its static Green’s function produces the exponentially screened form of the potential.
Hideki Yukawa: A Japanese theoretical physicist who proposed the meson theory of nuclear forces. His 1935 theory introduced the finite-range potential that bears his name.
Nuclear potential: A potential-energy function used to model interactions among nucleons in a nucleus. Yukawa-type terms model the short-range attraction between nucleons.
Coulomb potential: The electrostatic potential between point charges, proportional to inverse separation in three dimensions. Removing the exponential factor gives the unscreened, infinite-range limit.
Green's function: A function that gives a linear differential operator’s response to a localized source. The Yukawa form is the Green’s function of a massive field operator in three dimensions.
Yukawa interaction: A field-theoretic coupling between a fermion field and a scalar or pseudoscalar field. The potential is the static interaction associated with exchange in Yukawa’s theory.
Debye–Hückel theory: A theory that approximates electrostatic interactions in dilute electrolyte solutions by accounting for ionic screening. Its screened Coulomb potential has the same exponential-over-distance form.
Newtonian gravitational potential: The gravitational potential of a point mass in Newtonian theory, proportional to inverse distance. Like the Coulomb form, it lacks Yukawa’s exponential attenuation.
Compton wavelength: A particle’s characteristic quantum wavelength, inversely proportional to its mass. It sets the Yukawa potential’s exponential decay length for a particle mediator.
Meson theory of nuclear forces: A theory in which nuclear forces arise from the exchange of mesons between nucleons. It supplied the physical motivation for an exponentially decaying nuclear potential.

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