Yukawa potential

In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form:

${\displaystyle V_{\text{Yukawa}}(r)=-g^{2}{\frac {e^{-\alpha mr}}{r}},}$

where ${\displaystyle g}$ is a magnitude scaling constant, i.e. is the amplitude of potential, m is the mass of the particle, r is the radial distance to the particle, and α is another scaling constant, so that ${\displaystyle r\approx {\tfrac {1}{\alpha m}}}$ is the approximate range. The potential is monotonically increasing in r and it is negative, implying the force is attractive. In the SI system, the unit of the Yukawa potential is the inverse meter.

The Coulomb potential of electromagnetism is an example of a Yukawa potential with the ${\displaystyle e^{-\alpha mr}}$ factor equal to 1, everywhere. This can be interpreted as saying that the photon mass m is equal to 0. The photon is the force-carrier between interacting, charged particles.

In interactions between a meson field and a fermion field, the constant ${\displaystyle g}$ is equal to the gauge coupling constant between those fields. In the case of the nuclear force, the fermions would be a proton and another proton or a neutron.