Yukawa potential

In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential of the form





V

Yukawa


(
r
)
=
−

g

2





e

−
α
m
r


r


,


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



r
≈



1

α
m






{\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 (1/meters).
The Coulomb potential of electromagnetism is an example of a Yukawa potential with the




e

−
α
m
r




{\displaystyle e^{-\alpha mr}}
factor equal to 1, everywhere. This can be interpreted as saying that the photon mass m is equal to 0.
In interactions between a meson field and a fermion field, the constant 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.

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