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.