Yukawa potential

In <a href="/facts/Particle_physics/YgIuyj2t">particle</a>, <a href="/facts/Atomic_physics/7Jlm4I7k">atomic</a> and <a href="/facts/Condensed_matter_physics/EBVI5nmL">condensed matter physics</a>, a Yukawa potential (also called a screened <a href="/facts/Coulomb_potential/Nmqm6hm5">Coulomb potential</a>) is a <a href="/facts/Potential/8Fcbtnt9">potential</a> named after the Japanese physicist <a href="/facts/Hideki_Yukawa/Rz9vGmu3">Hideki Yukawa</a>. The potential is 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
 
 
 {\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 
 
 
 
 r
 ≈
 
 
 
 1
 
 α
 m
 
 
 
 
 
 
 {\displaystyle r\approx {\tfrac {1}{\alpha m}}}
 
 is the approximate range. The potential is <a href="/facts/Monotonic_function/MjQK0YL2">monotonically increasing</a> in r and it is negative, <a href="/facts/Force/533Q1uzq">implying</a> the force is attractive. In the SI system, the unit of the Yukawa potential is the <a href="/facts/Reciprocal_length/mlrDdsFD">inverse meter</a>.
The <a href="/facts/Coulomb_potential/Nmqm6hm5">Coulomb potential</a> of <a href="/facts/Electromagnetism/oAkmALHT">electromagnetism</a> 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 <a href="/facts/Photon/mFNhAEzA">photon</a> mass m is equal to 0. The photon is the force-carrier between interacting, charged particles.
In interactions between a <a href="/facts/Meson/9R0kIc1q">meson</a> field and a <a href="/facts/Fermion/LEckdDsR">fermion</a> field, the constant 
 
 
 
 g
 
 
 {\displaystyle g}
 
 is equal to the <a href="/facts/Coupling_constant/Queop1TR">gauge coupling constant</a> between those fields. In the case of the <a href="/facts/Nuclear_force/A2MyJoWE">nuclear force</a>, the fermions would be a <a href="/facts/Proton/clCjepXP">proton</a> and another proton or a <a href="/facts/Neutron/oRCM1geb">neutron</a>.

Yukawa potential open-in-new

Yukawa potential