Question

In particle and atomic physics, a Yukawa potential (also called a screened Coulomb potential) is a potential of the form ${\mathrm{V}}_{\mathrm{Yukawa}}\left(\mathrm{r}\right)=-{\mathrm{g}}^2\frac{{\mathrm{e}}^{-\mathrm{kmr}}}{\mathrm{r}}$, where g is the amplitude of potential, m is the mass of the mediating particle, r is the radial distance to the particle, and k is another constant. The potential is monotonically increasing. this can be realized by appropriate charge distribution. The Coulomb potential of a point charge is an example of a Yukawa potential with e^–kmr equal to 1 everywhere. The equation ${\mathrm{V}}_{\mathrm{Yukawa}}\left(\mathrm{r}\right)=-{\mathrm{g}}^2\frac{{\mathrm{e}}^{-\mathrm{kmr}}}{\mathrm{r}}$ simplifies to the form of the Coulomb potential ${\mathrm{V}}_{\mathrm{Coulomb}}\left(\mathrm{r}\right)=-{\mathrm{g}}^2\frac{1}{\mathrm{r}}$ A comparison of the long range potential strength for Yukawa and Coulomb is shown in figure. It can be seen that the Coulomb potential has effect over a greater distance whereas the Yukawa potential approaches zero rather quickly. However, any Yukawa potential or Coulomb potential are non-zero for any large r.