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wofsy
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I would appreciate an explanation of Yukawa potential
RedX said:In the Wikipedia link:
http://en.wikipedia.org/wiki/Yukawa_potential
it says that the Fourier transformation of the Yukawa potential is the amplitude for two fermions to scatter. But the Fourier transform ignores 4-momentum and only has 3-momentum. The amplitude to scatter should depend on a 4-momentum squared, and not 3-momentum. So how is this reconciled?
Brian_C said:There is a problem in Jackson's E&M book which asks you to derive the charge distribution corresponding to this potential. I could never quite get it right.
The simplified version of the Yukawa derivation takes place in the barycentric system where the energy component of the 4-momentum transfer vanishes. Then the 3D Fourier T can be made.RedX said:it says that the Fourier transformation of the Yukawa potential is the amplitude for two fermions to scatter. But the Fourier transform ignores 4-momentum and only has 3-momentum. The amplitude to scatter should depend on a 4-momentum squared, and not 3-momentum. So how is this reconciled?
clem said:The simplified version of the Yukawa derivation takes place in the barycentric system where the energy component of the 4-momentum transfer vanishes. Then the 3D Fourier T can be made.
clem said:The simplified version of the Yukawa derivation takes place in the barycentric system where the energy component of the 4-momentum transfer vanishes. Then the 3D Fourier T can be made.
The Yukawa potential is a mathematical model used in physics to describe the interaction between two particles through the exchange of a virtual particle. It is named after the Japanese physicist Hideki Yukawa who first proposed its use in the 1930s.
The Yukawa potential is calculated using the formula V(r) = k * (q1 * q2 / r) * e^(-kr)/r, where k is the coupling constant, q1 and q2 are the charges of the two particles, r is the distance between them, and e is the base of natural logarithms. This formula takes into account the attractive and repulsive forces between the particles.
The Yukawa potential is significant because it is used to explain the behavior of the strong nuclear force, which is responsible for holding the nucleus of an atom together. It has also been used to model other fundamental forces, such as the weak nuclear force and the gravitational force.
One limitation of the Yukawa potential is that it assumes the particles are point-like and do not have any internal structure. It also does not take into account the effects of quantum mechanics, which become important at very small distances.
The Yukawa potential is related to the Higgs field through the Higgs mechanism, which explains how particles acquire mass. In this mechanism, particles interact with the Higgs field and gain mass through their interactions with the Higgs boson, which is the particle associated with the Higgs field. The strength of this interaction is described by the Yukawa potential.