What Do K and Alpha Represent in Yukawa's Potential?

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SUMMARY

In Yukawa's potential, represented as W(r) = \frac{\alpha}{r} * e^{-Kr}, the constants K and α play crucial roles in defining the characteristics of the force. The constant α signifies the "strength" of the force, analogous to the fine structure constant in electromagnetism. Conversely, K represents the inverse of the force's range, calculated as R ≈ \frac{\hbar}{Mc}, where M is the mass of the mediating boson. For electromagnetic interactions, the range R is infinite, resulting in K being zero.

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Ayame17
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This may seem like a really obvious question to those that know it but...

We looked at Yukawa's potential the other day, in the form W(r)=\frac{\alpha}{r}*e^{-Kr}, but our lecturer never explained what K and \alpha actually are! I've looked on the net and all I can find is that they are constants. What does they actually stand for?
 
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Roughly speaking, alpha is a constant representing the "strength" of the force... for the EM force it would be the fine structure constant. K is a constant representing the inverse of the range of the force R\approx \frac{\hbar}{Mc}. (M is the mass of the mediating boson). For the EM force R would be infinite, so K would be 0.

Ref: Particle Physics, Martin and Shaw, 3rd Ed.
 
Ah, now that makes a lot of sense! Thanks very much!
 

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