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YukawaHooke Equasion... 
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#1
Jan1404, 06:57 AM

P: 989

Hooke's Law: [tex]W(x) =  \frac{kx^2}{2}[/tex] k  spring force constant Yukawa Potential: [tex]U(r) =  f^2 \frac{e^ \frac{(r/r_0)}{}}{r}[/tex] f  interaction strength r_{0} = 1.5*10^15 m [tex]U(r) = W(r)[/tex] YukawaHooke Equasion: [tex]f^2 \frac{e^ \frac{(r/r_0)}{}}{r} = \frac{kr^2}{2}[/tex] [tex]f^2 = \frac{kr^3}{2e^ \frac{(r/r_0)}{}}[/tex] [tex]f = \sqrt{ \frac{kr^3}{2e^ \frac{(r/r_0)}{}}}[/tex] [tex]r = \sqrt[3]{ \frac{2f^2 e^ \frac{(r/r_0)}{}}{k}}[/tex] [tex]E(r) = U(r) + W(r)[/tex] [tex]E(r) = f^2 \frac{e^ \frac{(r/r_0)}{}}{r}  \frac{kr^2}{2}[/tex] Yukawa Meson MassEnergy Spectrum: [tex]\pi ^o (135 Mev) > \eta ^o (548.8 Mev)[/tex] r_{1} = 1.461 Fm > .359 Fm [tex]E(r) = W(r)[/tex] [tex] \frac{\hbar c}{r_1} =  \frac{kr_1 ^2}{2}[/tex] [tex]k = \frac{2 \hbar c}{r_1 ^3}[/tex] [tex]E(r) = U(r)[/tex] [tex] \frac{\hbar c}{r_1} = f^2 \frac{e^ \frac{(r_1/r_0)}{}}{r_1}[/tex] [tex]\hbar c = f^2 e^ \frac{(r_1/r_0)}{}[/tex] [tex]f = \sqrt{ \frac{\hbar c}{{e^ \frac{(r_1/r_0)}{} }}[/tex] How effective is the YukawaHooke Equasion at emulating a Nuclear Force Mediator? What is the depth of such an equasion? and can it be applied to String Theory? 


#2
Jan1904, 07:20 AM

PF Gold
P: 2,893

The issue is relativistic invariance. Can one implement Hooke's law in a relativistic invariant way.?
Yukawa force is mediated via a particle of mass 1/R_0, so that relativity can be implemented simply by asking the particle propagator to fullfill it. I am not telling it does not exist a particle interpretation of Hooke's law, just I have never heard of it. Neither of a string interpretation Hooke's law... but it could be, because these strings somehow are relativitycomplient. 


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