1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Yukawa-Hooke Equasion

  1. Jan 14, 2004 #1

    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
    r0 = 1.5*10^-15 m

    [tex]U(r) = W(r)[/tex]

    Yukawa-Hooke 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 Mass-Energy Spectrum:
    [tex]\pi ^o (135 Mev) -> \eta ^o (548.8 Mev)[/tex]
    r1 = 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 Yukawa-Hooke Equasion at emulating a Nuclear Force Mediator?

    What is the depth of such an equasion? and can it be applied to String Theory?

    Last edited: Jan 20, 2004
  2. jcsd
  3. Jan 19, 2004 #2


    User Avatar
    Gold Member

    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 relativity-complient.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Yukawa-Hooke Equasion