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Yukawa Aqua

  1. Oct 3, 2004 #1

    Classical Quantum Electrodynamics: (QED)

    Classical QED gravitational Fine Structure Constant:
    [tex]\propto_g = \frac{Gm_p^2}{\hbar c}[/tex]
    [tex]m_p[/tex] - proton mass

    Classical QED Electromagnetism Fine Structure Constant:
    [tex]\propto_e = \frac{K_e q^2}{\hbar c}[/tex]
    [tex]K_e[/tex] - Coulomb's proportionality constant
    [tex]q[/tex] - proton charge

    Deuterium Binding Energy:
    [tex]E_b = ((m_p + m_n) - m_D)E_n[/tex]

    Yukawa Potential Well:
    [tex]U_y = f^2 \frac{e^{-\frac{r_D}{r_0}}}{r_D}[/tex]

    [tex]E_b = U_y[/tex]

    [tex]((m_p + m_n) - m_D) E_n = f^2 \frac{e^{- \frac{r_D}{r_0}}}{r_D}[/tex]

    [tex]f_D^2 = ((m_p + m_n) - m_D) E_n r_D e^{\frac{r_D}{r_0}}[/tex]

    [tex]\boxed{f_D = \sqrt{((m_p + m_n) - m_D) E_n r_D e^{\frac{r_D}{r_0}}}}[/tex]

    Classical QED Deuterium-Yukawa Fine Structure Constant:
    [tex]\boxed{\propto_y = \frac{f_D^2 e^{- \frac{r_D}{r_0}}}{\hbar c}}[/tex]

    [tex]E_n = 1.492*10^{-10} j*amu^{-1}[/tex] (931.437 Mev*amu^-1) - mass-energy equivalence
    [tex]m_p[/tex] - Proton mass
    [tex]m_n[/tex] - Neutron mass
    [tex]m_D[/tex] - Deuterium mass
    [tex]r_D[/tex] - Deuterium nuclear radius
    [tex]r_0[/tex] - Yukawa nuclear range

    Can Deuterium Binding Energy be described as existing inside a Yukawa Potential Well?

    What is the numeric value for [tex]\propto_y[/tex]?

    As compared to [tex]\propto_e[/tex], is this numeric value reasonable?

    Last edited: Oct 3, 2004
  2. jcsd
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