# Yukawa Aqua

1. Oct 3, 2004

### Orion1

Classical Quantum Electrodynamics: (QED)

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

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

Deuterium Binding Energy:
$$E_b = ((m_p + m_n) - m_D)E_n$$

Yukawa Potential Well:
$$U_y = f^2 \frac{e^{-\frac{r_D}{r_0}}}{r_D}$$

$$E_b = U_y$$

$$((m_p + m_n) - m_D) E_n = f^2 \frac{e^{- \frac{r_D}{r_0}}}{r_D}$$

$$f_D^2 = ((m_p + m_n) - m_D) E_n r_D e^{\frac{r_D}{r_0}}$$

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

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

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

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

What is the numeric value for $$\propto_y$$?

As compared to $$\propto_e$$, is this numeric value reasonable?

Last edited: Oct 3, 2004