Yukawa-Hooke Equasion...

[Orion1]

Hooke's Law:
W(x) = - \frac{kx^2}{2}
k - spring force constant

Yukawa Potential:
U(r) = - f^2 \frac{e^- \frac{(r/r_0)}{}}{r}
f - interaction strength
r0 = 1.5*10^-15 m

U(r) = W(r)

Yukawa-Hooke Equasion:
-f^2 \frac{e^- \frac{(r/r_0)}{}}{r} = -\frac{kr^2}{2}

f^2 = \frac{kr^3}{2e^- \frac{(r/r_0)}{}}

f = \sqrt{ \frac{kr^3}{2e^- \frac{(r/r_0)}{}}}

r = \sqrt[3]{ \frac{2f^2 e^- \frac{(r/r_0)}{}}{k}}

E(r) = U(r) + W(r)
E(r) = -f^2 \frac{e^- \frac{(r/r_0)}{}}{r} - \frac{kr^2}{2}

Yukawa Meson Mass-Energy Spectrum:
\pi ^o (135 Mev) -> \eta ^o (548.8 Mev)
r1 = 1.461 Fm -> .359 Fm

E(r) = W(r)

- \frac{\hbar c}{r_1} = - \frac{kr_1 ^2}{2}

k = \frac{2 \hbar c}{r_1 ^3}

E(r) = U(r)
- \frac{\hbar c}{r_1} = -f^2 \frac{e^- \frac{(r_1/r_0)}{}}{r_1}

\hbar c = f^2 e^- \frac{(r_1/r_0)}{}

f = \sqrt{ \frac{\hbar c}{{e^- \frac{(r_1/r_0)}{} }}

How effective is the Yukawa-Hooke Equasion at emulating a Nuclear Force Mediator?

What is the depth of such an equasion?