Solution (source code)

= Solution

Restoring units, the decaying <Yukawa potential> is $V(r)=C e^{-r/\lambda_m}/r$ with range $\lambda_m=\hbar/(mc)$. For $r_*=10^{-18}\,\mathrm m$,
$$
\boxed{\frac{V(r)}{V(r_*)}=\frac{r_*}{r}\exp\left[-\frac{r-r_*}{\lambda_m}\right].}
$$
The geometric $1/r$ factor belongs in the potential ratio; the exponential alone is the additional suppression relative to massless exchange. Using $\hbar c=197.32698\,\mathrm{MeV\,fm}$ gives
$$
\lambda_\pi=1.46168\times10^{-15}\,\mathrm m,\qquad
\lambda_H=1.57862\times10^{-18}\,\mathrm m.
$$
The following are ratios of potential magnitudes to the magnitude at $r_*$, with the same coupling held fixed:

|| Mediator
|| $r=10^{-15}\,\mathrm m$
|| $r=10^{-10}\,\mathrm m$

| $m_\pi=135\,\mathrm{MeV}/c^2$
| $5.05\times10^{-4}$
| $10^{-29719.98}$

| $m_H=125\,\mathrm{GeV}/c^2$
| $10^{-277.836}$
| $10^{-27511101.31}$

| Massless scalar
| $10^{-3}$
| $10^{-8}$

For example, the pion's nuclear exponential factor is $e^{-0.68346}=0.505$, whereas the Higgs nuclear exponent is about $-632.83$. The huge atomic suppressions are most reliably reported through logarithms, not through floating-point exponentiation that silently underflows to zero. These are <potential energy> ratios, not force ratios or absolute comparisons of different interaction strengths.