= Solution
At incident <wave number> $k$, low <kinetic energy> means $ka\ll1$: the <de Broglie wavelength> is much larger than the scattering region. A generic finite-range scatterer can then be described to leading order without resolving its angular structure. In <partial-wave scattering>, this is leading <S-wave scattering>. The $\ell=0$ <spherical harmonic> is constant, whereas the centrifugal term $\hbar^2\ell(\ell+1)/(2mr^2)$ impedes penetration to the potential for $\ell>0$.
For a <central potential> with regular threshold behaviour, the <finite-range partial-wave threshold law> gives $\delta_\ell=O(k^{2\ell+1})$. Thus
$$
f(\theta)=\frac1k\sum_{\ell=0}^{\infty}(2\ell+1)e^{i\delta_\ell}\sin\delta_\ell\,P_\ell(\cos\theta)
\simeq\frac{e^{i\delta_0}\sin\delta_0}{k},
$$
which is independent of scattering angle. For finite nonzero <scattering length> $a_s$, $f\to-a_s$ and \b[$d\sigma/d\Omega\to a_s^2$ is isotropic]. The potential range $a$ and <scattering length> $a_s$ are different quantities. The claim describes the generic leading <S-wave scattering> limit; tuned vanishing <S-wave scattering> amplitude or exceptional threshold resonances require separate analysis rather than a universal angular conclusion.
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