= Solution
Far from a neutral bound system, the slowest-decaying electron-removal amplitude is controlled by the first ionization energy $I=E_{N-1}-E_N>0$. Its asymptotic <wavefunction> satisfies a free-particle-like equation at negative energy $-I$, giving a decay exponent $\kappa=\sqrt{2m_eI}/\hbar$. Density is quadratic in the amplitude, so
$$
\boxed{a=2\kappa=\frac{2\sqrt{2m_eI}}{\hbar}}
$$
or $a=2\sqrt{2I}$ in <atomic units>. Power-law radial factors and angular dependence do not alter this leading exponential coefficient. It is the ionization energy, not the electron affinity, that controls this tail.
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