  We present a complete analytical solution to the quantum problem of a
particle in the Yukawa potential, using supersymmetry and a systematic
expansion of the corresponding super-potentials. Results for the critical
screening of the ground state improve in several figures existing results based
on both numerical solutions and approximation methods. Our calculation to order
$(a_{0}/D)^{2}$ for the squared ground state wavefunction at the origin, which
enter in darkonium transitions, yields a correction of $\pi^{4}/216$ to results
based on variational techniques.
