Bound states and critical behavior of the Yukawa potential

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We investigate the bound states of the Yukawa potential V(r)=-λ exp(-αr)/r,using different algorithms: solving the Schr(o)dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = αC, above which no bound state exists. We study the relation between αC and λ for various angular momentum quantum number l, and find in atomic units, αC(l) = λ[A1 exp(-1/B1) + A2 exp(-l/B2)], with A1 = 1.020(18), B1 = 0.443(14), A2 = 0.170(17), and B2 = 2.490(180).
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