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Bound States and Critical Behavior of the Yukawa Potential

Xiang-Qian Luo·Yong-Yao Li·Helmut Kroger
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Abstract

We investigate the bound states of the Yukawa potential $V(r)=-λ\exp(-αr)/ r$, using different algorithms: solving the Schrödinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical $α=α_C$, above which no bound state exists. We study the relation between $α_C$ and $λ$ for various angular momentum quantum number $l$, and find in atomic units, $α_{C}(l)= λ[A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})]$, with $A_1=1.020(18)$, $B_1=0.443(14)$, $A_2=0.170(17)$, and $B_2=2.490(180)$.

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Xiang-Qian Luo, Yong-Yao Li, Helmut Kroger. 2005-07-03. Bound States and Critical Behavior of the Yukawa Potential. https://doi.org/10.1007/s11433-004-0020-5

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