Bound States and Critical Behavior of the Yukawa Potential

Details Bound States and Critical Behavior of the Yukawa Potential Bound States and Critical Behavior of the Yukawa Potential

2004-07-21

arxiv.org/abs/hep-ph/0407258v2

Sci.China G35 (2005) 631-642

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages, 12 figures, 5 tables. Version to appear in Sciences in China G

Scientific paper

10.1007/s11433-004-0020-5

We investigate the bound states of the Yukawa potential $V(r)=-\lambda \exp(-\alpha r)/ r$, using different algorithms: solving the Schr\"odinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical $\alpha=\alpha_C$, above which no bound state exists. We study the relation between $\alpha_C$ and $\lambda$ for various angular momentum quantum number $l$, and find in atomic units, $\alpha_{C}(l)= \lambda [A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})]$, 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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