Bound States and Critical Behavior of the Yukawa Potential

Abstract

We investigate the bound states of the Yukawa potential $V(r)=-\lambda \exp (-\alpha r)/r$, using different algorithms: solving the Schrödinger 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 $B_2=2.490(180)$.

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