Abstract

We investigate the bound states of the Yukawa potential V(r)=λexp(αr)/rV(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 α=αC\alpha=\alpha_C, above which no bound state exists. We study the relation between αC\alpha_C and λ\lambda for various angular momentum quantum number ll, and find in atomic units, αC(l)=λ[A1exp(l/B1)+A2exp(l/B2)]\alpha_{C}(l)= \lambda [A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})], with A1=1.020(18)A_1=1.020(18), B1=0.443(14)B_1=0.443(14), A2=0.170(17)A_2=0.170(17), and B2=2.490(180)B_2=2.490(180).Comment: 15 pages, 12 figures, 5 tables. Version to appear in Sciences in China

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    Last time updated on 11/12/2019