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Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter
Authors:R Dutt  D Singh  Y P Varshni
Affiliation:(1) Department of Physics, University of Visva-Bharati, 731 235 Santiniketan, India;(2) Department of Physics, University of Ottawa, K1N 6N5 Ottawa, Canada
Abstract:Converging lower bound to the critical screening parameterD c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10−3% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD c ms ≈ [0.764435n −2+0.617737n −3]−1 wheren is the principal quantum number. The predictedD c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.
Keywords:Improved condition  absence of bound states  critical screening parameter
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