• Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

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      https://www.ias.ac.in/article/fulltext/pram/025/06/0641-0647

    • Keywords

       

      Improved condition; absence of bound states; critical screening parameter

    • Abstract

       

      Converging lower bound to the critical screening parameterDc 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 obtainDcms ≈ [0.764435n−2+0.617737n−3]−1 wheren is the principal quantum number. The predictedDc for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.

    • Author Affiliations

       

      R Dutt1 D Singh1 2 Y P Varshni1 2

      1. Department of Physics, University of Visva-Bharati, Santiniketan - 731 235, India
      2. Department of Physics, University of Ottawa, Ottawa - K1N 6N5, Canada
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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