Upper and Lower Bounds to Long-Range Forces between Two Hydrogen Atoms

Abstract

Bell's technique for the calculation of long-range dispersion-force coefficients is transformed to yield rigorous upper and lower bounds to these coefficients. The bounds involve in a systematic way the negative oscillator strength sums S(−k) of the two interacting atoms. By a slight modification, we are also able to bound the leading relativistic correction to the long-range potential. Application of the method to the interaction between two hydrogen atoms yields extremely tight bounds to all the relevant coefficients.