Improved Error Bounds for the Long-Range Forces between Atoms

Abstract

Error bounds for the long-range attractive potential between pairs of atoms and molecules have been calculated by constructing oscillator strength distributions which reproduce known dynamic polarizabilities, oscillator strengths, and photoionization cross sections. Results from the theory of moments are applied to construct these distributions so that they provide rigorous error bounds on the force constant. Approximate solutions to the moment equations which result are found by means of linear programming. Results obtained for rare-gas interactions are found to be consistent with known values, with error bounds significantly tighter than those obtained from previous calculations. These same oscillator strength distributions are used to calculate error bounds on the dynamic polarizabilities for frequencies between those of the existing measurements and the first dipole-allowed transition.