A new method is presented for using theoretical or experimental optical dispersion data to construct bounded estimates to dispersion force coefficients. The bounds are obtained from the Casimirndash;Polder integral formula and an analytic continuation of the power series expansion of the dynamic multipole polarizabilities for the interacting species. Recognition of the dynamic polarizabilities at imaginary frequency as series of Stieltjes allows construction of the necessary bounded continuations with Padeacute; approximants expressed directly in terms of Cauchy dispersion coefficients. The sequence of bounds obtained incorporates the London and Slaterndash;Kirkwood values in lowest order, and provides improvements to these two wellhyphen;known bounds in higher order. The method is applied to the twohyphen; and threehyphen;body dipole interactions of atomic and molecular hydrogen and of helium using theoretical Cauchy dispersion coefficients, and to the inert gases, alkali atoms, and molecular hydrogen, nitrogen, and oxygen using coefficients obtained from optical dispersion and absorption data. Comparison is made with dispersion force estimates obtained fromab initiocalculation, semiempirical methods, and molecular beam and lowhyphen;temperature gas kinetic measurements. In addition to supplying accurate numerical bounds for dispersion force coefficients, the Padeacute; procedure provides the basis for a discussion of previously devised techniques for estimating dispersion force coefficients. The importance of utilizing a proper analytic continuation of the dynamic polarizability in the successful application of these procedures is emphasized. Finally, the accuracy of wellhyphen;known dispersion force combination rules is discussed within the framework of the Padeacute; procedure, and the relation of the latter to alternative bounding methods which have recently appeared is discussed.
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