Retarded N - Body Dispersion Potential : Molecular QED Formulation

for 54 Sanibel Symposium, Saint Simons Island, GA 16-21 Feb., 2014 Retarded N-Body Dispersion Potential: Molecular QED Formulation J. Aldegunde and A. Salam 1 Department of Physical Chemistry, University of Salamanca, 37008 Salamanca, Spain 2 Department of Chemistry, Wake Forest University, Winston-Salem, NC 27109, USA A well-known success of the theory of non-relativistic quantum electrodynamics (QED) [1,2] is the calculation of the dispersion potential between two particles separated by a distance R, by Casimir and Polder [3]. They showed that accounting for the finite speed of propagation of electromagnetic signals weakened the energy shift by a factor of R relative to the R London dispersion formula. Aub and Zienau [4] later evaluated the leading non-additive term arising from three-bodies, extending the familiar Axilrod-Teller-Muto triple dipole dispersion potential [5,6], which was found to be the near-zone limit of the result valid for all separations. We present an expression, obtained using molecular QED, for the retarded N-body dispersion energy shift for atoms or molecules with arbitrary electric multipole polarizability, generalizing a formula that was limited to the electric dipole approximation [7]. Higher-order many-body contributions are now featuring in the interactions between rare gases, alkali and alkaline Earth metal atoms, and combinations thereof [8]. A response theory formulation is adopted in which each species in turn responds through its generalized electric multipole polarizability to the electric displacement field of the remaining N-1 bodies. This approach first entails the solution of the source dependent wave equation for the displacement field [9]. The formula derived is shown to agree with previously obtained generalized expressions for two-[10] and three-[11] body dispersion potentials between species with arbitrary electric multipole polarizable characteristics. [1] D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics, Academic Press, London, 1984. [2] A. Salam, Molecular Quantum Electrodynamics, John Wiley & Sons, Inc., New York, 2010. [3] H. B. G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948). [4] M. R. Aub and S. Zienau, Proc. Roy. Soc. Lond. A257, 464 (1960). [5] B. M. Axilrod and E. Teller, J. Chem. Phys. 11, 299 (1943). [6] Y. Muto, J. Phys. Math. Soc. Japan 17, 629 (1943). [7] E. A. Power and T. Thirunamachandran, Phys. Rev. A50, 3929 (1994). [8] L-Y. Tang, Z-C. Chen, T-Y. Shi, J. F. Babb and J. Mitroy, J. Chem. Phys. 136, 104104 (2012). [9] E. A. Power and T. Thirunamachandran, Proc. Roy. Soc. Lond. A401, 267 (1985). [10] A. Salam and T. Thirunamachandran, J. Chem. Phys. 104, 5094 (1996). [11] A. Salam, unpublished results.