A NEW GENERALIZATION OF THE CASIMIR-POLDER POTENTIAL TO HIGHER ELECTRIC MULTIPOLE POLARIZABILITIES

An elementary method for calculating retarded interaction energies for a pair of molecules with electric multipole polarizabilities of arbit rary order is presented. In the multipolar framework of quantum electr odynamics, the interaction energy is viewed as arising from two-photon exchange and calculated using fourth order perturbation theory. It is shown how the energy may be expressed in terms of derivatives of the Casimir-Polder formula written in a special form as an integral over i maginary frequency. Explicit formulas are presented for (a) an electri c dipole polarizable molecule interacting with an electric quadrupole polarizable molecule, (b) an electric dipole polarizable molecule inte racting with an electric octupole polarizable molecule, and (c) an ele ctric quadrupole polarizable molecule interacting with another electri c quadrupole polarizable molecule. The results are expressed in terms of reducible and irreducible components of multipole moments. For case (b) it is shown that in addition to the weight-3 components of the oc tupole moments, weight-1 components contribute to the interaction ener gy. For cases (a) and (c) traceless components (weight-2) of the quadr upole moments contribute. The results are compared with other calculat ions and discrepancies pointed out. (C) 1996 American Institute of Phy sics.