Abstract
In this chapter, diagrammatic time-dependent perturbation theory is employed to calculate the Casimir-Polder dispersion potential between two neutral electric dipole polarisable atoms or molecules. Its computation via the minimal-coupling scheme is summarised first. Next, it is shown how the energy shift may be computed more simply by adopting the multipolar Hamiltonian in the electric dipole approximation. In this second framework the force is mediated by the exchange of two virtual photons, and the Casimir-Polder formula results on summing the contribution from twenty-four time-ordered diagrams evaluated at fourth-order of perturbation theory. The potential is obtained for oriented as well as for isotropic systems separated beyond the region of wave function overlap. Asymptotically limiting forms of the interaction energy applicable in the near-and far-zone regions are also found. The former reproduces the London dispersion formula, while the latter exhibits an inverse seventh power law due to the effects of retardation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Göppert-Mayer M (1931) Über elementarakte mit zwei quantensprüngen. Ann Phys Leipzig 9:273
Casimir HBG, Polder D (1948) The influence of retardation on the London van der Waals forces. Phys Rev 73:360
London F (1937) The general theory of molecular forces. Trans Faraday Soc 33:8
Feynman RP (1949) The theory of positrons. Phys Rev 76:749
Feynman RP (1949) Space-time approach to quantum electrodynamics. Phys Rev 76:769
Schweber SS (1986) Feynman and the visualisation of space-time processes. Rev Mod Phys 58:449
Ward JF (1965) Calculation of nonlinear optical susceptibilities using diagrammatic perturbation theory. Rev Mod Phys 37:1
Power EA (1964) Introductory Quantum Electrodynamics. Longmans, London
Craig DP, Thirunamachandran T (1998) Molecular Quantum Electrodynamics. Dover, New York
Power EA, Thirunamachandran T (1983) Quantum electrodynamics with nonrelativistic sources. II. Maxwell fields in the vicinity of an atom. Phys Rev A 28:2663
Salam A (1997) Maxwell field operators, the energy density, and the Poynting vector calculated using the minimal-coupling framework of molecular quantum electrodynamics in the Heisenberg picture. Phys Rev A 56:2579
Power EA, Thirunamachandran T (1999) Time dependence of operators in minimal and multipolar nonrelativistic quantum electrodynamics. I. Electromagnetic fields in the neighbourhood of an atom. Phys Rev A 60:4927
Alligood BW, Salam A (2007) On the application of state sequence diagrams to the calculation of the Casimir-Polder potential. Mol Phys 105:395
Salam A (2010) Molecular Quantum Electrodynamics. John Wiley & Sons Inc, Hoboken
Andrews DL, Thirunamachandran T (1977) On three-dimensional rotational averages. J Chem Phys 67:5026
Craig DP, Power EA (1969) The asymptotic Casimir-Polder potential from second-order perturbation theory and its generalisation for anisotropic polarisabilities. Int J Quant Chem 3:903
Power EA, Thirunamachandran T (1983) Quantum electrodynamics with nonrelativistic sources. III. Intermolecular interactions. Phys Rev A 28:2671
Power EA, Thirunamachandran T (1993) Quantum electrodynamics with nonrelativistic sources. V. Electromagnetic field correlations and intermolecular interactions between molecules in either ground or excited states. Phys Rev A 47:2539
Salam A (2008) Molecular quantum electrodynamics in the Heisenberg picture: a field theoretic viewpoint. Int Rev Phys Chem 27:405
Casimir HBG (1949) Sur les forces van der Waals-London. J Chim Phys 46:407
Milonni PW (1994) The Quantum Vacuum. Academic Press, San Diego
Power EA, Thirunamachandran T (1994) Zero-point energy differences and many-body dispersion forces. Phys Rev A 50:3929
Feinberg G, Sucher J (1970) General theory of the van der Waals interaction: a model-independent approach. Phys Rev A 2:2395
Milonni PW (1982) Casimir forces without the vacuum radiation field. Phys Rev A 25:1315
Milonni PW, Shih M-L (1992) Source theory of Casimir force. Phys Rev A 45:4241
Schwinger JS, DeRaad LL Jr, Milton KA (1978) Casimir effect in dielectrics. Ann Phys 115:1 (NY)
Spruch L, Kelsey EJ (1978) Vacuum fluctuation and retardation effects on long-range potentials. Phys Rev A 18:845
Compagno G, Passante R, Persico F (1983) The role of the cloud of virtual photons in the shift of the ground-state energy of a hydrogen atom. Phys Lett A 98:253
Power EA, Thirunamachandran T (1993) Casimir-Polder potential as an interaction between induced dipoles. Phys Rev A 48:4761
Craig DP, Thirunamachandran T (1999) New approaches to chiral discrimination in coupling between molecules. Theo Chem Acc 102:112
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 The Author(s)
About this chapter
Cite this chapter
Salam, A. (2016). Dispersion Interaction Between Two Atoms or Molecules. In: Non-Relativistic QED Theory of the van der Waals Dispersion Interaction. SpringerBriefs in Molecular Science(). Springer, Cham. https://doi.org/10.1007/978-3-319-45606-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-45606-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45604-1
Online ISBN: 978-3-319-45606-5
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)