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On the Interaction between two identical neutral dipole systems, One in an excited state and the other in the ground state

Published online by Cambridge University Press:  26 February 2010

R. R. McLone  and
E. A. Power
R. R. McLone
Affiliation:
Mathematics Department, University College, London.
E. A. Power
Affiliation:
Mathematics Department, University College, London.
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Extract

In the theory of the interaction between simple electrically neutral systems with dipole moments, the interaction energy between two such systems when they are identical, one in an excited state and the other in the ground state, is of current interest. It is well-known that, within the Coulomb force approximation for the electron-electron interaction, the energy varies as

where q(r) is the electric dipole moment of the system r = 1, 2, and R is the vector displacement of system 2 from system 1. This is the so called resonance attraction between the systems. On the other hand it has been known since 1948 (see [1]) that for two systems both in their ground states the potential of interaction falls off at large separation faster than the London formula for the energy, namely

predicts. In equation (2) α(r) is the polarization of the system r, in terms of the dipole moments (here induced)

where E is the energy separation between the two states considered, i.e., the ground state and the excited state reached from the ground state by electric dipole transitions. In fact the asymptotic form of the potential energy at separation was given by Casimir and Polder as

Type
Research Article
Information
Mathematika , Volume 11 , Issue 1 , June 1964 , pp. 91 - 94
Copyright
Copyright © University College London 1964

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References

1.Casimir, H. B. G., and Polder, D., Phys. Rev., 73 (1948), 360–372.CrossRefGoogle Scholar
2.Power, E. A., Introductory quantum electrodynamics (Longmans, 1964), chapter 8, 108–112.Google Scholar
3.Simpson, W. T., Radiation research, 20 (1963), 87–100.CrossRefGoogle Scholar
4.Power, E. A. and Zienau, S., Phil. Trans. Roy. Soc. (A), 251 (1959), 427–454.Google Scholar