Question of gauge for the description of two-photon transitions or light scattering when using incomplete sets

Journal Article · Wed Sep 01 00:00:00 EDT 1982 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.26.1482· OSTI ID:6523737

Robinson, G W

In the calculation of two-photon transition probabilities and related radiation-matter interaction problems, the ''length'' and ''velocity'' forms of the dipole interaction give results that can differ by many orders of magnitude if a complete set of exact eigenfunctions is not used. These differences have been illustrated in the case of the 1s-2s two-photon transition in hydrogen by Bassani, Forney, and Quattropani (Phys. Rev. Lett. 39, 1070 (1977)), and it was concluded by these authors that for this problem the length form of the interaction is far superior to the velocity form when an incomplete set of bound states is used. In order to remove the question of gauge and thereby to improve the accuracy of such calculations when a complete set of exact eigenfunctions is not available, this paper proposes a modified form of the second-order equation. The modified equation, which employs a unique average-frequency approximation, is derived through incorporation of a sum rule that is a direct result of gauge invariance. It contains the length and velocity forms as limiting cases, and, like those equations, is exact for a complete set. Conventional length or velocity equations violate this sum rule for an incomplete set, and therefore are subject to large errors. The use of this modified equation is illustrated for the 1s-2s transition of hydrogen. Using only the 2p state as the ''set'' of intermediate states, the modified equation yields results that for all photon energies are within 2% of the exact probability amplitudes. For the 1s-2s problem, the accuracy is comparable to that obtained from length- and velocity-form equations employing an ordinary average-frequency approximation and closure.

• Research Organization: Picosecond and Quantum Radiation Laboratory, Texas Tech University, P.O. Box 4260, Lubbock, Texas 79409
• OSTI ID: 6523737
• Journal Information: Phys. Rev. A; (United States), Vol. 26:3
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HYDROGEN
MULTI-PHOTON PROCESSES
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ENERGY-LEVEL TRANSITIONS
FORM FACTORS
LIGHT SCATTERING
PROBABILITY
DIPOLES
ELEMENTS
FUNCTIONS
MULTIPOLES
NONMETALS
PARTICLE PROPERTIES
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