Abstract

The parity of the number of zeros of one-photon multipole transition matrix elements for an electron in a point Coulomb field is examined, generalising on some multipole transitions in the long-wavelength limit. Results are obtained for the general multipole matrix element with fixed angular momentum, Delta l not=0, retardation being included. For low multipolarities, results are compared with those obtained in the long-wavelength approximation, and cases in which results differ are indicated. The method involves determining the sign of the matrix element both at very low photon energy (for unphysical situations below the photoelectric threshold not corresponding to real bound-bound transitions) and in the limit of high photon energy.

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