Abstract
We present a proof that there are no zeros in the nonrelativistic Coulomb dipole matrix elements, considered as functions of energy, for transitions between any bound state and states of greater energy. This includes bound-bound and bound-free transitions and also transitions to unbounded negative energy states. Our result follows from the recursion relations for dipole matrix elements obtained by Infeld and Hall. By contrast, zeros occur in some Coulomb quadrupole matrix elements.
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