Positions of zeros in the bound-bound multipole matrix elements of the point Coulomb field

Minima in cross sections (Cooper minima) are known to occur for all types of transitions in atoms. These minima are caused by zeros in the transition matrix elements which are the result of a zero value for the radial integral of a particular energy. These minima can occur in both the bound-bound and bound-free transition matrix elements. In this paper the approximate position (energy) of the zeros in the bound-bound quadrupole and octupole matrix elements of the point Coulomb field are presented. The positions are found to change in the same manner as those found in the continuum, even to the extent that a zero first occurring in a bound-bound matrix element will move into the corresponding bound-free matrix element.