Optical dipole transitions between adjacent states

It is shown that, for optical dipole transitions between states which are degenerate in the limit of the nuclear charge Z being infinite, the dipole length formula is likely to give greater accuracy than the dipole velocity and dipole acceleration formulae. Formulae which are exact to O(1/ Z 3 ) are given for the transition matrix elements for the 2 1 S-2 1 P and 2 3 S-2 3 P transitions in the two-electron systems.