Merging of positions of zeros in dipole and quadrupole matrix elements of photoeffect from outer-shell and Rydberg states of high-Zelements

Abstract

The zeros in dipole and quadrupole matrix elements of photoeffect from the $n{s}_{\frac{1}{2}}$ subshells of uranium approach common positions as $n\ensuremath{\rightarrow}\ensuremath{\infty}$. This is an illustration of the more general feature that for sufficiently large ${n}_{0}$ photoeffect cross sections and angular distributions from $\mathrm{nJL}$ subshells, aside from the bound-state normalization factor which scales the cross section, are the same for all $n>{n}_{0}$ ($J$, $L$ fixed) except for energies very close to threshold. This behavior can be expected for all subshells and all elements and for all multipole matrix elements.