Existence of near-zero minima in elastic photon-atom scattering

We consider elastic photon-atom in the vicinity of resonances, in particular the region of resonant transitions involving the K shell. We use a relativistic S-matrix code to calculate the scattering cross section. In the case of scattering from ground-states of atoms there is a near-zero minimum in the scattering cross section as the K resonance region is approached from below. For more exotic targets, such as hollow atoms (with inner shells completely vacated), the S-matrix code predicts other types of near-zero minima: for example, in the case of a hollow atom with all electrons present in the L shell (i.e. completely vacant K shell) there is a near-zero minimum in the cross section just above the position of the downward L to K bound-bound transition. Understanding near-zeroes in scattering is potentially important, given the possibility of using synchrotron radiation in medical applications. The cross section associated with a high-Z trace element would be very sensitive to the frequency of the radiation in the vicinity of a real near-zero, while the cross section associated with surrounding bone and tissue would be comparatively insensitive. However the present S-matrix code performs an averaging over magnetic substates, weighted over the number of electrons actually present in each subshell, at the level of the scattering amplitude. This method is exact only for closed shells, and is approximate in the case of partially-filled subshells. A more proper approach is to average the cross sections for all possible magnetic substate occupations. We compare results using these two approaches and consider the consequences for the existence of near-zero minima in the cross section. The near-zero seen below the resonance region for scattering from ground-state atoms survives in the more proper treatment. However other types of near-zeros, such as those seen in the case of hollow atoms, can be spurious, depending on the details of the configuration. (author)