A quantum mechanical equivalent photon spectrum for heavy ion reactions

Radioactive nuclear beams are rapidly coming to the fore as an important alternative to traditional measurements in nuclear astrophysics. Radioactive nuclei are scattered off the strong electromagnetic fields of a heavy ion, such as lead, providing an independent measurement of electromagnetic cross sections that are difficult to measure otherwise. In this paper, we examine the corrections to the semi-classical ''equivalent photon spectrum'' used to analyze these experiments, and derive an improved spectrum, valid in the long wavelength limit, that includes the effects of the size of the heavy ion, the non-zero longitudinal momentum transfer required by kinematics, and the response of the target nucleus to be off-shell photon