Elastic photonuclear cross sections for bremsstrahlung from relativistic ions

Abstract

In this paper, we provide a procedure to calculate the bremsstrahlung spectrum for virtually any relativistic bare ion with charge 6$e$ or beyond, $Z\ge 6$, in ultraperipheral collisions with target nuclei. We apply the Weizsäcker-Williams method of virtual quanta to model the effect of the distribution of nuclear constituents on the interaction of the ion with the radiation target. This leads to a bremsstrahlung spectrum peaking at $2γ$ times the energy of the giant dipole resonance ($γ$ is the projectile energy in units of its rest energy). A central ingredient in the calculation is the cross section for elastic scattering of photons on the ion. This is only available in the literature for a few selected nuclei and, usually, only in a rather restricted parameter range. Hence we develop a procedure applicable for all $Z\geq6$ to estimate the elastic scattering. The elastic cross section is obtained at low to moderate photon energies, somewhat beyond the giant dipole resonance, by means of the optical theorem, a dispersion relation, and data on the total absorption cross section. The cross section is continued at higher energies by invoking depletion due to loss of coherence in the scattering. Our procedure is intended for any ion where absorption data is available and for moderate to high energies, $γ\gtrsim 10$.