Exact Dirac equation calculation of ionization and pair production induced by ultrarelativistic heavy ions

An exact solution of the time-dependent Dirac equation for ionization and pair production induced by ultrarelativistic heavy ion collisions is presented. Exact transition probabilities, equivalent to those that would be obtained in an untruncated basis coupled channels calculation, are presented. Exact bound-electron positron pair production probabilities are calculated to be mostly smaller than those calculated with the same potential in perturbation theory at impact parameters small enough for differences to occur. PACS: 34.90.+q, 25.75.-q The calculation of bound-electron positron pair production induced by relativisitic heavy ion collisions has been a subject great interest recently [1]. One motivation for this interest is the anticipated large rates of pair production with an electron captured into a bound state of one of the pair of fully stripped ions in a collider such as the Brookhaven Relativistic HeavyIon Collider (RHIC) or the CERN Large Hadron Collider (LHC). The capture process will provide an important limit on the beam lifetime since change of the charge of an ion leads to the loss of that ion from the beam. Early non-perturbative coupled channel calculations showed an enhancement of some two orders of magnitude [2] over corresponding perturbation theory calculations at small impact parameters for Pb + Pb reactions at relatively low relativistivc energies (e.g., γ=2.3). These results motivated an extensive investigation at ultrarelativistic energies such as will occur at RHIC (γ=23 000), and the problem of non-