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Register a new userImpact parameter dependence of heavy ion e+ e- pair production to all orders in Z alpha
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Authors
Anthony J. Baltz
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The heavy ion probability for continuum e+ e- pair production has been calculated to all orders in Z alpha as a function of impact parameter. The formula resulting from an exact solution of the semiclassical Dirac equation in the ultrarelativistic limit is evaluated numerically. In a calculation of gamma = 100 colliding Au ions the probability of e+ e- pair production is reduced from the perturbation theory result throughout the impact parameter range.
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The heavy ion total cross section for continuum e+ e- pair production has been calculated to all orders in Z alpha. The formula resulting from an exact solution of the semiclassical Dirac equation in the ultrarelativistic limit is evaluated numerically. An energy dependent spatial cutoff of the heavy ion potential is utilized, leading to an exact formula agreeing with the known perturbative formula in the ultrarelativistic, perturbative limit. Cross sections and sample momentum distributions are evaluated for heavy ion beams at SPS, RHIC, and LHC energies. e+ e- pair production probabilities are found to be reduced from perturbation theory with increasing charge of the colliding heavy ions and for all energy and momentum regions investigated.
The heavy ion cross section for continuum e+ e- pair production has been calculated to all orders in Z alpha. Comparison is made with available CERN SPS and RHIC STAR data. Computed cross sections are found to be reduced from perturbation theory with increasing charge of the colliding heavy ions and for all energy and momentum regions investigated. Au or Pb total cross sections are reduced by 28% (SPS), 17% (RHIC),and 11% (LHC). For very high energy (E_e+, E_e- > 3 GeV) forward pairs at LHC the reduction from perturbation theory is a bit larger (17%). Use of zero degree calorimeter triggering (and thus small impact parameter weighting) makes impact parameter representation of exact pair production useful. Preliminary exact calculations in the zero impact parameter limit show a much larger reduction from perturbation theory (about 40%) at both RHIC and LHC.
The correction to the Coulomb energy due to virtual production of $e^+e^-$ pairs, which is on the order of one percent of the Coulomb energy at nuclear scales is discussed. The effects of including a pair-production term in the semi-empirical mass formula and the correction to the Coulomb barrier for a handful of nuclear collisions using the Bass and Coulomb potentials are studied. With an eye toward future work using Constrained Molecular Dynamics (CoMD) model, we also calculate the correction to the Coulomb energy and force between protons after folding with a Gaussian spatial distribution.
The STAR collaboration at RHIC is measuring the production of electron-positron pairs at small impact parameters, larger than but already close to the range, where the ions interact strongly with each other. We calculate the total cross section, as well as, differential distributions of the pair production process with the electromagnetic excitation of both ions in a semiclassical approach and within a lowest order QED calculation. We compare the distribution of electron and positron with the one coming from the cross section calculation without restriction on impact parameter. Finally we give an outlook of possible results at the LHC.
In relativistic heavy-ion collisions, the strong Lorentz-contracted electromagnetic fields are capable of producing copious numbers of lepton pairs through the two-photon mechanism. Monte Carlo techniques have been developed that allow the exact calculation of production by this mechanism when a semi-classical approximation is made to the motion of the two ions. Here, we develop a hybrid Monte Carlo technique that enables us to calculate the impact parameter dependence of the two-photon mechanism for lepton-pair production, and by using this result, we obtain the probability distribution for multiple-pair production as a function of impact parameter. Computations are performed for S$+$Au and Pb$+$Pb systems at 200 A GeV and 160 A GeV, respectively. We also compare our results with the equivalent photon approximation and elucidate the differences.
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