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Register a new userCoulomb field correction due to virtual $e^+e^-$ production in heavy ion collisions
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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.
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A recently proposed method, based on quadrupole and multiplicity fluctuations in heavy ion collisions, is modified in order to take into account distortions due to the Coulomb field. This is particularly interesting for bosons produced in heavy ion collisions, such as $d$ and $alpha$ particles. We derive temperatures and densities seen by the bosons and compare to similar calculations for fermions. The resulting energy densities agree rather well with each other and with the one derived from neutrons. This suggests that a common phenomenon, such as the sudden opening of many reaction channels and/or a liquid gas phase transition, is responsible for the agreement.
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.
Recently the splitting of elliptic flow $v_2$ at finite rapidities has been proposed as a result of the global vorticity in non-central relativistic heavy ion collisions. Using a multi-phase transport model that automatically includes the vorticity field and flow fluctuations, we confirm the left-right (i.e., on opposite sides of the impact parameter axis) splitting of the elliptic flow at finite rapidities. However, we find that this $v_2$ splitting is a result of the non-zero directed flow $v_1$ at finite rapidities, with the splitting magnitude $approx 8v_1/3pi$. As a result, the $v_2$ splitting vanishes at zero transverse momentum ($p_{rm T}$), and its magnitude and sign may have non-trivial dependences on $p_{rm T}$, centrality, collision energy, and hadron species. Since the left-right $v_2$ splitting is a combined effect of $v_1$ and $v_2$, it will benefit studies of the three-dimensional structure and dynamics of the dense matter.
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.
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.
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