Light-Fronts Approach to a Two-Center Time-Dependent Dirac Equation
Consider the relativistic scattering problem of an electron in the external field of two point-like charges (ions), moving on parallel, straight-line trajectories in opposite directions at speeds which approach the speed of light, and at an impact parameter 2b. An external-field approach to the influence of the ions on the electron is appropriate for peripheral impact parameters, heavy-ions, and high energies, where, to a very good approximation, the ions travel on parallel, straight-line trajectories, and ion recoil is negligible. We review here our recent work on this problem [1, 2, 3]. In section 2, following Ref. [2], we show that the two center time dependent Dirac equation for the electron reduces in the high energy limit to Eq. (26) with the interactions of Eq. (29). In section 3, following Ref. [1], we solve this equation off the light fronts i.e. for an electron that both initially and asymptotically is not co-moving with an ion. The main result of our work is the transition amplitude given by Eqs. (90) and (67). In section 4, we discuss the application of this solution to electromagnetic pair production in heavy ion collisions, which we have used, for example, in Ref. [3], to explain recent experimental results. We note that one should distinguish between electron-positron pairs produced so that they are co-moving with the ions and those that are not. The two cases differ experimentally. They also differ theoretically, because they are described by different asymptotic boundary conditions. We have solved the problem only for electron-positron pairs that are not co-moving with the ions. Our solution to the two center Dirac equation in the high energy limit was confirmed by different methods, including a Green function approach [4], and resummation of the perturbation series [5]. The application to pair production on the other hand, has raised some controversy, which is also discussed in section 4. Section 5 concludes.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 788696
- Report Number(s):
- P01-112022; TRN: US0200560
- Resource Relation:
- Conference: International Association for Relativistic Dynamics, Bar Ilan (IL), 06/15/2000; Other Information: PBD: 1 Nov 2001
- Country of Publication:
- United States
- Language:
- English
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