Numerical Treatment of Lepton Pair Production in Relativistic Heavy Ion Collisions

Research Objectives

Electron-positron pair production will play a major role in colliders such as the Relativistic Heavy Ion Collider (RHIC) or the Large Hadron Collider (LHC). In particular, a copious amount of electron-positron pairs is expected to be produced at each of the interaction regions at RHIC. A good understanding and accounting of this process is very critical from the standpoint of background in these machines.

The purpose of this project is to use the T3E to solve numerically the time-dependent Dirac equation that describes the production of electron-positron pairs in relativistic heavy ion collisions. The solution on a grid will give a direct visualization of the pair-creation process as the collision between the ions evolves in time, providing a powerful nonperturbative treatment for an inherently difficult problem.

Computational Approach

Our code uses standard PVM for message passing, and the programming language is Fortran 90. The current version uses fairly standard numerical techniques to solve the integro-differential equation. The wave function itself is represented within a finite volume by defining a global three-dimensional interpolating function on a grid. This interpolating function is constructed from cubic splines. The integration over the momentum space showing as a right-hand side of the integro-differential equation is performed cell by cell, using three-dimensional Gaussian quadrature technique.

Accomplishments

After constructing analytically continuum wave packets representing electrons and positrons, we started a first set of intensive production runs on the T3E in January 1998. In these production runs, we limited the energy of the collision to up to 10 GeV/n, where we have the best handle on the level of precision and time integration of the computer code.

The comparison of the dynamic of the collision for different initial conditions constructed from the negative and positive energy continuum states, respectively, shows a very striking behavior of the quantum electrodynamics vacuum. We use the output at each time-step to generate a movie that shows the evolution of the electronic wave function as the collision unfolds with time.

As an example, we show in the figure some snapshots of the electron density at various times for the collision of a fully stripped uranium ion with a hydrogen-like gold. These snapshots are extracted from an animation that dramatically shows how the wave function grows, flows, recedes, and grows again throughout the period of the collision.

Significance

The animation of the collision allows a unique and direct look at the complexity and richness of what happens in the time domain in an atomic encounter. This unique information, which cannot be accessed in a laboratory, changes how we view relativistic atomic collisions.

Publications

D. Ionescu, A. Belkacem, and A. Sorensen, "Momentum-space imaging of electronic excitations in fast ion-ion collisions using parallel processing," Contributed paper to the 1998 Annual Meeting of the Division of Atomic, Molecular, and Optical Physics, Santa Fe, NM, 43 (1998), p. 1347.