Projectile-centered Rydberg states of highly charged, fast ions traversing thin solid targets show an unexpected abundance of high-/ states. We present a theory for the production of high-/ states based on classical stochastic dynamics. Diffusion into high-/ states is shown to be universal for single-particle orbits in three dimensions under the influence of a stochastic perturbation, i.e., largely independent of the details of the interaction potentials. Monte Carlo simulations using a Langevin equation for stochastically perturbed electrons in a dynamically screened Coulomb field yield quantitative agreement with experimental data.PACS numbers: 31.50.+W, 05.40.+J, 34.50.Fa Several recent experiments^"^ have established clear evidence for an unexpected, and so far, poorly understood abundance of Rydberg states with high angular momenta /^ 1 centered around fast (vp^ 1 a.u.), highly charged (q^l) projectiles traversing thin solid targets. The observed / distribution is in marked contrast to binary ion-atom collisions in gases under otherwise identical conditions of charge state, projectile velocity, and final-state principal quantum number n, which favors low-/ (-1) states. The latter is a direct consequence of the fact that the transition from an energetically lowlying initial state to a highly excited final state is mediated by the overlap of the wave function near the nucleus, which is maximal for states with low / (or, classically speaking, for orbits with large eccentricity). It is now widely recognized that the / distribution in ion-solid collisions is a bulk effect, ^' more specifically, a result of a complex evolution of the electronic charge cloud around the projectile under the influence of both the ionic projectile potential and the multiple scattering in the dense medium.In this Letter we present theoretical evidence within the framework of classical transport theory that the observed / distribution is a signature of the stochastic motion of an electron in the projectile field leading to diffusion in angular momentum (and energy). Even though highly desirable, the treatment of the evolution inside the solid in terms of a quantum mechanical transport problem appears to be a formidable task in view of the large number of coupled states, including those in the continuum, and of the nontrivial choice of an appropriate basis set that represents strongly perturbed atomic states in a dynamically screened projectile field. In fact, it has been the prevailing view for a long time that weakly bound states with radii larger than the nearest-neighbor spacing would not exist at all because of screening and rapid coUisional destruction. ^ The application of classical dynamics to Rydberg states relies on the limit of large quantum numbers (nj). The overall remarkably successful description of microwave ionization by classical dynamics^ (despite noticeable deviations^) attests to its validity. Clearly, truly quantal effects like coherent diffraction of electrons are neglected from the outset.We employ a microscopic L...

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We discuss a new numerical method for solving the relativistic hydrodynamic equations based upon the basis-spline collocation approach. Analytical and numerical results are compared for several problems, including one-dimensional expansions and collisions for which analytical solutions exist. Our methods, which may be easily and massively parallelized, are shown to give numerical results which agree to within a few percent of the analytic solutions. We discuss the relevance of the υ = z/t scaling solutions for the one-dimensional problem when applied to relativistic heavy-ion collisions. Finally, we discuss applications to three-dimensional problems, and present results for a typical three-dimensional expansion.

We describe the numerical methods used to solve the time-dependent Dirac equation on a three-dimensional Cartesian lattice. Efficient algorithms are required for computationally intensive studies of nonperturbative electromagnetic lepton-pair production in relativistic heavy-ion collisions. Discretization is achieved through the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions on a spatial lattice. For relativistic lepton fields on a lattice, the fermion-doubling problem is central in the formulation of the numerical method. All numerical procedures reduce to a series of matrix-vector operations which we perform on the Intel iPSC/860 hypercube, making full use of parallelism. We discuss solutions to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data stream parallel computers.