The time-dependent Dirac equation was solved for zero-impact-parameter bare U-U collisions in the monopole approximation using a mapped Fourier grid matrix representation. A total of 2048 states including bound, as well as positive-and negative-energy states for an N = 1024 spatial grid were propagated to generate occupation amplitudes as a function of internuclear separation.From these amplitudes spectra were calculated for total inclusive positron and electron production, and also the correlated spectra for (e + , e − ) pair production. These were analyzed as a function of nuclear sticking time in order to establish signatures of spontaneous pair creation, i.e., QED vacuum decay. Subcritical Fr-Fr and highly supercritical Db-Db collisions both at the Coulomb barrier were also studied and contrasted with the U-U results.

The spectrum of the Dirac equation for hydrogenlike systems with extended nuclei becomes complicated when the nuclear charge exceeds a critical value Z Ϸ 170, since the lowest bound state becomes a resonance in the negative energy continuum. We address the problem of computing the resonance parameters by extending the mapped Fourier grid method to incorporate either complex scaling of the radial coordinate, or alternatively a complex absorbing potential. The method is tested on the case of quasimolecular collisions in the monopole approximation.

An efficient numerical method is developed to solve the relativistic hydrogenic Coulomb problem. Combining a pseudospectral method and a change of coordinates, a matrix representation of the relativistic Hamiltonian is constructed in position space. The radial coordinate is mapped from the semiinfinite r-axis to a finite range. The accuracy of the calculation is tested by comparing eigenvalues, sum rules and eigenfunctions with known analytic results. The method can be applied to central field problems for which analytic solutions are unknown.

The analytic continuation methods of complex scaling (CS), smooth exterior scaling (SES), and complex absorbing potential (CAP) are investigated for the supercritical quasimolecular ground state in the U 92+ -Cf 98+ system at an internuclear separation of R = 20 fm. Padé approximants to the complex-energy trajectories are used to perform an extrapolation of the resonance energies, which, thus, become independent of the respective stabilization parameter. Within the monopole approximation to the two-center potential is demonstrated that the extrapolated results from SES and CAP are consistent to a high degree of accuracy. Extrapolated CAP calculations are extended to include dipole and quadrupole terms of the potential for a large range of internuclear separations R. These terms cause a broadening of the widths at the 0 / 00 level when the nuclei are almost in contact, and at the % level for R values where the 1Sσ state enters the negative continuum.

Xenon clusters in an intense soft-x-ray pulse are examined in detail and compared with recent experimental results by reproducing the experimental signals (Thomas et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 134018).Good agreement is found between our theoretical model and the experimental results. A detailed analysis of the experimental signals and their constituents is performed. We find that, unlike large clusters, the smaller N = 147 have a saturated electron kinetic energy distribution (Bostedt et al 2010 New J. Phys. 12 083004). We also find the highest charge states which are detected were initially on the outer shell of the cluster whereas the core ions recombine significantly and are detected as only moderately or singly charged (Hoener et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 181001). Further, we find it is the outer shell ions which obtain the highest kinetic energy upon disintegration (Trost et al