We present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultraviolet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time-dependent Dirac equation and compare its predictions with those of the corresponding nonrelativistic Schrödinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduce a finite yet small decrease in the probability of ionizing the atom.

Aims. We present a ground-based, near-infrared search for lensed supernovae behind the massive cluster Abell 1689 at z = 0.18, which is one of the most powerful gravitational telescopes that nature provides. Methods. Our survey was based on multi-epoch J-band observations with the HAWK-I instrument on VLT, with supporting optical data from the Nordic Optical Telescope. Results. Our search resulted in the discovery of five photometrically classified, core-collapse supernovae with high redshifts of 0.671 < z < 1.703 and magnifications in the range ∆m = −0.31 to −1.58 mag, as calculated from lensing models in the literature. Owing to the power of the lensing cluster, the survey had the sensitivity to detect supernovae up to very high redshifts, z ∼ 3, albeit for a limited region of space. We present a study of the core-collapse supernova rates for 0.4 ≤ z < 2.9, and find good agreement with previous estimates and predictions from star formation history. During our survey, we also discovered two Type Ia supernovae in A 1689 cluster members, which allowed us to determine the cluster Ia rate to be 0.14,B yr −1 ), where the error bars indicate 1σ confidence intervals, statistical and systematic, respectively. The cluster rate normalized by the stellar mass is 0.10. Furthermore, we explore the optimal future survey for improving the core-collapse supernova rate measurements at z 2 using gravitational telescopes, and for detections with multiply lensed images, and we find that the planned WFIRST space mission has excellent prospects. Conclusions. Massive clusters can be used as gravitational telescopes to significantly expand the survey range of supernova searches, with important implications for the study of the high-z transient Universe.Key words. supernovae: general -gravitational lensing: strong -galaxies: star formation -galaxies: clusters

We present a generalized velocity gauge form of the relativistic laser-matter interaction. In comparison with the (equivalent) regular minimal coupling description, this form of light-matter interaction results in superior convergence properties for the numerical solution of the time-dependent Dirac equation. This applies both to the numerical treatment and, more importantly, to the multipole expansion of the laser field. The advantages of the alternative gauge is demonstrated in hydrogen by studies of the dynamics following the impact of superintense laser pulses of extreme ultraviolet wavelengths and subfemtosecond duration.