A general expression for the angular correlation function of the two emitted photoelectrons in sequential two-photon double ionization of atoms is derived and discussed. The expression can be used in the analysis of angle-resolved coincidence experiments. The angular distributions of the emitted electrons as measured in non-coincidence experiments are also discussed. As an example, the cross sections, angular distributions of photoelectrons and angular correlation functions for the sequential two-photon double ionization of Ne and Ar atoms have been calculated within the MCHF and MCDF approaches. The results are compared with recent experiments performed at the free-electron laser (FLASH) facility.

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The Mott scattering of high-energetic twisted electrons by atoms is investigated within the framework of the first Born approximation and Dirac's relativistic equation. Special emphasis is placed on the angular distribution and longitudinal polarization of the scattered electrons. In order to evaluate these angular and polarization properties we consider two experimental setups in which the twisted electron beam collides with either a single well-localized atom or macroscopic atomic target. Detailed relativistic calculations have been performed for both setups and for the electrons with kinetic energy from 10 keV to 1000 keV. The results of these calculations indicate that the emission pattern and polarization of outgoing electrons differ significantly from the scattering of plane-wave electrons and can be very sensitive to the parameters of the incident twisted beam. In particular, it is shown that the angular-and polarization-sensitive Mott measurements may reveal valuable information about, both the transverse and longitudinal components of the linear momentum and the projection of the total angular momentum of twisted electron states. Thus, the Mott scattering emerges as a diagnostic tool for the relativistic vortex beams.

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The neutron-rich isotopes of cadmium up to the N ¼ 82 shell closure have been investigated by highresolution laser spectroscopy. Deep-uv excitation at 214.5 nm and radioactive-beam bunching provided the required experimental sensitivity. Long-lived isomers are observed in 127 Cd and 129 Cd for the first time. One essential feature of the spherical shell model is unambiguously confirmed by a linear increase of the 11=2 À quadrupole moments. Remarkably, this mechanism is found to act well beyond the h 11=2 shell. DOI: 10.1103/PhysRevLett.110.192501 PACS numbers: 21.10.Ky, 21.60.Cs, 31.15.aj, 32.10.Fn When first proposed, the nuclear shell model was largely justified on the basis of magnetic-dipole properties of nuclei [1]. The electric quadrupole moment could have provided an even more stringent test of the model, as it has a very characteristic linear behavior with respect to the number of valence nucleons [2,3]. However, the scarcity of experimental quadrupole moments at the time did not permit such studies. Nowadays, regardless of experimental challenges, the main difficulty is to predict which nuclei are likely to display this linear signature. The isotopes of cadmium, investigated here, proved to be the most revealing case so far. Furthermore, being in the neighborhood of the ''magic'' tin, cadmium is of general interest for at least two additional reasons. First, theory relies on nuclei near closed shells for predicting other, more complex systems. Second, our understanding of stellar nucleosynthesis strongly depends on the current knowledge of nuclear properties in the vicinity of the doubly magic tin isotopes [4]. Moreover, specific questions concerning the nuclear structure of the cadmium isotopes require critical evaluation, such as shell quenching [5,6], sphericity [7], deformation [8,9], or whether vibrational nuclei exist at all [10]. Some of these points will be addressed here quite transparently, while others require dedicated theoretical work to corroborate our conclusions. In this Letter we report advanced measurements by collinear laser spectroscopy on the very neutron-rich cadmium isotopes. Electromagnetic moments in these complex nuclei are found to behave in an extremely predictable manner. Yet, their description goes beyond conventional interpretation of the nuclear shell model.The measurements were carried out with the collinear laser spectroscopy setup at ISOLDE-CERN. High-energy protons impinging on a tungsten rod produced low-to medium-energy neutrons inducing fission in a uranium carbide target. Proton-rich spallation products, such as cesium, were largely suppressed in this manner. Further reduction of surface-ionized isobaric contamination was achieved by the use of a quartz transfer line [11], which allowed the more volatile cadmium to diffuse out of the target while impurities were retained sufficiently long to decay. Cadmium atoms were laser ionized, accelerated to an energy of 30 keV, and mass separated. The ion beam was injected into a gas-filled radio-frequency Paul trap [12]...

In-source resonant ionization laser spectroscopy of the even-A polonium isotopes (192-210,216,218)Po has been performed using the 6p(3)7s (5)S(2) to 6p(3)7p (5)P(2) (λ=843.38  nm) transition in the polonium atom (Po-I) at the CERN ISOLDE facility. The comparison of the measured isotope shifts in (200-210)Po with a previous data set allows us to test for the first time recent large-scale atomic calculations that are essential to extract the changes in the mean-square charge radius of the atomic nucleus. When going to lighter masses, a surprisingly large and early departure from sphericity is observed, which is only partly reproduced by beyond mean field calculations.

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We present the results of an experimental study of magnetic dipole (M1) transitions in highly charged argon ions (Ar X, Ar XI, Ar XIV, Ar XV) in the visible spectral range using an electron beam ion trap. Their wavelengths were determined with, for highly charged ions, unprecedented accuracy up to the sub-ppm level and compared with theoretical calculations. The QED contributions, calculated in this Letter, are found to be 4 orders of magnitude larger than the experimental error and are absolutely indispensable to bring theory and experiment to a good agreement. This method shows great potential for the study of QED effects in relativistic few-electron systems.