High Dimensional Atomic States of Hydrogenic Type: Heisenberg-like and Entropic Uncertainty Measures

High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The D-dimensional hydrogenic system (i.e., a negatively-charged particle moving around a positively charged core under a Coulomb-like potential) is the main prototype of the physics of multidimensional quantum systems. In this work, we review the leading terms of the Heisenberg-like (radial expectation values) and entropy-like (Rényi, Shannon) uncertainty measures of this system at the limit of high D. They are given in a simple compact way in terms of the space dimensionality, the Coulomb strength and the state’s hyperquantum numbers. The associated multidimensional position–momentum uncertainty relations are also revised and compared with those of other relevant systems.

A Missing Puzzle in Dissociative Electron Attachment to Biomolecules: The Detection of Radicals

Ionizing radiation releases a flood of low-energy electrons that often causes the fragmentation of the molecular species it encounters. Special attention has been paid to the electrons’ contribution to DNA damage via the dissociative electron attachment (DEA) process. Although numerous research groups worldwide have probed these processes in the past, and many significant achievements have been made, some technical challenges have hindered researchers from obtaining a complete picture of DEA. Therefore, this research perspective calls urgently for the implementation of advanced techniques to identify non-charged radicals that form from such a decomposition of gas-phase molecules. Having well-described DEA products offers a promise to benefit society by straddling the boundary between physics, chemistry, and biology, and it brings the tools of atomic and molecular physics to bear on relevant issues of radiation research and medicine.

Effect of the deformation parameter on the nonrelativistic energy spectra of the q-deformed Hulthen-quadratic exponential-type potential

In this study, an approximate solution of the Schr�dinger equation for the q-deformed Hulthen-quadratic exponential-type potential model within the framework of the Nikiforov�Uvarov method was obtained. The bound state energy equation and the corresponding eigenfunction was obtained. The energy spectrum is applied to study H2, HCl, CO and LiH diatomic molecules. The effect of the deformation parameters and other potential parameters on the energy spectra of the system were graphically and numerically analyzed in detail. Special cases were considered when the potential parameters were altered, resulting in deformed Hulthen potential, Hulthen potential, deformed quadratic exponential-type potential and quadratic exponential-type potential. The energy eigenvalues expressions agreed with what obtained in literature. Finally, the results can find many applications in quantum chemistry, atomic and molecular physics.

The Exact Evaluation of Basic Two-Center Coulomb Integrals Appearing in Intermolecular Electrostatic Interaction Energy in Molecular Coordinate System

We proposed a general and effective approach for accurate calculating method of the electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies. It is well known that electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies reduced to basic two-center Coulomb integrals. The analytical calculation of electrostatic interaction energies with respect to basic two-center Coulomb integrals over Slater type orbitals (STOs) in molecular coordinate systems allows us the routine evaluation of molecular structures and related properties. In this study we have introduced a new full analytical algorithm for calculation of the basic two-center Coulomb integrals over STOs by using Guseinov’s auxiliary functions especially interactions between electrons. The auxiliary functions has been calculated by using the exact recurrence relations which developed by Guseinov. The new approach is successfully tested on earlier published studies data and can be recommended for evaluation of related problems in atomic and molecular physics.

Generation and characterisation of isolated attosecond pulses at 100 kHz repetition rate

The generation of coherent light pulses in the extreme ultraviolet (XUV) spectral region with attosecond pulse durations constitutes the foundation of the field of attosecond science [1]. Twenty years after the first demonstration of isolated attosecond pulses [2], they continue to be a unique tool enabling the observation and control of electron dynamics in atoms, molecules and solids [3, 4]. It has long been identified that an increase in the repetition rate of attosecond light sources is necessary for many applications in atomic and molecular physics [5, 6], surface science [7], and imaging [8]. Although high harmonic generation (HHG) at repetition rates exceeding 100 kHz, showing a continuum in the cut-off region of the XUV spectrum was already demonstrated in 2013 [9], the number of photons per pulse was insufficient to perform pulse characterisation via attosecond streaking [10], let alone to perform a pump-probe experiment. Here we report on the generation and full characterisation of XUV attosecond pulses via HHG driven by near-single-cycle pulses at a repetition rate of 100 kHz. The high number of 106 XUV photons per pulse on target enables attosecond electron streaking experiments through which the XUV pulses are determined to consist of a dominant single attosecond pulse. These results open the door for attosecond pump-probe spectroscopy studies at a repetition rate one or two orders of magnitude above current implementations.

Symbolic Evaluation of Expressions from Racah’s Algebra

Based on the rotational symmetry of isolated quantum systems, Racah’s algebra plays a significant role in nuclear, atomic and molecular physics, and at several places elsewhere. For N-particle (quantum) systems, for example, this algebra helps carry out the integration over the angular coordinates analytically and, thus, to reduce them to systems with only N (radial) coordinates. However, the use of Racah’s algebra quickly leads to complex expressions, which are written in terms of generalized Clebsch–Gordan coefficients, Wigner n-j symbols, (tensor) spherical harmonics and/or rotation matrices. While the evaluation of these expressions is straightforward in principle, it often becomes laborious and prone to making errors in practice. We here expand Jac, the Jena Atomic Calculator, to facilitate the sum-rule evaluation of typical expressions from Racah’s algebra. A set of new and revised functions supports the simplification and subsequent use of such expressions in daily research work or as part of lengthy derivations. A few examples below show the recoupling of angular momenta and demonstrate how Jac can be readily applied to find compact expressions for further numerical studies. The present extension makes Jac a more flexible and powerful toolbox in order to deal with atomic and quantum many-particle systems.

Group Theory: Mathematical Expression of Symmetry in Physics

The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we first note that the basic principles imply that the state space of a quantum system has an intrinsic structure of pre-Hilbert space that one completes into a genuine Hilbert space. In this framework, the description of the invariance under a group G is based on a unitary representation of G. Next, we survey the various domains of application: atomic and molecular physics, quantum optics, signal and image processing, wavelets, internal symmetries, and approximate symmetries. Next, we discuss the extension to gauge theories, in particular, to the Standard Model of fundamental interactions. We conclude with some remarks about recent developments, including the application to braid groups.

Asymmetric Rydberg blockade of giant excitons in Cuprous Oxide

The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics to quantum optics and technology. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This is made possible by two-color pump-probe experiments that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character.

An Overview of the Compton Scattering Calculation

The Compton scattering process plays significant roles in atomic and molecular physics, condensed matter physics, nuclear physics and material science. It could provide useful information on the electromagnetic interaction between light and matter. Several aspects of many-body physics, such us electronic structures, electron momentum distributions, many-body interactions of bound electrons, etc., can be revealed by Compton scattering experiments. In this work, we give a review of ab initio calculation of Compton scattering process. Several approaches, including the free electron approximation (FEA), impulse approximation (IA), incoherent scattering function/incoherent scattering factor (ISF) and scattering matrix (SM) are focused on in this work. The main features and available ranges for these approaches are discussed. Furthermore, we also briefly introduce the databases and applications for Compton scattering.

Philip George Burke. 18 October 1932—4 June 2019

The development of theoretical and computational atomic and molecular physics in the second half of the twentieth century owes a great deal to Phil Burke. His knowledge and insight, his enthusiasm and encouragement, his vision and determination were essential characteristics for the success of his work and that of many others. He developed and used the R-matrix method in the study of the interaction between, on the one hand, atoms and molecules and their ions and, on the other, light or electrons. He published many original research papers and was author or editor of a number of books. Especially significant and far-reaching was his setting up of the journal Computer Physics Communications to enable an international field of scientists, initially to share computer codes, but subsequently also to discuss and develop methods in computational physics. While based at the Daresbury Laboratory, he established a number of Collaborative Computational Projects, thus providing a forum for scientists working in specific scientific disciplines to meet periodically to discuss current issues and in particular how the ever advancing cutting-edge of high-end computing could begin to address previously intractable problems. A consequence was his clarity of thinking about which new computer architectures were needed to make significant advances in each field of study, expertly guiding the UK's provision of high-end computers to academia for over 20 years. He was a clear and methodical teacher, at both graduate and undergraduate level, and was generous with the time he gave to his students. In short, he demonstrated a balanced level of excellence in all aspects of his career. He was a consummate academic and a fine role model for his colleagues.