Atoms, Volume 10, Issue 2 (June 2022) – 32 articles

The spin polarization of photoelectrons in two-color XUV + optical multiphoton ionization is theoretically considered using strong field approximation. We assume that both the XUV and the optical radiation are circularly polarized. It is shown that the spin polarization is basically determined by the XUV photoabsorption and that the sidebands are spin polarized as well. Their polarization may be larger or smaller than that of the central photoelectron line depending on the helicity of the dressing field. Full article

The Wigner-Kirkwood expansion of the quantum correction to the classical free energy is generally said to be in powers of ${\hslash }^2$ and only its first few terms are presented. In this work, we use the Bloch differential equation to obtain a general description of all terms in a dimensionless form. The first corrective term turns out to be proportional to the product of ${\lambda }^2/a^2$, where $\lambda$ is the thermal de Broglie wavelength and $a^3$ is the volume per particle, by an effective coupling constant. This dimensionless parameter can be used to assess the magnitude of the quantum correction. Using the one-component plasma as an illustration we highlight the importance of the magnitude of the potential on the quantum correction. The results presented are not formally new; the emphasis is placed on a simple and didactic presentation. Full article

We investigate the effects of higher-order quantum fluctuations on the bulk properties of self-bound droplets in three-, two- and one-dimensional binary Bose mixtures using the Hartree–Fock–Bogoliubov theory. We calculate higher-order corrections to the equation of state of the droplet at both zero and finite temperatures. We show that our results for the ground-state energy are in a good agreement with recent quantum Monte Carlo simulations in any dimension. Our study extends to the finite temperature case where it is found that thermal fluctuations may destabilize the droplet state and eventually destroy it. In two dimensions, we reveal that the droplet occurs at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature. Full article

Electron collision cross-sections of c-C₄F₈ were investigated at low energies by using the R-matrix method. The static exchange (SE), static exchange with polarization (SEP), and close-coupling (CC) models of the R-matrix method were used for the calculation of the scattering cross-section. The shape resonance was detected with all the models at around 3~4 eV, and a Feshbach resonance was detected with the SEP model at 7.73 eV, in good agreement with the previous theoretical calculation. The resonance detected was also associated with the experimental dissociative electron attachment of c-C₄F₈, which displayed the resonances at the same energy range. The cross-sections calculated are important for plasma modeling and applications. Full article

The concept of treating subranges of the electron energy spectrum as species in chemical models is investigated. This is intended to facilitate simple modification of chemical models by incorporating the electron interactions as additional rate equations. It is anticipated that this embedding of fine details of the energy dependence of the electron interactions into rate equations will yield an improvement in computational efficiency compared to other methods. It will be applicable in situations where the electron density is low enough that the electron interactions with chemical species are significant compared to electron–electron interactions. A target application is the simulation of electron processes in the D-region of the Earth’s atmosphere, but it is anticipated that the method would be useful in other areas, including enhancement of Monte Carlo simulation of electron–liquid interactions and simulations of chemical reactions and radical generation induced by electrons and positrons in biomolecular systems. The aim here is to investigate the accuracy and practicality of the method. In particular, energy must be conserved, while the number of subranges should be small to reduce computation time and their distribution should be logarithmic in order to represent processes over a wide range of electron energies. The method is applied here to the interaction by inelastic and superelastic collisions of electrons with a gas of molecules with only one excited vibrational level. While this is unphysical, it allows the method to be validated by checking for accuracy, energy conservation, maintenance of equilibrium and evolution of a Maxwellian electron spectrum. Full article

This article briefly reviews topics related to actinide research discussed at the virtual workshop Atomic Structure of Actinides & Related Topics organized by the University of Mainz, the Helmholtz Institute Mainz, and the GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany, and held on the 26–28 May 2021. It includes references to recent theoretical and experimental work on atomic structure and related topics, such as element production, access to nuclear properties, trace analysis, and medical applications. Full article

In the present work, we assess the effectiveness of singly differential cross sections (SDCS) due to electron-impact ionization by invoking the binary-encounter-Bethe (BEB) model on various atomic and molecular targets. The computed results were compared with the experimental and theoretical data. A good agreement was observed between the present and the available results. This agreement improves as the incident energy of the projectile increases. The model can be applied to compute the SDCS for the ions produced due to the electron-impact dissociative ionization process and the average energy due to the secondary electrons. Both these quantities are of interest in plasma processing and radiation physics. Full article

The heaviest actinide elements are only accessible in accelerator-based experiments on a one-atom-at-a-time level. Usually, fusion–evaporation reactions are applied to reach these elements. However, access to the neutron-rich isotopes is limited. An alternative reaction mechanism to fusion–evaporation is multinucleon transfer, which features higher cross-sections. The main drawback of this technique is the wide angular distribution of the transfer products, which makes it challenging to catch and prepare them for precision measurements. To overcome this obstacle, we are building the NEXT experiment: a solenoid magnet is used to separate the different transfer products and to focus those of interest into a gas-catcher, where they are slowed down. From the gas-catcher, the ions are transferred and bunched by a stacked-ring ion guide into a multi-reflection time-of-flight mass spectrometer (MR-ToF MS). The MR-ToF MS provides isobaric separation and allows for precision mass measurements. In this article, we will give an overview of the NEXT experiment and its perspectives for future actinide research. Full article

In this work, we have applied polarization spectroscopy to study electromagnetically induced transparency involving hot $\mathrm{Rb}_{85}^{}$ Rydberg state in a vapor cell using a Laguerre–Gaussian mode beam. Such spectroscopy technique generates a dispersive signal, which allows a direct measurement of the transition linewidth. Our results show that the measured transition linewidth for a Laguerre–Gaussian mode control beam is narrower than for a Gaussian mode. Besides, it can be well reproduced by a simplified Lindblad master equation model. Full article

Laser spectroscopic studies of elements in the heavy actinide and transactinide region help understand the nuclear ground state properties of these heavy systems. Pioneering experiments at GSI, Darmstadt identified the first atomic transitions in the element nobelium. For the purpose of determining nuclear properties in nobelium isotopes with higher precision, a new apparatus for high-resolution laser spectroscopy in a gas-jet called JetRIS is under development. To determine the spectral resolution and the homogeneity of the gas-jet, the laser-induced fluorescence of ¹⁶⁴Dy atoms seeded in the jet was studied. Different hypersonic nozzles were investigated for their performance in spectral resolution and efficiency. Under optimal conditions, a spectral linewidth of about 200–250 MHz full width at half maximum and a Mach number of about 7 was achieved, which was evaluated in context of the density profile of the atoms in the gas-jet. Full article

A new database and viewer for mass spectra resulting from collision processes is presented that follows the standards of the Virtual Atomic and Molecular Data Centre (VAMDC). A focus was placed on machine read and write access, as well as ease of use. In a browser-based viewer, mass spectra and all parameters related to a given measurement can be shown. The program additionally enables a direct comparison between two mass spectra, either by plotting them on top of each other or their difference to identify subtle variations in the data. Full article

Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations. Full article

The generation of high-order harmonics in a semi-infinite cell by femtosecond laser pulses is a common practice for reliable coherent and low divergence XUV source beams for applications. Despite the relative simplicity of the experimental method, several phenomena coexist that affect the generated spectral and divergence characteristics of the high harmonic XUV frequency comb. The ionisation degree of the medium and the consequent plasma formation length imposes a spatiotemporal evolution of the fundamental EM field and XUV absorption. Varying the laser pulse chirp and the focusing conditions, as well as the gas density, we measured intense harmonic spectral and divergence variations attributed mainly to self-phase modulations of the laser EM field in the partially ionised medium. Additionally, low-divergence high harmonics are observed for certain laser chirp values attributed to the strong phase matching of only the short electron quantum path. Thus, a tunable, low divergent, and coherent XUV source can be realised for spatiotemporal imaging applications in the nanoscale. Full article

The article is devoted to a brief description of the ATOM computer program system, designed to study the structure, transition probabilities and cross sections of various processes in multielectron atoms. The theoretical study was based on the concept of a computational experiment, the main provisions of which are discussed in the article. The main approximate methods used in the system of programs for taking many-electron correlations into account and determining their role in photoionization processes, elastic and inelastic electron scattering, the decay of vacancies, and many others are presented. The most significant results obtained with this software are listed. Full article

The atomic structure of californium is probed by two-step resonance ionization spectroscopy. Using samples with a total amount of about $2\times {10}^{10}$ Cf atoms (ca. 8.3 pg), ground-state transitions as well as transitions to high-lying Rydberg states and auto-ionizing states above the ionization potential are investigated and the lifetimes of various atomic levels are measured. These investigations lead to the identification of efficient ionization schemes, important for trace analysis and nuclear structure investigations. Most of the measurements are conducted on ${}^{250}$Cf. In addition, the isotope shift of the isotopic chain ${}^{249-252}$Cf is measured for one transition. The identification and analysis of Rydberg series enables the determination of the first ionization potential of californium to $E_{\mathrm{IP}}=50,666.76\left(5\right)$${\mathrm{cm}}^{-1}$. This is about a factor of 20 more precise than the current literature value. Full article

Triple differential cross section (TDCS) results are reported for the electron impact ionization of nitrogen molecules. The TDCSs have been calculated in distorted wave Born formalism using orientation averaged molecular orbital (OAMO) approximation. The TDCS results are presented as average and weighted sum for the outer molecular orbital $3{\sigma }_g$, $1{\pi }_u$, $2{\sigma }_u$ and the inner $2{\sigma }_g$ molecular orbital. The obtained theoretical TDCSs are compared with the available measurements. The results are analysed in terms of the positions and relative intensities of binary and recoil peaks. Within a first order model and for a complex molecule, a reasonable agreement is obtained with the experimental data in the binary peak region with certain discrepancies in position and magnitude in the recoil peak region. Full article

We review the definition of cooperative Lamb shift originally introduced by ourselves and S. R. Hartmann in 1973. We point out that the definition specified the preparation of a sample of identical two-level atoms prepared with partial excitation by a short pulse. We spell out in some detail the reasoning behind our assertion that the CLS does not enter into the dielectric constant, which determines the transmission of cw radiation through a sample. We give a prescription, using the transfer matrix formalism, for determining the transmission coefficient through a slab, given the thickness in wavelengths and the dielectric constant. We explore the possibility of achieving a true measurement of the CLS in a gaseous cold-atom cloud, with the help of a large foreign gas broadening of the resonant line. Full article

The four-component relativistic Dirac–Coulomb Hamiltonian and the multireference configuration interaction (MRCI) model were used to provide the reliable energy levels and spectroscopic properties of the Lr${}^{+}$ ion and the Lu${}^{+}$ homolog. The energy spectrum of Lr${}^{+}$ is very similar to that of the Lu${}^{+}$ homolog, with the multiplet manifold of the 7s${}^2$, 6d${}^1$7s${}^1$ and 7s${}^1$7p${}^1$ configurations as the ground and low-lying excited states. The results are discussed in light of earlier findings utilizing different theoretical models. Overall, the MRCI model can reliably predict the energy levels and properties and bring new insight into experiments with superheavy ions. Full article

There have been many observations of the solar and astrophysical spectra of various ions. The diagnostics of these observations require atomic data that include energy levels, oscillator strengths, transition rates, and collision strengths. These have been calculated using the Superstructure and Distorted-wave codes. We describe calculations for various ions. We calculate intensity ratios and compare them with observations to infer electron densities and temperatures of solar plasmas. Full article

Atomic-level lifetimes span a wide range, from attoseconds to years, relating to transition energy, multipole order, atomic core charge, relativistic effects, perturbation of atomic symmetries by external fields, and so on. Some parameters permit the application of simple scaling rules, others are sensitive to the environment. Which results deserve to be tabulated or stored in atomic databases? Which results require high accuracy to give insight into details of the atomic structure? Which data may be useful for the interpretation of plasma experiments or astrophysical observations without any particularly demanding accuracy threshold? Should computation on demand replace pre-fabricated atomic databases? Full article

Turbulent radiation flow is ubiquitous in many physical systems where light–matter interaction becomes relevant. Photon bubble instabilities, in particular, have been identified as a possible source of turbulent radiation transport in astrophysical objects such as massive stars and black hole accretion disks. Here, we report on the experimental observation of a photon bubble instability in cold atomic gases, in the presence of multiple scattering of light. Two different regimes are identified, namely, the growth and formation of quasi-static structures of depleted atom density and increased photon number, akin to photon bubbles in astrophysical objects, and the destabilisation of these structures in a second regime of photon bubble turbulence. A two-fluid theory is developed to model the coupled atom–photon gas and to describe both the saturation of the instability in the regime of quasi-static bubbles and the low-frequency turbulent phase associated with the growth and collapse of photon bubbles inside the atomic sample. We also employ statistical dimensionality reduction techniques to describe the low-dimensional nature of the turbulent regime. The experimental results reported here, along with the theoretical model we have developed, may shed light on analogue photon bubble instabilities in astrophysical scenarios. Our findings are consistent with recent analyses based on spatially resolved pump–probe measurements. Full article

The present study is devoted to isolate and study the effect of charge migration on the photoionization from the X@C₆₀. The noble gas atoms, Ar, Kr, and Xe, are confined in the C₆₀ to investigate the impact of charge migration from the entrapped atom to the C₆₀ side. The present work concludes that the confinement oscillations in the photoionization features are amplified due to the charge migration. Further, the angle-resolved, spin average time delay is also investigated in the light of confinement. Features in the time delay due to the charge migration are more amplified relative to those in the cross-section or angular distribution. Full article

This article reports a comprehensive theoretical study of electron scattering from vinyl ether and its isomers. The electron–molecule quantum collision problem is solved through a complex optical potential approach. From the solution of the Schrödinger equation corresponding to this scattering problem, various cross sections were obtained for energies from ionization threshold of target to 5 keV. To deal with the non-spherical and complex structure, a multi-center group additivity approach is used. Furthermore, geometrical screening correction is applied to compensate for the overestimation of results due to electron charge density overlap. We found an interesting correlation between maximum ionization cross section with polarizability and ionization energy of the target molecule. The fitting of the total cross section as a function of the incident electron energy is reported in this article. The correlation between the effective diameter of the target and the projectile wavelength at maximum ionization energy is also reported for vinyl ether and its isomers. The data presented here will be useful to biomedical field, mass spectrometry, and chemical database for military range applications. The cross sections are also important to model Mars’s atmosphere due to their presence in its atmosphere. The gas-kinetic radius and the van der Waals coefficients are estimated from the electron-impact total scattering cross sections. In addition, the current study predicts the presence of isomeric effects in the cross section. Full article

The present article describes a complete reanalysis of all published data on observed spectral lines and energy levels of the first three spectra of actinium (Ac I–III). In Ac I, three previously determined energy levels have been rejected, 12 new energy levels have been found; for six previously known levels, either the J values or the energies have been revised, and the ionization energy has been redetermined with an improved accuracy. In the line list of Ac I, three previous classifications have been discarded, 16 new ones have been found, and three have been revised. In Ac II, 16 new energy levels have been established, and 36 new identifications have been found for previously observed but unclassified lines. In both Ac I and Ac II, new sets of transition probabilities have been calculated. For all three spectra, complete datasets of critically evaluated energy levels, observed lines, and transition probabilities have been constructed to serve as recommended data on these spectra. Full article

RAdiation-Detected Resonance Ionization Spectroscopy (RADRIS) is a versatile method for highly sensitive laser spectroscopy studies of the heaviest actinides. Most of these nuclides need to be produced at accelerator facilities in fusion-evaporation reactions and are studied immediately after their production and separation from the primary beam due to their short half-lives and low production rates of only a few atoms per second or less. Only recently, the first laser spectroscopic investigation of nobelium ($Z=102$) was performed by applying the RADRIS technique in a buffer-gas-filled stopping cell at the GSI in Darmstadt, Germany. To expand this technique to other nobelium isotopes and for the search for atomic levels in the heaviest actinide element, lawrencium ($Z=103$), the sensitivity of the RADRIS setup needed to be further improved. Therefore, a new movable double-detector setup was developed, which enhances the overall efficiency by approximately 65% compared to the previously used single-detector setup. Further development work was performed to enable the study of longer-lived (t${}_{1/2}>1$ h) and shorter-lived nuclides (t${}_{1/2}<1$ s) with the RADRIS method. With a new rotatable multi-detector design, the long-lived isotope ${}^{254}$Fm (t${}_{1/2}=3.2 \mathrm{h}$) becomes within reach for laser spectroscopy. Upcoming experiments will also tackle the short-lived isotope ${}^{251}$No (t${}_{1/2}=0.8 \mathrm{s}$) by applying a newly implemented short RADRIS measurement cycle. Full article

A program of research towards the high-resolution optical spectroscopy of actinide elements for the study of fundamental nuclear structure is currently ongoing at the IGISOL facility of the University of Jyväskylä. One aspect of this work is the development of a gas-cell-based actinide laser ion source using filament-based dispensers of long-lived actinide isotopes. We have observed prominent phenomena in the resonant laser ionization process specific to the gaseous environment of the gas cell. The development and investigation of a laser ionization scheme for plutonium atoms is reported, focusing on the effects arising from the collision-induced phenomena of plutonium atoms in helium gas. The gas-cell environment was observed to greatly reduce the sensitivity of an efficient plutonium ionization scheme developed in vacuum. This indicates competition between resonant laser excitation and collisional de-excitation by the gas atoms, which is likely being enhanced by the very high atomic level density within actinide elements. Full article

A review of experimental studies of the measurement of the photoionization cross-section for the excited states of the alkali atoms, alkaline earth atoms, and rare-gas atoms is presented, with emphasis on using multi-step laser excitation, ionization, and the saturation technique. The dependence of the photoionization cross-section from different intermediate states populated in the first step and ionized in the second step are discussed, including results on the photoionization cross-sections measured above the first ionization threshold. Results based on different polarizations of the exciting and the ionizing dye lasers are also discussed. Examples are provided, illustrating the photoionization cross-sections measured using thermionic diode ion detector, atomic beam apparatus in conjunction with a time-of-flight mass spectrometer and DC/RF glow discharge cell as an optogalvanic detection. Full article

A ring of radius $\hslash k_0$ in the momentum distribution of a Bose–Einstein condensate is visible when the atoms scatter a single photon. Here, we describe an approximated theory of this effect, leading to an analytic expression of the isotropic momentum scattering rate. Full article

Ions with multiple inner-shell vacancies frequently arise due to their interaction with different targets, such as (intense) light pulses, atoms, clusters or bulk material. They are formed, in addition, if highly charged ions approach surfaces and capture electrons at rather large distances. To explore the interaction of such hollow ions and their subsequent relaxation, photon spectra in different frequency regions have been measured and compared to calculations. To support these and related measurements, we here show within the framework of the Jena Atomic Calculator (Jac) how (additional) electrons in outer shells modify photon emission and lead to characteristic shifts in the observed spectra. Further, for highly charged Ar ions in KL${}^m(m=1\dots 8)$ configurations, we analyze the mean relaxation time for their stabilization into the different ground configurations. These examples demonstrate how a powerful and flexible toolbox such as Jac will be useful (and necessary) in order to model the photon and electron emission of ions as they occur not only near surfaces but also in astro-, atomic and plasma physics. Full article