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The study of atomic and ionic lifetimes and transition probabilities has undergone a period of intense activity, facilitated largely by the application of the technique of Beam-Foil Spectroscopy. This area is now a mature field of study (having been pursued for 40 years), and has provided much new data, elucidated fundamental atomic processes, and furthered applications in many fields. However, technical advances have now broadened the field to permit new types of measurements of unprecedented accuracy and scope. Thus, this occasion offers an appropriate opportunity to review some of the successful applications of the method, to survey the present state of knowledge, and to indicate areas that hold promise for future research.

Various methods for evaluating electron binding energies and affinities are discussed, and the (all-order) perturbative method is described in some detail. It is shown that for a single valence electron or valence hole the exact binding energy/affinity is given by the energy eigenvalue of the valence Brueckner or Dyson orbital.

The need for quantitative evaluation of complex line emission spectra as observed in hot fusion plasmas initiated a challenging development of sophisticated interpretation tools based on integrating advanced atomic modelling with detailed treatment of the plasma environment. The successful merging of the two worlds has led to routine diagnostic procedures which have contributed enormously to the understanding of underlying plasma processes and also to a wide acceptance of spectroscopy as a reliable diagnostic method.

In this paper three characteristic types of spectra of current and continuing interest are presented. The first is that of medium/heavy species with many ionisation stages revealed in survey VUV and XUV spectra. Such species occur as control gases, as wall materials, as ablated heavy species and possible as layered wall dopants for monitoring erosion. The spectra are complex with line-like and quasi-continuum regions and are amenable to advanced `pattern recognition' methods.

The second type is of few electron, highly ionised systems observed as line-of-sight integrated passive emission spectra in the soft x-ray region. They are analysed successfully in terms of plasma parameters through matching of observation with predicted synthetic spectra. Examples used here include highly resolved helium-like emission spectra of argon, iron and titanium observed on the tokamaks TEXTOR and Tore Supra.

The third type, and the emphasis of this work, comprises spectra linked to active beam spectroscopy, that is, charge exchange recombination spectroscopy (CXRS) and beam emission spectroscopy (BES). In this case, a complex spectrum is again composed of a (usually) dominating active spectrum and an underlying passive emission spectrum. Its analysis requires modelling of both active and passive features. Examples used here are from the CXRS diagnostic at JET and TEXTOR. They display characteristic features of the main light impurity ions (C⁺⁶, He⁺², N⁺⁷, Ne⁺¹⁰ and Ar⁺¹⁸), as well as that of the bulk plasma ions, H⁺, D⁺ and T⁺.

A main conclusion is that spectral complexity is not necessarily negative, but that `complex structures' can provide a rich source of information on the plasma and its parameters—provided it is matched with integrated analysis—and that the methods can have universal applicability. In the present preparatory phase of the next generation fusion experiment ITER (International Thermonuclear Experimental Reactor) the concepts and expectations of complex spectra and integrated data analysis play an important role in the design and optimisation procedure of the ITER diagnostic assembly.

The present article summarizes a talk given at a symposium in honour of Indrek Martinson at the occasion of his retirement. The theme of the present contribution is the study of rare states and rare processes that was made possible by the ion beam technique.

Spectroscopy performed with the three Livermore electron beam ion traps is reviewed, which is continuing and complementing the innumerable contributions to atomic physics provided over the years by heavy-ion accelerators. Numerous spectrometers were developed that cover the spectral bands from the visible to the hard x-ray region. These enabled exhaustive line surveys useful for x-ray astrophysics and for systematic studies along iso-electronic sequences, such as the 4s–4p, 3s–3p, and 2s–2p transitions in ions of the Cu-I, Na-I, and Li-I sequences useful for studying QED and correlation effects as well as for precise determinations of atomic-nuclear interactions. They also enabled measurements of radiative transition probabilities of very long-lived (milli- and microseconds) and very short-live (femtosecond) levels. Because line excitation processes can be controlled by choice of the electron beam energy, the observed line intensities are used to infer cross sections for electron-impact excitation, dielectronic recombination, resonance excitation, and innershell ionization. These capabilities have recently been expanded to simulate x-ray emission from comets by charge exchange. Specific contributions to basic atomic physics, nuclear physics, and high-temperature diagnostics are illustrated.

A brief description of the operational principles of an Electron Beam Ion Trap is given with specific reference to the currently under development/construction Shanghai EBIT. This is followed by an introduction to some of the frontier physics problems of highly charged ions that can be studied with such devices. Also a discussion of the use of EBITs as a powerful tool in hot-plasma diagnostics is presented.

An electron beam ion trap (EBIT) has been designed and is currently under construction for use in atomic physics experiments at the Queen's University, Belfast. In contrast to traditional EBITs where pairs of superconducting magnets are used, a pair of permanent magnets will be used to compress the electron beam. The permanent magnets have been designed in conjunction with bespoke vacuum ports to give unprecedented access for photon detection. Furthermore, the bespoke vacuum ports facillitate a versatile, reconfigurable trap structure able to accommodate various in-situ detectors and in-line charged particle analysers. Although the machine will have somewhat lower specifications than many existing EBITs in terms of beam current density, it is hoped that the unique features will facilitate a number of hitherto impossible studies involving interactions between electrons and highly charged ions. In this article the new machine's design is outlined along with some suggestions of the type of process to be studied once the construction is completed.

When beam-foil experiments on ions of the iron group were done at the Bochum Dynamitron tandem accelerator, line identifications of intercombination lines in Mg- and Al-like Fe matched previously unclassified lines that appear in the EUV spectrum of the solar corona. Beam-foil work continued on Si- to Cl-like Fe ions, identifying in particular decays of high-J levels with nanosecond lifetimes. Millisecond lifetimes in the same ions were then measured at a heavy-ion storage ring and at an electron beam ion trap. Remaining problems and prospects for solutions are discussed.

As part of a project to compile a comprehensive catalog of astrophysically relevent emission lines, we used the low-energy capability of the Lawrence Livermore electron beam ion traps to extend the spectroscopy of neon-like ions and the neighboring charge states to silicon, sulfur, and argon. We present wavelength data of Si V and demonstrate the effect of collisional deexcitation of electric dipole forbidden lines on the 2–3 L-shell spectra of Si V, S VII, and Ar IX.

The beam-foil method and the computation of oscillator strengths with correlated wave functions both had their beginning in the late 1960s. The stimulating interplay between theory and experiment will be reviewed. With the power of todays computers, great progress has been made in computation. The current state of spectrum calculations using the multiconfiguration Hartree–Fock method will be described and the importance of relativistic effects mentioned.

Some of our early exploratory calculations of oscillator strengths were described (Crossley 1984 Physica ScriptaT8 117) as `over-ambitious'. In this article, we examine these and other earlier simple calculations in the light of more recent and more extensive calculations, to show how they led to an understanding of the types of calculation needed to achieve accurate results.

After reviewing current perceptions about the electron correlation problem, a general selected configuration interaction (CI) method to calculate highly accurate energies for atoms and medium-sized molecules is described. For a given orbital basis, selected CI may be implemented to yield the best energy and corresponding wave function for given selection thresholds together with an estimate of the full CI energy. The linked cluster expansion is used as an intermediate device to reveal relationships between variational coefficients in the CI expansion. These relationships allow to predict CI coefficients that are used in an a priori and fast-to-evaluate variational estimate of individual configuration energy contributions via Brown's formula both for selection purposes, and to estimate the truncation energy error caused by unselected configurations. Concepts based on natural orbitals are used likewise for configurations not amenable to the above analysis. An application to the ground state of the Ne atom achieves an accuracy of two µhartrees using very large orbital bases, increasing accuracy more than a hundredfold and at fair computational cost.

The role of tensorial and symmetry properties of the quantities of theoretical atomic spectroscopy, increasing the efficiency of the relevant mathematical apparatus, is discussed. The main attention is paid to the progress of research in this field carried out by Adolfas Jucys scientific school of theoretical physicists in Lithuania, particularly to the second quantization in a coupled tensorial form as well as to the role of quasispin in the new version of Racah algebra. The role of Professor Indrek Martinson in strengthening the scientific cooperation between the atomic physicists of a Lund University and theoretical physicists from Lithuania will be emphasized.

Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum-mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position of the plasma span the entire region from weak to strong fields, and there is a need for a unified treatment. In this paper we present the detailed quantum-mechanical derivation of the exact eigenenergies and eigenstates of hydrogen-like atoms and ions in a static magnetic field. Notably, these formulas are not much more complicated than the better-known approximations. Moreover, the derivation allows the value of the electron spin gyromagnetic ratio g_s to be different from 2. For completeness, we then review the details of dipole transitions between two hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various approximations made in the derivation are also discussed in details.

We consider the conditions necessary for the development of an inverted population among the energy levels of free atoms in a medium exposed to radiation in spectral non-equilibrium. In particular, we focus on monochromatic radiation occurring as a result of an accidental wavelength coincidence between a pumping emission line and a pumped absorption line in two different elements. We examine especially the influence of `pseudo-metastable' states (at medium excitation) in the complex spectrum of Fe II, which cause a `bottleneck' in the radiative decay leading to an inverted level population. We also discuss the effect of `spectral compression' of the Lyman continuum into HLyα radiation at a high effective temperature. In conclusion we describe those differences between microwave astrophysical masers (APM) and optical astrophysical lasers (APL) that make the latter a more rare phenomenon in Nature.

This partly historical paper is based on a presentation at the conference `Spectroscopy of Highly Charged Ions: Not Just the Light at the End of an Accelerator'. It starts with an experiment taking place on a Saturday morning/afternoon at The Research Institute in Stockholm a long, long time ago. The development of our understanding of multiply-excited states in simple and complex atoms owes much to the efforts of Professor Martinson and his colleagues since the late 1960s and continues to this day. We give a brief historical survey of what we consider to be important events in these developments and include some of the latest results of ongoing research. We conclude with a few historic pictures of the collaborators of Professor Indrek Martinson.

The life and work of Professor Indrek Martinson is reviewed on his retirement.