Few-electron Ions Research Articles

On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent properties in two-electron atoms/ions which include the negatively charged Ps$^{-}$ ($e^{-} e^{+} e^{-}$) and H$^{-}$ ions, He atom and positively charged, helium-like ions from Li$^{+}$ to Ni$^{26+}$. All these ions are considered in their ground $1^{1}S-$state(s). The slowly convergent properties selected in this study include the electron-nulceus $\langle r^{2 k}_{eN} \rangle$ and electron-electron $\langle r^{2 k}_{ee} \rangle$ expectation values for $k$ = 2, 3, 4 and 5.

Lifetime measurements of nuclei in few-electron ions

In this review lifetime measurements of ions with at most two electrons are summarized. Such highly ionized systems have been studied—until now—only in the experimental storage ring of the GSI in Darmstadt. Emphasis is put on decays via the weak interaction. The first observations of beta-decay into bound atomic states are described as well as its time mirrored counterpart, the electron-capture decay. In the latter case the decays of hydrogen- and helium-like ions are compared with a surprising result. Further on, the observation of sinusoidal modulations of the decay rate in two-body decays is summarized. As a possible cause an interference due to the emission of neutrinos with different rest mass is discussed.

Absolute radiative and Auger transition rates of K-shell excited few-electron iron ions

SynopsisThe iron Kα lines are among the most prominent features in the x-ray spectra of many celestial sources. However, transition rates used to model these spectra were only known by theoretical calculations. Here we present an absolute measurement of iron K-shell transition rates for Li-like to C-like iron ions. These ions were created with an electron beam ion trap and excited with x rays from the PETRA III synchrotron source. Measuring x-ray fluorescence and Auger decay simultaneously allows to determine absolute decay rates independent of most experimental parameters.

Status of deceleration and laser spectroscopy of highly charged ions at HITRAP

Heavy few-electron ions are relatively simple systems in terms of electron structure and offer unique opportunities to conduct experiments under extremely large electromagnetic fields that exist around their nuclei. However, the preparation of highly charged ions (HCI) has remained the major challenge for experiments. As an extension of the existing GSI accelerator facility, the HITRAP facility was conceived as a multi-stage decelerator for HCI produced at high velocity. It is designed to prepare bunches of around 105 HCI and to deliver them at low energies to various experiments. One of these experiments is SpecTrap, aiming for laser spectroscopy of trapped, cold HCI. We present the latest results on deceleration of ions in a radio-frequency quadrupole, synchrotron cooling of electrons in a trap as a preparation step for the prospective electron cooling of the HCI decelerated in HITRAP, as well as laser cooling of singly charged Mg ions for sympathetic cooling of HCI in SpecTrap.

The theory of the Bohr–Weisskopf effect in the hyperfine structure

Description of the Bohr–Wesskopf effect in the hyperfine structure of few-electron heavy ions is a challenging problem, which can be used as a test of both QED and atomic calculations. However, for twenty years the research has actually been going in a wrong direction, aimed at fighting the Bohr–Weisskopf effect through its cancellation in specific differences. Alternatively, we propose the constructive model-independent way, which enables the nuclear radii and their momenta to be retrieved from the hyper-fine splitting (HFS). The way is based on analogy of HFS to internal conversion coefficients, and the Bohr–Weisskopf effect – to the anomalies in the internal conversion coefficients. It is shown that the parameters which can be extracted from the data are the even nuclear momenta of the magnetization distribution. The radii R2 and – for the first time – R4 are obtained in this way by analysis of the experimental HFS values for the H- and Li-like ions of 209Bi. The critical prediction concerning the HFS for the 2p12 state is made. The present analysis shows high sensitivity of the method to the QED effects, which offers a way of precision test of QED. Experimental recommendations are given, which are aimed at retrieving data on the HFS values for a set of a few-electron configurations of each atom.

Radioactive decays of highly-charged ions

Access to stored and cooled highly-charged radionuclides offers unprecedented opportunities to perform high-precision investigations of their decays. Since the few-electron ions, e.g. hydrogen- or helium-like ions, are quantum mechanical systems with clear electronic ground state configurations, the decay studies of such ions are performed under well-defined conditions and allow for addressing fundamental aspects of the decay process. Presented here is a compact review of the relevant experiments conducted at the Experimental Storage Ring ESR of GSI. A particular emphasis is given to the investigations of the two-body beta decay, namely the bound-state β-decay and its time-mirrored counterpart, orbital electron-capture.

Analytical Solution to the Dirac Equation for Few-Electron Ions of Transuranium Elements

The paper presents relativistic generalization of the well-known method of multidimensional angular Coulomb functions. Two-component multidimensional angular functions have been constructed and they are used as a basis for expanding in series the many- electron wave function of the many-particle Dirac equation. A system of ordinary differential equations which factors are expressed in terms of matrix elements of various operators of the Dirac equation has been obtained for the expansion amplitudes. The binding energy of helium-, lithium-, beryllium- and carbon-like ions of transuranium elements has been calculated (Z = 92-101). Wave functions have been constructed for some states of transuranium ions. The developed method allows taking into account the many-particle effects during the calculation of relativistic many-electron systems which are described by the manyparticle Dirac equation with Coulomb interactions. The obtained results can be applied to specify the probability of transitions and particle paths in high energydensity processes.

Reverse conversion in 161Dy ions as an extension of dielectronic recombination

A new method for studying nucleus excitation by means of reverse conversion is proposed. This method can be applied on the storage rings of accelerators and is based on data accumulated in studies of dielectronic recombination. A cascade of 2–3 conversion transitions produces a unique facsimile of the process. Reverse conversion cross sections are calculated for beams of few-electron 161Dy ions (e.g., H-, He-, Li-, and Be-like).

Two-photon transitions in few-electron ions in the presence of static electric fields

Two-photon transitions in H- and He-like heavy ions in the presence of an external static electric field are explored using a relativistic Greens function approach and an independent particle model. The effects of Stark mixing on angular correlations, spectral distributions and total transition rates are analyzed in detail. Special emphasis is placed on the 2p1/2 → 1s1/2 two-photon transition in H-like ions and the 1s1/22p1/2:23P0 → 1s21/2:11S0 and 1s1/22s1/2:21S0 → 1s21/2:11S0 two-photon transitions in He-like ions.

Beta decay of highly charged ions

A brief overview is presented in this paper on some experiments conducted at the Experimental Storage Ring (ESR) of GSI which addressed the β decay of stored and cooled highly charged ions. Special emphasis is placed on the two-body beta decay of bare or few-electron ions: bound-state β− decay (βb) and its time-mirrored counterpart, orbital electron capture. The former decay mode was detected experimentally 20 years ago at the ESR. The latter could be investigated there for the first time in detail for the simplest quantum systems: hydrogen- and helium-like atoms. The main results of these experiments will be presented. Also their impact on stellar nucleosynthesis, in particular the s-process, is discussed.

Half-life measurements of highly charged radionuclides

In recent years several measurements of the orbital electron capture half-lives of few-electron ions have been carried out employing the storage ring ESR at GSI. Hydrogen-like and helium-like 140Pr and 142Pm as well as hydrogen-like 122I were studied. Half-lives of the corresponding fully ionized nuclides provide the three-body β+ decay constants.

Hyperfine-induced effects on the linear polarization ofKα1emission from heliumlike ions

The linear polarization of the characteristic photon emission from few-electron ions is studied for its sensitivity with regard to the nuclear spin and magnetic moment of the ions. Special attention is paid, in particular, to the K$\alpha_1$ ($1s 2p_{3/2} ^{1,3}P_{1,2} \to 1s^2 ^1S_0$) decay of selected helium-like ions following the radiative electron capture into initially hydrogen-like species. Based on the density matrix theory, a unified description is developed that includes both, the many-electron and hyperfine interactions as well as the multipole-mixing effects arising from the expansion of the radiation field. It is shown that the polarization of the K$\alpha_1$ line can be significantly affected by the mutipole mixing between the leading $M2$ and hyperfine-induced $E1$ components of $1s2p ^3P_2, F_i \to 1s^2 ^1S_0, F_f$ transitions. This $E1$-$M2$ mixing strongly depends on the nuclear properties of the considered isotopes and can be addressed experimentally at existing heavy-ion storage rings.

The ILIMA project at FAIR

The Isomeric beams, LIfetimes and MAsses (ILIMA) collaboration will exploit heavy-ion storage rings at the Facility for Antiproton and Ion Research (FAIR) for the study of exotic nuclei. Single-ion sensitivity and exceptional production rates of bare or few-electron radioactive ions, with atomic numbers up to Z=92, promise access to a wide range of short-lived nuclides for the first time. Measuring the masses, lifetimes and decay modes of ground and isomeric states with t1/2>10 μs will reveal key features of nuclear structure and nuclear astrophysics, extending, for example, to r-process waiting-point nuclides in the 208Pb region.

QED theory of the spectral line profile for few-electron atoms and ions

A review of the current status of the theoretical study of spectral line profile for systems with few electrons is presented. The line-profile approach (LPA) is introduced for the investigation of the energy levels within the framework of QED. In particular, the energy of the levels, transition probabilities and electron recombination processes are considered.

Quantum correlations in the two-photon decay of few-electron ions

The photon-photon polarization entanglement in the two-photon decay of metastable ionic states has been analyzed in the framework of the density matrix and second-order perturbation theory. Emphasis is placed especially upon the relativistic and non-dipole effects along the hydrogen- and helium-isoelectronic sequence.

Half-life measurements of stored fully ionized and hydrogen-like 122 I ions

The half-lives of fully ionized and hydrogen-like (H-like) I-122 ions have been measured in a heavy-ion storage ring. The beta(+)-decay constants for both charge states and the electron capture (EC) decay constant of H-like ions have been determined. The EC-decay constant in H-like I-122 ions lambda(H-like)(EC) = 7.35(33) . 10(-4) s(-1) is, within the uncertainty, the same as the one in neutral atoms. This result is in agreement with the estimates of recent theoretical considerations on the EC-decay of few-electron ions that explicitly take into account the conservation of the total angular momentum of the nucleus plus lepton(s) system and its projections. No firm confirmation could be concluded from our results on the predicted effect that allowed Gamow-Teller transitions become forbidden if the initial and final total angular momenta are not equal.

Two-photon absorption of few-electron heavy ions

The two-photon absorption of few-electron ions has been studied by using second-order perturbation theory and Dirac's relativistic equation. Within this framework, the general expressions for the excitation cross sections and rates are derived including a full account of the higher-order multipole terms in the expansion of the electron-photon interaction. While these expressions can be applied to any ion, independent of its particular shell structure, detailed computations are carried out for the two-photon absorption of hydrogen-, helium-, and berylliumlike ions and are compared with the available theoretical and experimental data. The importance of relativistic and nondipole effects in the analysis and computation of induced two-photon transitions is pointed out. Moreover, we discuss the potential of these transitions for atomic parity-violation studies in the high-$Z$ domain.

The RMT method for many-electron atomic systems in intense short-pulse laser light

We describe a new ab initio method for solving the time-dependent Schrödinger equation for multi-electron atomic systems exposed to intense short-pulse laser light. We call the method the R-matrix with time-dependence (RMT) method. Our starting point is a finite-difference numerical integrator (HELIUM), which has proved successful at describing few-electron atoms and atomic ions in strong laser fields with high accuracy. By exploiting the R-matrix division-of-space concept, we bring together a numerical method most appropriate to the multi-electron finite inner region (R-matrix basis set) and a different numerical method most appropriate to the one-electron outer region (finite difference). In order to exploit massively parallel supercomputers efficiently, we time-propagate the wavefunction in both regions by employing Arnoldi methods, originally developed for HELIUM.

Laser spectroscopy of the (1s22s2p) 3P0–3P1 level splitting in Be-like krypton

Heavy few-electron ions, such as He-, Li- and Be-like ions, are ideal atomic systems to study the effects of correlation, relativity and quantum electrodynamics. Very recently, theoretical and experimental studies of these species achieved a considerable improvement in accuracy. Be-like ions are interesting because their first excited state, i.e. (1s22s2p)3P0, has an almost infinite lifetime (τ0) in the absence of nuclear spin (I), as it can only decay by a two-photon E1M1 transition to the (1s22s2)1S0 ground state. In addition, the energy difference between the 3P0 and the next higher-lying 3P1 state is expected to remain almost completely unaffected by QED effects, and should thus be dominated by the effects of correlation and relativity. Therefore, we want to determine the (1s22s2p) 3P0–3P1 level splitting in Be-like krypton (84Kr32+), which has I=0, by means of laser spectroscopy at the experimental storage ring at GSI. In such an experiment, the energy splitting can be obtained with very good accuracy and can be compared with recent calculations.

Precision studies of fundamental atomic structure with heaviest few-electron ions

One- and few-electron ions traditionally serve as an important testing ground for fundamental atomic structure theories and for the effects of QED, relativity and electron correlation. In the domain of high nuclear charges, new opportunities open up for precise testing and consolidating of the present understanding of the atomic structure in the regime of extreme electromagnetic fields. In this review, the current progress in experimental investigations of the heaviest H- and He-like systems at GSI Darmstadt is presented together with the planned future developments.