Helium-like Research Articles

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.

Nuclear magnetic dipole moment effect on the angular distribution of the Kα lines

We present a theoretical analysis of the fine-structure transitions for helium-like heavy ions with non-zero nuclear spin. The angular distribution of these transitions is studied for its sensitivity with regard to the nuclear magnetic dipole moment . Detailed calculations, performed for the helium-like , and ions with nuclear spin , indicate that the emission pattern of the fine-structure resolved photons is significantly affected by and that this effect can be addressed experimentally at present storage ring facilities.

Investigation of the heavy-ion mode in the FAIR High Energy Storage Ring

High energy storage ring (HESR) as a part of the future accelerator facility FAIR (Facility for Antiproton and Ion Research) will serve for a variety of internal target experiments with high-energy stored heavy ions (SPARC collaboration). Bare uranium is planned to be used as a primary beam. Since a storage time in some cases may be significant—up to half an hour—it is important to examine the high-order effects in the long-term beam dynamics.A new ion optics specifically for the heavy ion mode of the HESR is developed and is discussed in this paper. The subjects of an optics design, tune working point and a dynamic aperture are addressed. For that purpose nonlinear beam dynamics simulations are carried out. Also a flexibility of the HESR ion optical lattice is verified with regard to various experimental setups. Specifically, due to charge exchange reactions in the internal target, secondary beams, such as hydrogen-like and helium-like uranium ions, will be produced. Thus the possibility of separation of these secondary ions and the primary beam is presented with different internal target locations.

Resonances in two-electron atoms below the critical charge

The critical nuclear charge Zc required for a heliumlike atom to have at least one bound state was recently determined with high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state changes smoothly into a shape resonance as Z crosses the critical value. Using variational calculations combined with the complex coordinate rotation method, we study the energy and width of the resonance for Z \textless{} Zc, thus providing direct evidence of the validity of this hypothesis. The variation of the resonance width with Z is found to be in good agreement with a model derived from analysis of the 1/Z perturbation series.

Startup impurity diagnostics in Wendelstein 7-X stellarator in the first operational phase

An essential element for stationary stellarator operation is the understanding of the impurity transport behavior. Neoclassical theory predicts an impurity transport towards the plasma core for the standard ion root regime in stellarators [1,2]. The performance of a quasi-stationary device like Wendelstein 7-X stellarator (W7-X, presently in the commissioning phase in Greifswald, Germany) could be limited in case of strong impurity accumulation. Therefore, a set of plasma diagnostics is foreseen to obtain key experimental quantities for the neoclassical transport modeling as ion temperature profile, density gradients and impurity concentration [1]. The core impurity content is monitored by the High Efficiency eXtreme ultraviolet Overview Spectrometer system (HEXOS) [2], covering the wavelength range 2.5–160 nm (intermediate ionization states of all relevant heavy intrinsic impurity species) with high spectral resolution and a time resolution of 1 ms, adequate for transport analysis. Impurity radiation at shorter wave lengths (4 nm–0.06 nm) will be monitored with the SX pulse height analysis system (PHA) [3]. The ion temperature profile can be deduced from inversion of data from the High Resolution X-ray Imaging Spectrometer (HR-XIS), which measures the concentration and temperature of argon tracer gas in helium-like ionization stages [6,7,8]. A second X-ray Imaging Crystal Spectrometer (XICS), which will additionally provide the poloidal ion rotation velocity, is under preparation [8,9]. The total radiation will be measured by two bolometer cameras [10,11]. The status of the impurity diagnostics for the first operational phase in W7-X is summarized in this paper and an outlook for the next experimental campaign is given.

Spectroscopic diagnosis in electronic temperature of photoionise plasmas

In this work, we are interested in the diagnostics in electronic temperature of a plasma purely photoionized, based on the intensity ration of lines emitted by ions helium-like, which have an atomic number Z relatively small. We considered the three lines corresponding to the transitions starting from the excited levels 1s 2l towards the fundamental level 1s 2 1 S 0 , like appropriate lines. More precisely, the line of resonance w due to the transition 1s2p 1 P 1 --- 1s 21 S 0 , the line of intercombinaison (x,y) 1s2p 3 P 2,1 --- 1s 21 S 0 as well as prohibited line z due to the transition 1s 23 S 1 --- 1s2 1 S 0 . These lines appear clearly in the spectra of astrophysical plasmas. As helium-like ion, we chose two, the oxygen O 6+ (Z=8) and neon Ne 8+ (Z=10). We carried out calculations of the ration of lines intensity G=(z+x+y)/w of O 6+ and Ne 8+ according to the electronic temperature in the range going from 10 5 to 10 7 K. We will see that, like it was shown by Gabriel and Jordan in 1969 [1], this intensity ration can be very sensitive to the temperature electronic and practically independent of the electronic density. Consequently, the ration G can be used to determine in a reliable way the electronic temperature of plasma observed [2]. Keywords: Strongly charged ions, lines emission, radiative and dielectronic recombination.

A Balancing Act: Stability versus Reactivity of Mn(O) Complexes.

A large class of heme and non-heme metalloenzymes utilize O2 or its derivatives (e.g., H2O2) to generate high-valent metal-oxo intermediates for performing challenging and selective oxidations. Due to their reactive nature, these intermediates are often short-lived and very difficult to characterize. Synthetic chemists have sought to prepare analogous metal-oxo complexes with ligands that impart enough stability to allow for their characterization and an examination of their inherent reactivity. The challenge in designing these molecules is to achieve a balance between their stability, which should allow for their in situ characterization or isolation, and their reactivity, in which they can still participate in interesting chemical transformations. This Account focuses on our recent efforts to generate and stabilize high-valent manganese-oxo porphyrinoid complexes and tune their reactivity in the oxidation of organic substrates. Dioxygen can be used to generate a high-valent Mn(V)(O) corrolazine (Mn(V)(O)(TBP8Cz)) by irradiation of Mn(III)(TBP8Cz) with visible light in the presence of a C-H substrate. Quantitative formation of the Mn(V)(O) complex occurs with concomitant selective hydroxylation of the benzylic substrate hexamethylbenzene. Addition of a strong H(+) donor converted this light/O2/substrate reaction from a stoichiometric to a catalytic process with modest turnovers. The addition of H(+) likely activates a transient Mn(V)(O) complex to achieve turnover, whereas in the absence of H(+), the Mn(V)(O) complex is an unreactive "dead-end" complex. Addition of anionic donors to the Mn(V)(O) complex also leads to enhanced reactivity, with a large increase in the rate of two-electron oxygen atom transfer (OAT) to thioether substrates. Spectroscopic characterization (Mn K-edge X-ray absorption and resonance Raman spectroscopies) revealed that the anionic donors (X(-)) bind to the Mn(V) ion to form six-coordinate [Mn(V)(O)(X)](-) complexes. An unusual "V-shaped" Hammett plot for the oxidation of para-substituted thioanisole derivatives suggested that six-coordinate [Mn(V)(O)(X)](-) complexes can act as both electrophiles and nucleophiles, depending on the nature of the substrate. Oxidation of the Mn(V)(O) corrolazine resulted in the in situ generation of a Mn(V)(O) π-radical cation complex, [Mn(V)(O)(TBP8Cz(•+))](+), which exhibited more than a 100-fold rate increase in the oxidation of thioethers. The addition of Lewis acids (LA; Zn(II), B(C6F5)3) to the closed-shell, diamagnetic Mn(V)(O)(TBP8Cz) stabilized a paramagnetic valence tautomer Mn(IV)(O)(TBP8Cz(•+))(LA), which was characterized as a second π-radical cation complex by NMR, EPR, UV-vis, and high resolution cold spray ionization MS. The Mn(IV)(O)(TBP8Cz(•+))(LA) complexes are able to abstract H(•) from phenols and exhibit a rate enhancement of up to ∼100-fold over the parent Mn(V)(O) valence tautomer. In contrast, a large decrease in rate is observed for OAT for the Mn(IV)(O)(TBP8Cz(•+))(LA) complexes. The rate enhancement for hydrogen atom transfer (HAT) may derive from the higher redox potential for the π-radical cation complex, while the large rate decrease seen for OAT may come from a decrease in electrophilicity for an Mn(IV)(O) versus Mn(V)(O) complex.

Partial-wave decomposition of the ground-state wavefunction of the two-electron harmonium atom

An exact formula for the collective occupancy of natural orbitals with an angular momentum l is derived for the ground state of the two-electron harmonium atom. For confinement strengths $$\omega $$ that correspond to polynomial correlation factors as well as at the weak ( $$\omega \rightarrow \infty $$ ) and strong ( $$\omega \rightarrow 0$$ ) correlations limits, it reduces to closed-form expressions. At the former limit, a similar result obtains for the partial-wave contributions to the ground-state energy. Slow convergence of the collective occupancies to their leading large-l asymptotics provided by Hill’s formula is uncovered. As the rate of convergence decreases strongly with $$\omega $$ , a complete breakdown of Hill’s formula ensues upon the confinement strength becoming infinitesimally small. The relevance of these findings to the performance of the extrapolation schemes for the estimation of the complete-basis-set limits of quantum-mechanical observables is discussed.

On the Q-dependence of the lowest-order QED corrections and other properties of the ground 11S-states in the two-electron ions

Formulas and expectation values which are need to determine the lowest-order QED corrections (∼α3) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important properties of the two-electron ions are also determined to high accuracy, including the expectation values of the quasi-singular Vinti operator and 〈reN−2〉 and 〈ree−2〉 expectation values. Elastic scattering of fast electrons by the two-electron ions in the Born approximation is considered. Interpolation formulas are derived for the bound state properties of the two-electron ions as the function of the nuclear electric charge Q.

Two-photon triple ionization of Li

A time-dependent close-coupling method is used to calculate the two-photon triple ionization of Li. Our method combines approaches previously used for two-photon double ionization of two-electron atoms with approaches that have been used for single-photon triple ionization of three-electron atoms. At a photon energy of 115.0 eV the three outgoing electrons share an energy of 31.4 eV. We explore the energy and angle differential cross sections of the three outgoing electrons and compare and contrast these distributions with those arising from single-photon triple ionization of Li.

Solar X-rays from 0.3 a.u.: the ChemiX Bragg Spectrometer on Interhelioprobe

AbstractChemiX is a Bragg crystal spectrometer that will fly on the two Interhelioprobe spacecraft due for launch in 2025 and 2026. The spacecraft perihelion will be only 0.3 a.u. and the orbit inclination up to 30°, and so instruments on board will have a close view of solar active regions and flares and regions near each solar pole. The ChemiX X-ray spectrometer, built by a consortium of groups led by the Space Research Centre, Polish Academy of Sciences, will fly on each of the spacecraft, and observe X-ray spectra in the 1.5 - 9 Å range. Spectral lines in this range include resonance lines of helium-like and hydrogen-like ions of elements such as Fe, Ca, Ar, S, and Si, with less abundant elements such as K and Cl represented by weaker lines which the high sensitivity of ChemiX should be able to detect. The free–free and free–bound continua should also be detected since instrumental background will be eliminated. Three of the seven channels of ChemiX will be in a “dopplerometer” arrangement by which spatial and spectral shifts present in flare impulsive stages can be disentangled.

Electron correlation in the Quasi Sturmian approach for two-electron continuum problems

SynopsisThe driven equation describing an (e, 3e) process on helium in the framework of the Temkin-Poet model is solved numerically using expansions of Convoluted Quasi Sturmian functions. As we observe first that the convergence rate of the solution is rather poor, we propose to significantly improve the expansion by introducing a phase factor corresponding the electron-electron interaction into the basis functions.

Spherically symmetric states of Hookium in a cavity

When a two-electron atom or ion is enclosed in an impenetrable spherical cavity, level crossings and avoided crossings are observed as the cavity radius changes. The locations of those crossings depend on the cavity radius and the nuclear charge of the system. The question arises as to whether this crossing behavior is unique to the one-electron Coulomb potential or whether it can be observed in other confined single-particle electron potentials. In this work we examined some low-lying singlet and triplet states of two-electron systems with isotropic harmonic single-particle 3D potentials. The spherically symmetric S states are analyzed using variational energies calculated with Hylleraas-type function. The energy dependence of low-lying states is considered as a function of the cavity radius and the harmonic force constant. For positive force constants, there exist cavity radii where the 21S and 13S states are degenerate. Analogous points do not exist for the two-electron quantum dot where the one-electron potential corresponds to an infinite rectangular box. The structure of the energy spectrum for negative force constants is also studied. The similarities and differences of the two-electron S states for the Coulomb and harmonic potentials are considered.

Electron- and proton-impact excitation of He-like uranium

SynopsisIn this contribution, we present an experimental and theoretical study of the proton- and electron- impact excitation effects in helium-like uranium ions in relativistic collisions with different gaseous targets. The experiment was carried out at the experimental storage ring at GSI Darmstadt. Our experimental results are in agreement with predictions of the state-of-the art theory which treats both processes within the relativistic framework.

Doubly Excited Nonautoionizing F and G States of Two-Electron Ions

We have investigated the doubly excited nonautoionizing states of heliumlike two electron ions from Li+ through Mg10+ using the exponential correlated exponential wave functions in the framework of the Ritz variational method. The metastable bound-excited 2pnf1,3Fe(4 ≤ n ≤ 7) and 2png1,3Go (5 ≤ n ≤ 8) states energies of heliumlike two-electron ions are reported along with the 2png1,3 Go (5 ≤ n ≤ 9) state energy eigenvalues of helium atom. Our upper-bound results for the 2pnf1,3Fe and 2png1,3Go states energies of Li+, Be2+, B3+ are the lowest values up to this date. The doubly excited nonautoionizing F and G states energy eigenvalues for heliumlike two-electron systems from C4+ through Mg10+ are reported for the first time in the literature.

Effect of nuclear motion on the critical nuclear charge for two-electron atoms

A variational method for calculating the critical nuclear charge ${Z}_{C}$ required for the binding of a nucleus to two electrons is reported. The method is very effective and performs well compared to the traditional variational principle for calculating energy. The critical nuclear charge, which corresponds to the minimum charge required for the atomic system to have at least one bound state, has been calculated for heliumlike systems with both infinite and finite nuclear masses. The value of ${Z}_{C}=0.911\phantom{\rule{0.16em}{0ex}}028\phantom{\rule{0.16em}{0ex}}2(3)$ is in very good agreement with recent values in the literature for two-electron atoms with an infinite nuclear mass. When nuclear motion is considered, the value for ${Z}_{C}$ varies from 0.911 030 3(2) for that with a nuclear mass of Ne (the largest heliogenic system considered) to $0.921\phantom{\rule{0.16em}{0ex}}802\phantom{\rule{0.16em}{0ex}}4(4)$ for a system with the nuclear mass of a positron. In all cases the energy varies smoothly as $Z\ensuremath{\rightarrow}0$. It is found that for the finite nuclear mass case, in agreement with previous work for the fixed nucleus mass system, the outer electron remains localized near the nucleus at $Z={Z}_{C}$. Additionally, the electron probability distribution is calculated to determine the behavior of the electrons at low $Z$.

Communication: practical and rigorous reduction of the many-electron quantum mechanical Coulomb problem to O(N(2/3)) storage.

It is tacitly accepted that, for practical basis sets consisting of N functions, solution of the two-electron Coulomb problem in quantum mechanics requires storage of O(N(4)) integrals in the small N limit. For localized functions, in the large N limit, or for planewaves, due to closure, the storage can be reduced to O(N(2)) integrals. Here, it is shown that the storage can be further reduced to O(N(2/3)) for separable basis functions. A practical algorithm, that uses standard one-dimensional Gaussian-quadrature sums, is demonstrated. The resulting algorithm allows for the simultaneous storage, or fast reconstruction, of any two-electron Coulomb integral required for a many-electron calculation on processors with limited memory and disk space. For example, for calculations involving a basis of 9171 planewaves, the memory required to effectively store all Coulomb integrals decreases from 2.8 Gbytes to less than 2.4 Mbytes.

One-electron reduced density matrices of strongly correlated harmonium atoms.

Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω(5/6) asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω(2/3) scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill's asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.

Line emission radiation during early-time interaction of an intense short laser pulse with an ultrathin planar aluminum target

The interaction of an intense short laser pulse with an ultrathin planar aluminum foil is investigated with a fully relativistic particle-in-cell model self-consistently coupled to an atomic dynamics model describing the non-local thermodynamic equilibrium level population dynamics and radiative behavior of a plasma evolving on a picosecond timescale. For typical experimental conditions, laser pulses with energy 1 J, intensity 1020 W cm−2, and duration 40 fs, a synthetic spectrum for the emission lines is generated as a function of time for lines emanating in the hydrogen- and helium-like ionization stages. It is found that Heα, Heβ, Lyα, and Lyβ lines have intensities above the Bremsstrahlung continuum and could serve as diagnostics for the evolving plasma condition.

Weak-field asymptotic theory of tunneling ionization: benchmark analytical results for two-electron atoms

The recently developed many-electron weak-field asymptotic theory of tunneling ionization of atoms and molecules in an external static electric field (Tolstikhin et al 2014, Phys. Rev. A 89, 013421) is extended to the first-order terms in the asymptotic expansion in field. To highlight the results, here we present a simple analytical formula giving the rate of tunneling ionization of two-electron atoms H− and He. Comparison with fully-correlated ab initio calculations available for these systems shows that the first-order theory works quantitatively in a wide range of fields up to the onset of over-the-barrier ionization and hence is expected to find numerous applications in strong-field physics.