Ground State Of Ion Research Articles

Influence of driving-laser wavelength on emission of high-order harmonic wave generated by atoms irradiated by ultrashort laser pulse

With the numerical solution of the time-dependent Schrodinger equation, we theoretically investigate the high-order harmonic emissions generated by the atoms irradiated by the ultrashort lasers with different wavelengths but the same pondermotive energy. As the driving-laser wavelength increases, the intensity of the high-harmonic emission decreases. Comparing with the harmonic spectra of atoms driven by a 1000-nm-wavelength laser pulse, a new peak structure appears in the spectra of atoms driven by a 5000-nm-wavelength laser wavelength. It is shown by the time-frequency analysis of the harmonic emission, the time-dependent evolution of the electron density, and the time-dependent population analysis of the eigenstate, that the physical mechanism behind the new peak appearing in the harmonic spectra is the interference between the harmonic emission generated by the electrons ionized out of the excited atoms returning to the parent ions and the harmonic emissions resulting from the ground state ionization.

Theoretical Research on Ground State of 3d Transition Metal Ions in Inorganic Compounds and Their Charge Transition Tendencies

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Расчеты релятивистских, корреляционных, ядерных и квантово-электродинамических поправок к энергиям и потенциалам ионизации основного состояния литиеподобных ионов

This paper presents all the leading contributions to the relativistic total energies and ionization potentials of the ground state of lithium-like ions with a nuclear charge in the range Z = 3 − 20. Correlation, relativistic and quantum-electrodynamics corrections as well as contributions due to the finite size of the nucleus (field shift) and finite mass of the nucleus (recoil effect) are evaluated. Relativistic calculations are performed by means of the configuration-interaction method in the basis of the Dirac-Fock-Sturm orbitals using the Dirac-Coulomb-Breit Hamiltonian.

Reaction chain used to describe the process and mechanism of helium breakdown under high pressure

In this study, we establish a two-dimensional axisymmetric fluid model and verify its efficacy via experiments. We analyze the reaction rates to introduce a concept that we have termed “reaction chain” to describe the process and mechanism of helium discharge at high pressure. We observe that the entire process of discharge can be perfectly described by the reaction chains, which indicates that the breakdown process of helium involves a series of chain reactions, just like the nuclear fission. The results revealed that ground-state ionization reaction predominates the early discharge stage, whereas with the quick accumulation of He2*, penning ionization reaction will eventually play a dominant role. Our study confirms that metastable atoms play an important role in helium discharge. We demonstrated that He* is converted into He2* as an intermediate and that the number density of He2* eventually influences the breakdown of helium.

On the Feasibility of Rovibrational Laser Cooling of Radioactive RaF+ and RaH+ Cations

Polar radioactive molecules have been suggested to be exceptionally sensitive systems in the search for signatures of symmetry-violating effects in their structure. Radium monofluoride (RaF) possesses an especially attractive electronic structure for such searches, as the diagonality of its Franck-Condon matrix enables the implementation of direct laser cooling for precision experiments. To maximize the sensitivity of experiments with short-lived RaF isotopologues, the molecular beam needs to be cooled to the rovibrational ground state. Due to the high kinetic energies and internal temperature of extracted beams at radioactive ion beam (RIB) facilities, in-flight rovibrational cooling would be restricted by a limited interaction timescale. Instead, cooling techniques implemented on ions trapped within a radiofrequency quadrupole cooler-buncher can be highly efficient due to the much longer interaction times (up to seconds). In this work, the feasibility of rovibrationally cooling trapped RaF+ and RaH+ cations with repeated laser excitation is investigated. Due to the highly diagonal nature between the ionic ground state and states in the neutral system, any reduction of the internal temperature of the molecular ions would largely persist through charge-exchange without requiring the use of cryogenic buffer gas cooling. Quasirelativistic X2C and scalar-relativistic ECP calculations were performed to calculate the transition energies to excited electronic states and to study the nature of chemical bonding for both RaF+ and RaH+. The results indicate that optical manipulation of the rovibrational distribution of trapped RaF+ and RaH+ is unfeasible due to the high electronic transition energies, which lie beyond the capabilities of modern laser technology. However, more detailed calculations of the structure of RaH+ might reveal possible laser-cooling pathways.

Relativistic and QED corrections for the ground state lithiumlike ionization energies

The ground state ionization energies of Z ⩽ 10 lithiumlike ions are calculated using fully correlated Gaussian wavefunctions. Leading-order relativistic corrections are evaluated, while QED corrections are established with small uncertainties by directly calculating the Araki–Sucher energy and expanding the three-electron Bethe logarithm in 1/Z. The non-relativistic α6 level shifts have also been calculated, and we have used these energies to recommend ionization energies, which include estimates of the influence of the relativistic portion of the α6 energy. The results emphasize the importance of the direct computation of the complete α6 correction, but also the need for new, higher accuracy experimental ionization limits.

Generation of quantum vortices in photodetachment: The role of the ground-state wave function

Formation of quantum vortices in laser-induced photodetachment from negative ions is analyzed. The driving laser field consists of a single ultrashort pulse of circular polarization and the unperturbed ground-state wave function of the anion is found in either the $s$ or $p$ state. In particular, numerical illustrations for the photodetachment from ${\mathrm{H}}^{\ensuremath{-}},$ ${\mathrm{O}}^{\ensuremath{-}},$ ${\mathrm{K}}^{\ensuremath{-}},$ and a model ${\mathrm{A}}^{\ensuremath{-}}$ anion are presented. Special attention is paid to the symmetry of the ground-state wave function and ionization potential over the final vortex pattern. It is shown that the two-dimensional spectra of photoelectrons in momentum space comprise three well-defined regions: The low-energy (central) region, multiphotonlike zone, and supercontinuum. While the supercontinuum does not contribute to vorticity and the multiphoton zone depends only on the laser field characteristics, vortices in the low-energy region strongly depend on the bound-state wave function and its ionization potential.

Negative ion of hydrogen in dense semi-classical plasmas: Stability and zero-energy resonances

The effects of dense semi-classical plasma (DSCP) on the ground state of the negative ion of hydrogen (H−) and on the dynamics of electron–hydrogen scattering have been investigated. DSCP is described by an effective potential which takes care of the collective effects of the plasma at large distances as well as the quantum mechanical effects of diffraction at small distances. An elaborative wave function is employed in the Rayleigh–Ritz variational method to compute the ground state energy of H− for various values of the plasma parameters. In particular, critical values of the plasma parameters are calculated accurately to make a detailed study on the stability of the ion embedded in DSCP. Furthermore, parameters related to the ground state of H− and H are used in the effective range theory to study the effects of DSCP on the dynamics of low-energy e − H(1s) scattering. Special emphasis is given to investigate the phenomenon of zero-energy resonances by computing the singlet scattering length near the critical values of the plasma parameters.

Radiative and photon-exchange corrections to new-physics contributions to energy levels in few-electron ions

The influence of hypothetical new interactions beyond the Standard Model on atomic spectra has attracted recent interest. In the present work, interelectronic photon-exchange corrections and radiative quantum electrodynamic corrections to the hypothetical contribution to the energy levels of few-electron ions from a new interaction are calculated. The $1s$, $2s$ and $2p_{1/2}$ ground states of H-like, Li-like and B-like ions are considered, as motivated by proposals to use isotope shift spectroscopy of few-electron ions in order to set stringent constraints on hypothetical new interactions. It is shown that, for light Li-like and B-like ions, photon-exchange corrections are comparable to or even larger, by up to several orders of magnitude, than the leading one-electron contribution from the new interaction, when the latter is mediated by heavy bosons.

Quantum Dissipative Dynamics (QDD): A real-time real-space approach to far-off-equilibrium dynamics in finite electron systems

In this paper, we present “QDD” (Quantum Dissipative Dynamics), a code package for simulating the dynamics of electrons and ions in finite electron systems (atoms, molecules, clusters) under the influence of external electromagnetic fields. Electron emission is properly accounted for. The novel feature of the present code is that it also covers the description of dissipative dynamics induced by dynamical correlations generated by electron-electron collisions.The paper reviews the underlying theoretical as well as numerical methods and demonstrates the code's capabilities on a selection of typical examples. Program summaryProgram Title: QDDCPC Library link to program files:https://doi.org/10.17632/jpwzm9knmb.1Licensing provisions: GPLv3Programming language: Fortran 90 (with Fortran 2008 standard)Supplementary material: User Manual, input and output filesNature of problem: The QDD code serves to simulate the dynamics of finite electron systems (atoms, molecules, clusters) excited by strong electromagnetic fields as delivered by lasers or highly charged ions. Basis of the description is Time-Dependent Density Functional Theory (TDDFT) at the level of the Time-Dependent Local-Density Approximation (TDLDA) augmented by an approximate Self-Interaction Correction (SIC), the latter being crucial for proper description of electron emission. The novel feature of the present code is that it allows one to track the dissipative dynamics induced by dynamical correlations from the earliest times of excitation on. This is done here at a fully quantum mechanical level within the Relaxation-Time Approximation (RTA). Electron dynamics is also coupled to ionic motion treated by classical molecular dynamics.Solution method: The numerical representation uses a 3D coordinate-space grid for electronic wave functions and fields. The kinetic energy operator is evaluated in momentum space connected by a Fast Fourier Transform (FFT). Standard schemes for electronic ground state, ionic ground state, and propagation of TDLDA in real time as well as ionic dynamics are used. Electron emission is enabled by absorbing boundary conditions using a mask function near the boundaries. The time evolution of dissipation (by RTA) is evaluated in a large space of occupied and unoccupied single-electron states.Additional comments including restrictions and unusual features: Only the actual computing hardware (RAM, number of nodes on board) limits the system size which can be treated. The code package allows sequential and parallel (OpenMP) computation. The simulation can be continued from a previously saved dynamical configuration.

Long-range additive and nonadditive potentials in a hybrid system: Ground-state atom, excited-state atom, and ion

We report a theoretical study on the long-range additive and nonadditive potentials for a three-body hybrid atom-atom-ion system composed of one ground $S$ state Li atom, one excited $P$ state Li atom and one ground $S$ state Li$^+$ ion, Li($2\,^{2}S$)-Li($2\,^{2}P$)-Li$^+(1\,^{1}S$). The interaction coefficients are evaluated with highly accurate wave functions calculated variationally in Hylleraas coordinates. For this hybrid system the three-body nonadditive collective interactions (appearing in second-order) induced by the energy degeneracy and enhanced by the induction effect of the Li$^+$ ion through the internal electric field can be strong and even stronger than the two-body additive interactions at the same order. We find that for particular geometries the two-body additive interactions of the system sum to zero leaving only three-body nonadditive collective interactions making the present system potentially a platform to explore quantum three-body collective effects. We also extract first-principles leading coefficients of the long-range electrostatic, induction, and dispersion energies of Li$^+_2$ electronic states correlating to Li($2\,^{2}P$)-Li$^+(1\,^{1}S$), which until now were not available in the literature. The results should be especially valuable for the exploration of schemes to create trimers with ultracold atoms and ions in optical lattices.

Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method

This study aims to use hydrogenic orbitals within an analytic and numeric parameter-free truncated-matrix method to solve the projected Schrödinger equation of some Helium-like ions (3 ≤ Z ≤ 10). We also derived a new analytical expression of the ion ground state energies, which was simple and accurate and improved the accuracy of the analytic calculation, numerically using Mathematica. The standard matrix method was applied, where the wave function of the ions was expanded in a finite number of eigenvectors comprising hydrogenic orbitals. The Hamiltonian of the systems was calculated using the wave function and diagonalized to obtain their ground state energies. The results showed that a simple analytic expression of the ground state energies of He-like ions was successfully derived. Although the analytic expression was derived without involving any variational parameter, it was reasonably accurate with a 0.12% error for Ne8+ ion. From this method, the accuracy of the analytic energies was also numerically improved to 0.10% error for Ne8+ ion. The results clearly showed that the energies obtained using this method were more accurate than the hydrogenic perturbation theory and the uncertainty principle-variational approach. In addition, for Z > 4, our results were more accurate than those from the geometrical model.

Saturation Mechanisms in Common LED Phosphors.

Commercial lighting for ambient and display applications is mostly based on blue light-emitting diodes (LEDs) combined with phosphor materials that convert some of the blue light into green, yellow, orange, and red. Not many phosphor materials can offer stable output under high incident light intensities for thousands of operating hours. Even the most promising LED phosphors saturate in high-power applications, that is, they show decreased light output. The saturation behavior is often poorly understood. Here, we review three popular commercial LED phosphor materials, Y3Al5O12 doped with Ce3+, CaAlSiN3 doped with Eu2+, and K2SiF6 doped with Mn4+, and unravel their saturation mechanisms. Experiments with square-wave-modulated laser excitation reveal the dynamics of absorption and decay of the luminescent centers. By modeling these dynamics and linking them to the saturation of the phosphor output intensity, we distinguish saturation by ground-state depletion, thermal quenching, and ionization of the centers. We discuss the implications of each of these processes for LED applications. Understanding the saturation mechanisms of popular LED phosphors could lead to strategies to improve their performance and efficiency or guide the development of new materials.

Chaotic evolution of the energy of the electron orbital and the hopping integral in diatomic molecule cations subjected to harmonic excitation

We analysed the dynamics of the positively charged ions of diatomic molecules (X2+ and XY+), in which the bond is realized by the single electron. We assumed that the atomic cores separated by the distance R were subjected to the external excitation of the harmonic type with the amplitude A and frequency Ω. We found the ground states of ions using the variational approach within the formalism of second quantization (the Wannier function was reproduced by means of Gaussian orbitals). It occurred that, on the account of the highly non-linear dependence of the total energy on R, the chaotic dynamics of cores induced the chaotic evolution of the electronic Hamiltonian parameters (i.e. the energy of the electron orbital ε and the hopping integral t). Changes in cation masses or in the charge arrangement does not affect qualitatively the values of Lyapunov exponents in the A-Ω parameter space.

Radially localized electron heating in helicon plasmas by X-wave microwave injection

Here, we report on modifications to the electron energy distribution function during X-mode microwave injection in argon and helium helicon plasmas. No electron heating is observed in argon helicon plasmas. Significant electron heating, ΔTe∼1 eV, is observed in helium plasmas. The heating is spatially localized to the upper hybrid resonance layer. Previously absent helium ion emission lines, from states over 50 eV above the helium ion ground state, are observed with the injection of X-mode microwaves.

Investigation of the complex vibronic structure in the first excited and ionic ground states of 3-chloropyridine by means of REMPI and MATI spectroscopy and Franck-Condon analysis.

3-Chloropyridine (3-CP) has been investigated by means of resonance-enhanced multi-photon ionization (REMPI) and mass-analyzed threshold ionization (MATI) spectroscopy to elucidate the effect of m-chlorine substitution on the vibronic structure of the first electronically excited and ionic ground states. The S1 excitation energy has been determined to be 34 840 ± 2 cm-1 (4.3196 ± 0.0002 eV) with a difference of less than 0.2 cm-1 between both isotopomers, which is the first reported value for this transition in the gas phase so far. The S1 state has been assigned to the 1π* ← n transition. It is subject to strong vibronic coupling via ν16b to one or both of the lowest 1ππ* states. In addition, strong coupling via at least one more non-totally symmetric vibration is very likely to exist but the vibration could not be identified yet. Overall, the coupling results in a minimum S1 structure with C1 symmetry. The adiabatic ionization energy of the nN-LP orbital (14a') has been determined to be 75 879 ± 6 cm-1 (9.4078 ± 0.0007 eV) with a difference of less than 2 cm-1 between the two isotopomers, which is the first value reported for this state so far. The ionic ground state exhibits a distinct vibronic coupling via ν16a and ν10a to either the D1 state (4a'') and/or D2 state (3a''), which results in a twisted D0 geometry with C1 symmetry. As a consequence of the warped geometry in both S1 and D0 states, very complicated MATI spectra were obtained when exciting S1 states at higher wavenumbers.

Numerical solution of mathematical physics problems by the collocation method

A modified collocation method for the numerical solving boundary value problems of mathematical physics is proposed. The irregular arrangement of collocation nodes in the problem solving domain can sharply increase the accuracy of the numerical solution by improving the quality of the linear algebraic equations system, to which the solved boundary value problem leads. Various basis functions systems are considered. The proposed method allows one to obtain an approximate solution of boundary value problems for a wide range of linear and nonlinear elliptic, parabolic and wave equations in an analytical form. This numerical method makes it possible to significantly expand the application field of traditional numerical methods when solving applied problems for modelling fields of various physical natures, described by linear and nonlinear equations of mathematical physics. The developed method is used to solve a quantum-mechanical problem for a hydrogen molecule ion. The results obtained in this work show the high potentialities of the complete collocation method, which are based on the universality of the method and high accuracy of numerical solutions. The energy of the ion ground state calculated with the minimum number of collocation nodes differs from the experimentally obtained value by 13%.

Lanthanide-doped metal-organic frameworks with multicolor mechanoluminescence

Metal-organic frameworks (MOFs) and mechanoluminescent (ML) materials have been considered as two types of promising materials that have their own application fields. It would be amazing to endow one material with the advantages of ML and MOFs, thus broadening their applications. However, there are quite few investigations on this topic, and the ML mechanism in ML-MOFs remains unclear. In this study, we proposed a strategy for developing ML-MOFs by doping lanthanide ions into the non-centrosymmetric SBD ([Sr(μ-BDC)(DMF)]∞) MOF, and successfully synthesized a series of lanthanide-doped MOFs Ln-SBD (Ln = Tb, Dy, Sm, Eu) and Tb1−xEux-SBD (x = 0.2, 0.4, 0.6, 0.8) with multicolor ML. The lanthanide ions were uniformly distributed in the matrix of the SBD-MOF, and occupied the Sr site. The MLMOFs exhibited intense multicolor ML emissions varying from green to yellow to red by changing the co-doping ratios and species of lanthanide ions. The similar ML and photoluminescence (PL) spectra indicated that the ML emission was assigned to the radiative transition from the excited states to the ground states of lanthanide ions. The radiative transition was induced by the electron bombardment process that originated from the piezoelectric effect of the non-centrosymmetric SBD host. In addition, a pioneering temperature sensing research based on ML was carried out, which is promising for realizing dual-functional detection of stress and temperature without excitation light sources. This study gives a unique insight for developing more versatile and interesting smart materials by combining the versatility of MOF with the ML emission, imparting additional values to both MOF and ML materials. Moreover, this study provides a general rule for selecting MOFs with an acentric structure as the host for ML materials.

Critical Theory of Non-Fermi Liquid Fixed Point in Multipolar Kondo Problem

When the ground state of a localized ion is a non-Kramers doublet, such localized ions may carry multipolar moments. For example, Pr$^{3+}$ ions in a cubic environment would possess quadrupolar and octupolar, but no magnetic dipole, moments. When such multipolar moments are placed in a metallic host, unusual interactions between these local moments and conduction electrons arise, in contrast to the familiar magnetic dipole interactions in the classic Kondo problem. In this work, we consider the interaction between a single quadrupolar-octupolar local moment and conduction electrons with $p$-orbital symmetry as a concrete model for the multipolar Kondo problem. We show that this model can be written most naturally in the spin-orbital entangled basis of conduction electrons. Using this basis, the perturbative renormalization group (RG) fixed points are readily identified. There are two kinds of fixed points, one for the two-channel Kondo and the other for a novel fixed point. We investigate the nature of the novel fixed point non-perturbatively using non-abelian bosonization, current algebra and conformal field theory approaches. It is shown that the novel fixed point leads to a, previously unidentified, non-Fermi liquid state with entangled spin and orbital degrees of freedom, which shows resistivity $\rho \sim T^{\Delta}$ and diverging specific heat coefficient $C/T \sim T^{-1 + 2\Delta}$ with $\Delta=1/5$. Our results open up the possibility of myriads of non-Fermi liquid states, depending on the choices of multipolar moments and conduction electron orbitals, which would be relevant for many rare-earth metallic systems.

Self-energy screening effects in the g factor of Li-like ions

We report an investigation of the self-energy screening effects for the $g$ factor of the ground state of Li-like ions. The leading screening contribution of the relative order $1/Z$ is calculated to all orders in the binding nuclear strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). We also extend the known results for the $Z\alpha$ expansion of the QED screening correction by deriving the leading logarithmic contribution of order $\alpha^5\ln\alpha$ and obtaining approximate results for the $\alpha^5$ and $\alpha^6$ contributions. The comparison of the two approaches yields a stringent check of consistency of the two calculations and allows us to obtain improved estimations of the higher-order screening effects.