Helium-like Research Articles

To the Theory of <i>Low-Dimensional</i> Hydrogen Molecules

Using analytical and numerical methods, the possibility of existence of the <i>elongated</i> and <i>flat</i> hydrogen molecules <i>H</i>₂ is first analyzed by analogy with the possibility of existence of <i>low-dimensional</i> single- and two-electron atoms previously proved theoretically (including us) and the impossibility of existence of the same multi-electron atom first pointed out in one of our previous works. In principle, conclusions of the present work can be verified experimentally, since <i>low-dimensional</i>, that is, <i>one</i>- and <i>two-dimensional</i> atoms were obtained experimentally long time ago. In our opinion, the material presented in the Appendix is of independent methodical interest because of its possible inclusion in traditional courses of quantum mechanics.

Probing new spin-independent interactions through precision spectroscopy in atoms with few electrons

The very high precision of current measurements and theory predictions of spectral lines in few-electron atoms allows to efficiently probe the existence of exotic forces between electrons, neutrons and protons. We investigate the sensitivity to new spin-independent interactions in transition frequencies (and their isotopic shifts) of hydrogen, helium and some helium-like ions. We find that present data probe new regions of the force-carrier couplings to electrons and neutrons around the MeV mass range. We also find that, below few keV, the sensitivity to the electron coupling in precision spectroscopy of helium and positronium is comparable to that of the anomalous magnetic moment of the electron. Finally, we interpret our results in the dark-photon model where a new gauge boson is kinetically mixed with the photon. There, we show that helium transitions, combined with the anomalous magnetic moment of the electron, provide the strongest indirect bound from laboratory experiments above 100keV.

On the Energy of a “Two-Dimensional” Two-Electron Atom

With the use of the known solution of the Schrodinger equation for an electron in the nucleus field in the polar coordinates, the energy of a “two-dimensional” two-electron atom in the ground state, as well as its single ionization energy, has been calculated both in perturbation theory and with an almost century-old method of variation of the parameter Z in a trial wavefunction of the ground state. Since such two-dimensional atoms, e.g., helium atoms, can in principle be implemented in experiments by “freezing” of one degree of freedom in the phase of Bose–Einstein condensate, the conclusions made in this work can be tested. Fundamental features of the calculation of the energy of “one-dimensional” two-electron atoms and the formation of their Bose–Einstein condensate have also been discussed. The results obtained in this work coincide in a number of particular cases with the results obtained in a previous work, where some results were absent.

Exact solution for the hydrogen atom confined by a dielectric continuum and the correct basis set to study many-electron atoms under similar confinements

The Schrödinger equation associated to the hydrogen atom confined by a dielectric continuum is solved exactly and suggests the appropriate basis set to be used when an atom is immersed in a dielectric continuum. Exact results show that this kind of confinement spread the electron density, which is confirmed through the Shannon entropy. The basis set suggested by the exact results is similar to Slater type orbitals and it was applied on two-electron atoms, where the H− ion ejects one electron for moderate confinements for distances much larger than those commonly used to generate cavities in solvent models.

Bremsstrahlung from few-electron ions

We have developed the new approach which can be used for accurate evaluations of the bremsstrahlung cross-sections in the case of few-electron atoms and ions. Our approach is based on the explicit formula for the electron density distribution in such systems. We derive the closed analytical formula for the matrix elements which are needed for highly accurate computations of atomic form-factors of two-electron atoms and ions. Multiple bremsstrahlung from few-electron ions is considered. We also discuss the energy loss due to bremsstrahlung in a plasma which contains multi-charged ions and free electrons. Bremsstrahlung from a high-temperature plasma is considered as well as its role in the high-temperature burn-up of deuterium plasma.

Spin dependent inelastic collisions between metastable state two-electron atoms and ground state alkali-atoms

Experimentally the spin dependence of inelastic collisions between ytterbium (Yb) in the metastable state and lithium (Li) in the ground state manifold is investigated at low magnetic fields. Using selective excitation all magnetic sublevels mJ of Yb() are accessed and four of the six lowest lying magnetic sublevels of are prepared by optical pumping. On the one hand, mJ-independence of collisions involving Li() atoms is found. A systematic mJ-dependence in collisions with Li() atoms, in particular suppressed losses for stretched collisional states, is observed on the other hand. Further, mJ-changing processes are found to be of minor relevance. The span of observed inelastic collision rates is between and , and a possible origin of the observed behavior is discussed.

State-dependent interactions in ultracold 174Yb probed by optical clock spectroscopy

We report on the measurement of the scattering properties of ultracold 174Yb bosons in a three-dimensional optical lattice. Site occupancy in an atomic Mott insulator is resolved with high-precision spectroscopy on an ultranarrow, metrological optical clock transition. Scattering lengths and loss rate coefficients for 174Yb atoms in different collisional channels involving the ground state 1S0 and the metastable 3P0 states are derived. These studies set important constraints for future experimental studies of two-electron atoms for quantum-technological applications.

Two Body IsoElectronium Model of the Heliumic Systems

In preceding works, one of us (R. M. Santilli) has shown that, according to quantum chemistry, identical electrons cannot create the strong bond occurring in molecular structures due to their strongly repulsive Coulomb interaction; has constructed hadronic chemistry as a non-unitary covering of quantum chemistry solely valid at mutual distances of 10-13cm; has introduced contact non-Hamiltonian interactions in the deep penetration of the wavepackets of valence electrons that overcomes said Coulomb repulsion, resulting in a strongly attractive bond of valence electron pairs in singlet called ’isoelectronium’ and shown that the new valence bond allows an exact and time invariant representation of the binding energy of the hydrogen and water molecules. By using these advances and our inference that (from the fact that an atomic lone pair of electrons form a coordinate covalent bond identified by G. N. Lewis) the lone pairs of electrons are indeed isoelectronium, in this paper we present, apparently for the first time, a new structure model of the Helium atom under the name of Iso-Helium, in which the two electrons of a given orbital are strongly coupled into the isoelectronium that provided a quantitative description of Pauli exclusion principle. In particular, as a result of the strongly bound state of Santilli isoelectronium, the iso-Helium reduces to be a two-body system, thus admitting exact analytic solution. The presented analytic solution is applicable to all Helium-like systems. Using it we have calculated effective charge on the nuclei of Helium-like systems that are in excellent agreement with the literature values.

Exploring Unorthodox Dimensions for Two-Electron Atoms.

Melding quantum and classical mechanics is an abiding quest of physical chemists who strive for heuristic insights and useful tools. We present a surprisingly simple and accurate treatment of ground-state two-electron atoms. It makes use of only the dimensional dependence of a hydrogen atom, together with the exactly known first-order perturbation value of the electron-electron interaction, both quintessentially quantum, and the D → ∞ limit, entirely classical. The result is an analytic formula for D-dimensional two-electron atoms with Z ≥ 2. For D = 3 helium, it gives accuracy better than 2 millihartrees, which is better than current density functional theory. A kindred explicit formula for correlation energy exploits interpolation between D → ∞ and D = 1 or 2; when added to the Hartree-Fock energy, it improves accuracy for D = 3 helium to better than 0.1 millihartrees.

Angle-resolved x-ray spectroscopic scheme to determine overlapping hyperfine splittings in highly charged heliumlike ions

An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For helium-like ions, in particular, we propose to measure either the angular distribution or polarization of the $1s2p~^{3}P_{1}, F \rightarrow 1s^{2}~^{1}S_{0}, F_{f}$ emission following the stimulated decay of the initial $1s2s~^{1}S_{0}, F_{i}$ level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depends on the (relative) \textit{splitting} of the partially overlapping hyperfine $1s2p~^{3}P_{1}, F$ resonances and may thus help resolve their hyperfine structure. The proposed scheme is feasible with present-day photon detectors and allows a measurement of the hyperfine splitting of helium-like ions with a relative accuracy of about $10^{-4}$.

Accessing the hyperfine splitting in highly charged helium-like ions via angle-resolved x-ray spectroscopic analysis

SynopsisA new scheme is presented for determining the hyperfine splitting of highly charged ions via angle-resolved spectroscopic analysis. In particular, we propose two measurements on the angular distribution and linear polarization of the emission line 1s2p 3P1, F = I − 1, I, I + 1 → 1s2 1S0, Ff = I of He-like isotopic ions, following the stimulated decay of the 1s2s 1S0, Fi = I level. We find that the angular and polarization behavior of the emitted photons strongly depends on the splitting of the overlapping hyperfine 1s2p 3P1, F resonances, which could be a promising “signature” for the hyperfine splitting determination.

Link between generalized nonidempotency and complexity measures.

The nonidempotency measure of Löwdin is found to be proportional to the disequilibrium. It is shown that there exists a simple relationship between the LMC (López-Ruiz-Mancini-Calbet) and the generalized statistical complexities and the generalized nonidempotency measure of Löwdin. Results are illustrated for an exactly solvable two-electron model atom.

Kinetic energy partition method applied to ground state helium-like atoms

We have used the recently developed kinetic energy partition (KEP) method to solve the quantum eigenvalue problems for helium-like atoms and obtain precise ground state energies and wave-functions. The key to treating properly the electron-electron (repulsive) Coulomb potential energies for the KEP method to be applied is to introduce a "negative mass" term into the partitioned kinetic energy. A Hartree-like product wave-function from the subsystem wave-functions is used to form the initial trial function, and the variational search for the optimized adiabatic parameters leads to a precise ground state energy. This new approach sheds new light on the all-important problem of solving many-electron Schrödinger equations and hopefully opens a new way to predictive quantum chemistry. The results presented here give very promising evidence that an effective one-electron model can be used to represent a many-electron system, in the spirit of density functional theory.

Two-electron atom with a screened interaction

We present analytical solutions to a quantum-mechanical three-body problem in three dimensions, which describes a helium-like two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced by harmonic potentials. The electron-electron interaction potential is taken to be both screened (decaying faster than the inverse of the interparticle separation) and regularized (in the limit of zero separation). We reveal the exactly solvable few-electron ground state, which explicitly includes electron correlation, for certain values of the harmonic containment.

Potential energy surfaces in atomic structure: The role of Coulomb correlation in the ground state of helium

For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a conditional amplitude, which depends functionally on the interelectronic distance $r_{12}$ and parametrically on $r_1$ and $r_2$. Applying the variational principle, we derive pseudoeigenvalue equations for these two amplitudes, which cast the internal Schr\"odinger equation in a form akin to the Born-Oppenheimer separation of nuclear and electronic degrees of freedom in molecules. The marginal equation involves an effective radial Hamiltonian, which contains a nonadiabatic potential energy surface that takes into account all interparticle correlations in an averaged way, and whose unique eigenvalue is the internal energy. At each point $(r_1,r_2)$, such surface is, in turn, the unique eigenvalue in the conditional equation. Employing the ground state of He as prototype, we show that the nonadiabatic potential energy surface affords a molecularlike interpretation of the structure of the atom, and aids in the analysis of energetic and spatial aspects of the Coulomb correlation, in particular correlation-induced symmetry breaking and quantum phase transition.

Formation of Slow Electron Pairs in an External Coulomb Field

The wave equation for two electrons in an external Coulomb field (helium-like atoms) has been shown to be a problem in a three-dimensional half-space. The wave-equation becomes quasi-separable in inertial coordinates. This allows to work out the electron motion in the frame of principal inertia axes. We find that non-adiabatic coupling terms constitute a fictitious force and lead to a deformation of the static potential surface. Incoming and outgoing modes of electron pairs are studied in detail, and applied to the threshold ionization of hydrogen-like atoms by electrons. Our analysis confirms the classical work by Wannier. However, we go beyond Wannier and present bending and stretch vibrations of electron pairs. The bending vibration has no influence onto the total ionization cross-section. The pair formation below threshold destroys the existence of high double Rydberg resonances. Finally, we describe the propagation of an electron pair through a linear chain of Rydberg atoms.

Ionization-Excitation of helium-like ions by high-energy electrons

The differential and total cross sections are calculated for the ionization of helium-like ions that is accompanied by the excitation of residual ions to ns states owing to an electron impact. Nonrelativistic perturbation theory in electron–electron interaction with Coulomb functions used for a zero-order approximation underlies these calculations. The expressions obtained in this way have a universal character. They are applicable at moderate values of the target charge number Z and high energies of incident electrons. A comparison with total cross sections calculated for the helium atom within various theoretical approaches is performed.

First-order correction terms in the weak-field asymptotic theory of tunneling ionization in many-electron systems

The many-electron weak-field asymptotic theory of tunneling ionization including the first-order correction terms in the asymptotic expansion of the ionization rate in field strength was highlighted in our recent fast track communication (Trinh et al 2015 J. Phys. B: At. Mol. Opt. Phys. 48 061003) by demonstrating its performance for two-electron atoms. Here we present a thorough derivation of the first-order terms omitted in the previous publication and provide additional numerical illustrations of the theory.

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.

Two-electron atoms under spatially compressed Debye plasma

Rayleigh–Ritz variational method has been employed to estimate precise energy-eigenvalues of spherically compressed two-electron atoms (Z=1−10) embedded in Debye plasma with a view to modelling atom under dense plasma environment. The trial wave function is expanded in terms of explicitly correlated Hylleraas-type basis set satisfying Dirichlet's boundary condition. The combined effect of decrease in the size of spatial confinement domain and increase in Debye screening parameter pushes the system towards gradual destabilization and subsequent ionization or complete fragmentation of the system. Present results are in reasonable agreement with other results existing in literature. Within finite domain, the thermodynamic pressure experienced by the ions due to the plasma electrons is also estimated.