Ground State Of Helium Atom Research Articles

Rubidium D1 and D2 atomic lines’ pressure broadened by ground-state helium atoms

Full quantum calculations are performed to determine the spectral broadening of the rubidium D1 and D2 lines induced by collisions with helium perturbers. The potential curves of the low-lying RbHe molecular states, as well as the corresponding transition dipole moments, are generated theoretically with ab initio methods based on SA-CASSCF-MRCI calculations, including the spin–orbit effects. The absorption and emission coefficients at wavelengths lying between 650 and and temperatures ranging from 100 to 3000 K are determined. The absorption profile reveals it is dominated by the free–free transitions, whereas the emission spectral shape arises from the free–free and bound–free transitions. The resulting red- and blue-wing profiles are compared with previous experimental and theoretical works.

Solvation of Intrinsic Positive Charge in Superfluid Helium

On the basis of electronic structure calculations, the structure of intrinsic positive charge solvated in superfluid helium is identified as triatomic He3(+) ion, which is bound to the surrounding ground state helium atoms through the charge–charge induced dipole interaction in a pairwise additive manner. Bosonic density functional theory calculations show that this ion forms the well-known Atkins’ snowball solvation structure where the first rigid helium shell is effectively disconnected from the rest of the liquid. Evaluation of the total energy vs helium droplet size N shows distinct regions related to the completion of solvent shells near N = 16 and N = 47. These regions can be assigned to magic numbers observed in positively charged helium droplets appearing at N = 15 and in the range between 20 and 50 helium atoms. The calculated added mass for the positive ion in bulk superfluid helium (18 mHe) is much smaller than the previous experiments suggest (30–40 mHe), indicating that there may be yet some unidentified additional factor contributing to the measured effective mass. Both previous experiments and the present calculations agree on the effective mass of the negative charge (240–250 mHe). The main difference between the solvated negative and positive charges in liquid helium is that the latter forms a chemically bound triatomic molecule surrounded by highly inhomogeneous liquid structure whereas the former remains as a separated charge with a smoothly varying liquid density around it.

Atmospheric helium capillary dielectric barrier discharge for soft ionization: broadening of spectral lines, gas temperature and electron number density

The capillary helium dielectric barrier discharge (DBD) operating at atmospheric pressure was investigated by means of optical emission spectroscopy with the aim to determine the dominant broadening mechanism of the helium spectral lines, gas temperature and electron number density. The dependence of emission profiles of helium 388 nm, 501 nm, 587 nm, 667 nm, 706 nm and 728 nm lines on discharge voltage, helium pressure and position along the DBD capillary was investigated. Also, the pressure and voltage dependence of the profiles of hydrogen H-alpha and H-beta lines was examined. The Lorentzian widths of the normalized helium line profiles were found to be constant with respect to the applied voltage and the position along the capillary. The dominant broadening mechanism for all investigated lines was identified to be due to collisions with ground-state helium atoms, with the Stark broadening being negligible. It was determined that the temperature of the gas was constant along the capillary and independent of the voltage applied on the DBD electrodes and that its value coincided with the room temperature. The measurements of the dependence of the Lorentzian width of hydrogen H-alpha and H-beta lines on helium pressure, combined with gas temperature determined in the experiment, yielded the following values for the broadening parameters due to broadening by neutral helium: γνHe(Hα) = 1.56 × 10−9 cm3 s−1 and γνHe(Hβ) = 3.16 × 10−9 cm3 s−1. From the analysis of the measured H-alpha and H-beta line profiles the upper limit of the electron number density in the investigated plasma was obtained as ne ≤ 1.4× 1012 cm−3.

Double-differential cross sections for single ionization of helium by bare ion impact

Double-differential cross sections (DDCS) for single ionization of helium by impact of proton and highly charged carbon ion have been calculated in the framework of four-body formalism using the three-Coulomb wave model (3C-4B) and first Born approximation (FBA-4B), respectively. The correlated motion of the particles interacting through long-range Coulomb potential is properly taken into account in the final state. In this paper, the energy and angular distributions of DDCS of low- and high-energy electron emission for ground-state helium atoms have been investigated. The ejected electrons are affected by the two-center field of the target and the projectile ion. The two-center effects are confined to comparison with other theoretical results. The results obtained, both from the 3C-4B and FBA-4B models, are compared with other theoretical and experimental findings. The present results are found to reproduce the peak structure of the experimental observations. Large discrepancy occurs between the present two theories at forward and backward angles except about the emission angle 90°. The present computed results obtained by the 3C-4B model are in good agreement with the available experimental findings.

Description of electronic excited states using electron correlation operator

The electron correlation energy in a chemical system is defined as a difference between the energy of an exact energy for a given Hamiltonian, and a mean-field, or single determinant, approximation to it. A promising way to model electron correlation is through the expectation value of a linear two-electron operator for the Kohn-Sham single determinant wavefunction. For practical reasons, it is desirable for such an operator to be universal, i.e., independent of the positions and types of nuclei in a molecule. The correlation operator models the effect of electron correlation on the interaction energy in a electron pair. We choose an operator expanded in a small number of Gaussians as a model for electron correlation, and test it by computing atomic and molecular adiabatic excited states. The computations are performed within the Δ Self-Consistent Field (ΔSCF) formalism, and are compared to the time-dependent density functional theory model with popular density functionals. The simplest form of the correlation operator contains only one parameter derived from the helium atom ground state correlation energy. The correlation operator approach significantly outperforms other methods in computation of atomic excitation energies. The accuracy of molecular excitation energies computed with the correlation operator is limited by the shortcomings of the ΔSCF methodology in describing excited states.

Ejection of Quasi-Free-Electron Pairs from the Helium-Atom Ground State by Single-Photon Absorption

We investigate the single-photon double ionization of helium at photon energies of 440 and 800eV. We observe doubly charged ions with close to zero momentum corresponding to electrons emitted back to back with equal energy. These slow ions are the unique fingerprint of an elusive quasifree photon double ionization mechanism predicted by Amusia etal. nearly four decades ago [J. Phys. B 8, 1248 (1975)]. It results from the nondipole part of the electromagnetic interaction. Our experimental data are supported by calculations performed using the convergent close-coupling and time-dependent close-coupling methods.

Comparison and union of the Temple and Bazley lower bounds

The Lehmann-Maehly approach and Bazley’s method of special choice are matrix eigenvalue problems that allow the calculation of lower bounds to energies of atomic and molecular systems. We introduce a common derivation of their scalar versions using the overlap of a trial function with the unknown ground-state wave function. In the scalar setting, the Lehmann-Maehly approach reduces to the Temple formula. The common derivation allows us to easily unite and improve both methods in several stages within this restricted application. Finally we offer a different union that allows generalization to arbitrary dimension matrix methods. Calculations on the helium atom ground state illustrate the improvements and mergers.

Near-threshold photoelectron angular distributions from two-photon resonant photoionization of He

Two-photon resonant photoionization of helium is investigated both experimentally and theoretically. Ground state helium atoms are excited to the 1s4p, 1s5p and 1s6p 1P states by synchrotron radiation and ionized by a synchronized infrared pulsed picosecond laser. The photoelectron angular distributions of the emitted electrons are measured using a velocity map imaging (VMI) spectrometer. The measured asymmetry parameters of the angular distribution allow the phase differences and the ratios of the dipole matrix elements of the 1sϵs and 1sϵd channels to be determined. The experimental results agree with the calculated values obtained in a configuration–interaction calculation with a Coulomb–Sturmian basis set. The effects of the radiative decay of the intermediate state and the static electric field of the VMI spectrometer on the measurements are discussed.

Computing many-body wave functions with guaranteed precision: The first-order Møller-Plesset wave function for the ground state of helium atom

We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order Møller-Plesset wave function of a helium atom. The computed second-order Møller-Plesset energy is precise to ~2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.

A Paramagnetic Bonding Mechanism for Diatomics in Strong Magnetic Fields

Elementary chemistry distinguishes two kinds of strong bonds between atoms in molecules: the covalent bond, where bonding arises from valence electron pairs shared between neighboring atoms, and the ionic bond, where transfer of electrons from one atom to another leads to Coulombic attraction between the resulting ions. We present a third, distinct bonding mechanism: perpendicular paramagnetic bonding, generated by the stabilization of antibonding orbitals in their perpendicular orientation relative to an external magnetic field. In strong fields such as those present in the atmospheres of white dwarfs (on the order of 10(5) teslas) and other stellar objects, our calculations suggest that this mechanism underlies the strong bonding of H(2) in the (3)Σ(u)(+)(1σ(g)1σ(u)*) triplet state and of He(2) in the (1)Σ(g)(+)(1σ(g)(2)1σ(u)(*2)) singlet state, as well as their preferred perpendicular orientation in the external field.

Potential energy of the K**-He quasimolecule

The potential curves of the nl(2Λ) electronically excited states of the K**-He quasimolecule (n, l, and Λ are the principal quantum number, angular momentum, and its projection on the molecular axis) are calculated. To describe the interaction of the weakly bound electron with the singly charged potassium ion and the ground-state helium atom (with taking into account their long-range electrostatic interactions), the formalism of two-center scattering theory and the finite-range pseudopotential method are used. A comparison with the results of calculations performed by the MRD CI method is carried out. The findings showed that, for small principal quantum numbers n, these methods complement each other, because the first is more reliable for large interatomic distances, R ≥ n, whereas second for small, R < n. The characteristic features of the behavior of the potential curves of the K**-He quasimolecule at large n and l are discussed.

Coulomb–Born distorted wave approximation applied to the proton–helium single-electron capture process

The single-electron capture process in the collision of fast protons with ground-state helium atoms is studied assuming an independent-particle model. The three-body first-order Coulomb–Born distorted wave formalism, including nuclear–electronic and internuclear interactions, with correct boundary conditions is applied to the considered rearrangement process. A single-zeta Roothaan–Hartree–Fock wave function describing helium in its ground state is used to carry out the calculations. Differential and integrated cross sections are calculated for a range of the incident energy for which the present formalism is valid. The comparison of the obtained results with the corresponding experimental measurements and other three- and four-body theoretical calculations shows reasonable agreement.

Hyperfine structure of the ground state muonic 3He atom

On the basis of the perturbation theory in the fine structure constant α and the ratio of the electron to muon masses we calculate one-loop vacuum polarisation and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of the muonic helium atom (µ e 3 2He). We obtain total results for the ground state hyperfine splitting Δ ν hfs = 4166.648 MHz which improves the previous calculation of Lakdawala and Mohr due to new corrections of orders α 5 and α 6. The remaining differences between our theoretical result and experimental value of the hyperfine splitting lie in the range of theoretical and experimental errors and require the subsequent investigation of higher order corrections.

How to solve the problem of dynamical correlation of electrons in the ground state helium atom?

AbstractIt is found that, for the ground state helium atom, a stationary wave function obtained from the stationary Shrödinger equation for one of the interacting electrons is much more physically meaningful than that from the equation for both electrons. Hamiltonian includes one‐electron Laplacian and operators of electron–nuclear attraction and electron–electron repulsion. Corresponding energy is equal to the first ionization potential. This approach recovers evident insufficiency of summation of potential energies accompanied by determination of kinetic energy from the virial relation. It appears that the kinetic energy must be determined independently. The kinetic energy of both electrons lowers due to inertia of the electron movement. It demands for a time‐resolved consideration of the electron movement in helium. The total energy cannot be minimized in one step, that is, by help of a single stationary wave function. It should be minimized with means of two wave functions in accord with experimental sequential ionization. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

The ground state energy of a helium atom under strong confinement

We analyze the helium atom ground state under strong confinement where the atom is embedded in a spherical box with impenetrable walls. In previous studies, variational calculations of the ground state energy for strongly confined helium have proven to be a difficult numerical task, especially when large basis set expansions were considered. In the present work we have solved the time-independent Schrödinger equation using first-order Rayleigh–Schrödinger perturbation theory and then extended the calculations using fifth-order variational perturbation theory. Our results show that these approaches provide good alternative approaches for calculation of the ground state energy for a strongly confined helium atom.

An ellipsoidal mirror for focusing neutral atomic and molecular beams

Manipulation of atomic and molecular beams is essential to atom optics applications including atom lasers, atom lithography, atom interferometry and neutral atom microscopy. The manipulation of charge-neutral beams of limited polarizability, spin or excitation states remains problematic, but may be overcome by the development of novel diffractive or reflective optical elements. In this paper, we present the first experimental demonstration of atom focusing using an ellipsoidal mirror. The ellipsoidal mirror enables stigmatic off-axis focusing for the first time and we demonstrate focusing of a beam of neutral, ground-state helium atoms down to an approximately circular spot, (26.8±0.5) μm×(31.4±0.8) μm in size. The spot area is two orders of magnitude smaller than previous reflective focusing of atomic beams and is a critical milestone towards the construction of a high-intensity scanning helium microscope.

A finite volume approach for solving the ground state helium

A three-dimensional finite volume discretization of the time-independent Schrödinger equation is formulated for the ground state helium atom. A set of algebraic equations arising from the second-order discretization of the PDE are solved for the wavefunction using the Gauss–Seidel algebraic multigrid solver coupled with a modified Stodola–Vianello method in extracting the ground state energy. A thorough mesh refinement study results in the ground state energy of the helium atom to be −2.903 230 au, which is only 0.017% above the Frankowski–Pekeris value. Mesh convergence of the wavefunction solution suggests that it correctly approximates to the unknown exact solution.

An exact one-electron model of atomic structure: The helium atom ground state

An exact one-electron model of atomic structure: The helium atom ground state

An exact one-electron model of the helium atom ground state

Expression of the Helium atom ground state wavefunction as a product of marginal and conditional factors together with averaging over the configuration space except for the distance of one electron from the nucleus, leads to a radial Schrodinger equation for the motion of one electron in an effective field produced by the nucleus and the other electron. The potential in this radial Schrodinger equation is in principle exact (i.e. it includes all of the correlation energy). Values of the potential are reported computed from correlated wavefunctions and from a Hartree-Fock wavefunction; the correlated and Hartree-Fock potentials are similar, the former being below the latter by and amount that averages to the correlation energy (0.04 a.u.). Thus Hartree's concept of a self-consistent field for the motion of one electron is seen to be in principle exact. The exact theory has not, however, thus far yielded a set of simultaneous equations analogous with the Hartree-Fock equations; the exact theory if a one-electron model rather than an ab initio method for computing wave functions.

Singer polymals. II. Tempering methods

Tempering of Singer polymal basis sets is introduced to reduce the number of variational parameters to be optimized. Two types of tempering are studied and compared: generalized “even tempering” and generalized “Monte Carlo tempering.” Comparisons of total energy are made for various temperings of Singer geminals using the ground state of the helium atom for a model system. Generalized Monte Carlo tempering is found to be superior. The benefit-to-cost ratio is measured for extending the basis size versus extending the number of tempering parameters; for small basis and small numbers of parameters it is more beneficial to add more parameters, but for sufficiently large basis it is more beneficial to extend the basis than to add more parameters. Monte Carlo tempering exploits the benefits of extending the basis without increasing the number of variational parameters.