Faddeev calculation of energy states in two-electron atoms

The Faddeev equations are used to calculate the ground state as well as a few ortho- and para-excited states of e^–e⁺e^–, H^–, He, Li⁺ and Be⁺⁺ atoms. The Coulomb potential is represented in a separable form using the appropriate Coulombic Sturmians for both the attractive and repulsive interactions. Up to 36 Sturmians are employed in each interaction leading to the solution of a maximum of 56 coupled one-variable integral equations. Results are compared with data or predictions from variational calculations.     

Spin-singlet Bose-Einstein condensation of two-electron atoms

We report the observation of a Bose-Einstein condensation of ytterbium atoms by evaporative cooling in a novel crossed optical trap. Unlike the previously observed condensates, a ytterbium condensate is a two-electron system in a singlet state and has distinct features such as the extremely narrow intercombination transitions which are ideal for future optical frequency standard and the insensitivity to external magnetic field which is important for precision coherent atom optics, and the existence of the novel metastable triplet states generated by optical excitation from the singlet state.     

Comment on the accuracy of the total energy of atoms

We discuss the quality of the theoretical calculation of binding energies for atoms and ions which, hopefully, can be tested soon with a new generation of ion traps. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the energy levels of neutral atoms

By applying the hypervirial-Padé calculation to the model Yukawa potential with a modified screening parameter, we obtain the shell binding energies of neutral atoms which yield accurate results over the entire range of the atomic number.     

Exact correlated kinetic energy related to the electron density for two-electron model atoms with harmonic confinement

For arbitrary interparticle interaction u(r₁₂), the model two-electron atom in the title is shown to be such that the ground-state electron density ρ(r) is determined uniquely by the correlated kinetic energy density t_R(r) of the relative motion. Explicit results for t_R(r) are presented for the Hookean atom with force constant k=1/4, and also for . Possible relevance of the Hookean atom treatment to the ground state of the helium atom itself is briefly discussed.     

Scaling laws for the photoionization cross section of two-electron atoms

The cross sections for single-electron photoionization in two-electron atoms show fluctuations which decrease in amplitude when approaching the double-ionization threshold. Based on semiclassical closed orbit theory, we show that the algebraic decay of the fluctuations can be characterized in terms of a threshold law sigma proportional to |E|(mu) as E --> 0(-) with exponent mu obtained as a combination of stability exponents of the triple-collision singularity. It differs from Wannier's exponent dominating double-ionization processes. The details of the fluctuations are linked to a set of infinitely unstable classical orbits starting and ending in the nonregularizable triple collision. The findings are compared with quantum calculations for a model system, namely, collinear helium.     

Spherically confined two-electron atoms immersed in Debye plasma

The effect of spatial confinement in the presence of plasma environment on the dipole allowed transition properties for the first five helium-like atoms (He through C⁴⁺) is studied. The Debye screening describes the effect of plasma. Additionally, the effect of a spatial confinement (as, for example, it is in the case of atoms surrounded by liquid helium) is described by locating the atom in the center of a spherical box. Time-dependent variation perturbation theory is applied to estimate the orbital energies, polarizabilities, transition energies, oscillator strengths, and transition probabilities. The effect of spatial confinement in the plasma environment shows interesting features. The decrease of the radius of confinement exerts pressure within the system and produces instability in the energy values ultimately ionizing the system. The ionization pressures at different plasma screenings are estimated. The ionization pressure at zero Debye screening for helium agrees with existing data.     

Collective and independent-particle motion in two-electron artificial atoms

Investigations of the exactly solvable excitation spectra of two-electron quantum dots with a parabolic confinement, for different values of the parameter R(W) expressing the relative magnitudes of the interelectron repulsion and the zero-point kinetic energy, reveal for large R(W) a rovibrational spectrum associated with a linear trimeric rigid molecule composed of the two electrons and the infinitely heavy confining dot. This spectrum transforms to that of a "floppy" molecule for smaller R(W). The conditional probability distribution calculated for the exact two-electron wave functions allows identification of the rovibrational excitations as rotations and stretching/bending vibrations.     

Rydberg quantum computation with nuclear spins in two-electron neutral atoms

Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states |0〉 and |1〉 are excited to Rydberg states |r〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state |1〉 can be fully excited to the Rydberg state while |0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.     

On the role of correlation energy produced by the spin-spin interaction in the formation of binding energy for two-electron atomic systems

An algorithm is proposed for computing the correlation energy produced by the spin-spin interaction V _SS of electrons in He-like atomic systems. The algorithm takes into account the singular nature of V _SS and the formation of a compact finite motion of electrons in the range of distances Ze ²/mc ² < r ₁₂ < ħ/mc between the electrons under the action of the magnetic fields of spins for a singlet ground state. Good agreement with experimental values of the ionization potential is attained for a wide set of two-electron atomic systems without resorting to variational procedures, but only using hydrogen-like wavefunctions and correctly taking into account the singular nature of the spin-spin interaction of electrons.     

On the total binding energy of spherical nuclei

The total binding energy of nuclei is determined by means of many-body field theory. The problem is then reduced to finding the energy-dependent average potential (mass operator) and solving the single-particle equations of motion. Such a potential can be established phenomenologically by using data on low excitations and reactions knocking out nucleons from deep “hole” levels. Calculations of the total binding energy of the nuclei ¹⁶O, ⁴⁰Ca and ⁵⁸Ni with this potential are in satisfactory agreement with experiment.     

Electron correlation energy in confined two-electron systems

Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted Hartree-Fock and radial limit energies over a range of confinement radii from 0.05-10a₀. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R, systems with Z?1 exhibit a characteristic maximum in the correlation energy resulting from an increase in the angular correlation energy which is offset by a decrease in the radial correlation energy.     

Time-dependent perturbation calculations for transition properties of two-electron atoms under Debye plasma

Systematic investigation have been performed for the dynamic polarizabilities, energy levels, oscillator strengths and transition probabilities for the first few members of helium isoelectronic series He, Li⁺,Be²⁺,B³⁺ and C⁴⁺ embedded in the Debye plasma. The effect of plasma is described by introducing an exponential screening (the Debye screening) to the nuclear Coulomb potential. Systematic trend is observed for all the properties under study with respect to increased screening. The ionization potential decreases with an increased screening and the number of bound excited states supported by the Debye screened potential is finite.     

Modern methods for calculating photoionization and electron-impact ionization of two-electron atoms and molecules

A number of recently developed methods for calculating multifold differential cross sections for photoionization and electron impact ionization of atoms and molecules with two active electrons are reviewed. The methods are based on unique approaches to the calculation of three-body Coulomb wave functions. The exterior scaling method and the driven Schrödinger equation formalism are considered. The effectiveness of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. A novel numerical method is formulated, which has been developed by the authors to solve the six-dimensional Schrödinger equation for an atom with two active electrons on the basis of the Chang-Fano transformation and the discrete variable representation. The threshold behavior manifested by the angular distributions of the two-electron photoionization of a negative hydrogen ion and a helium atom and the multifold differential cross sections for the electronimpact ionization of hydrogen and nitrogen molecules are analyzed on the basis of numerical simulations. The Wannier law for the angular distribution of double ionization is demonstrated to be incorrect even at very low energies.