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Conventional Quantum Chemical Correlation Energy versus Density-Functional Correlation Energy

We analyze the difference between the correlation energy as defined within the conventional quantum chemistry framework and its namesake in density-functional theory. Both quantities are rigorously defined concepts; one finds that $E_c^{QC} \geq E_c^{DFT}$. We give numerical and analytical arguments suggesting that the numerical difference between the two rigorous quantities is small. Finally, approximate density functional correlation energies resulting from some popular correlation energy functionals are compared with the conventional quantum chemistry values.

atom-ph

Squeezing in the interaction of radiation with two-level atoms

We propose a simple experimental procedure to produce squeezing and other non-classical properties like photon antibunching of radiation, and amplification without population inversion. The method also decreases the uncertainties of the angular-momentum quadratures representing the two-level atomic system in the interaction of the two-level atoms with quantized radiation.

atom-ph

The Periodic Table in Flatland

The $D$-dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in $D$ dimensions. This rule together with an {\it Aufbau Prinzip} is applied to produce a $D$-dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of an Hamiltonian, invariant under the $q$-deformed algebra $U_q($so$(D))$, that breaks down the SO($D+1$) dynamical symmetry of the hydrogen atom in $D$ dimensions. The $D=2$ case (Flatland) is investigated with some details. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values $q=0.8$ and $q=1$, respectively, of the deformation parameter $q$.

atom-ph

Coulomb Energy Averaged over the $n\ell^N$-Atomic States with a Definite Spin

A purely group-theoretical approach (for which the symmetric group plays a central rôle), based upon the use of properties of fractional-parentage coefficients and isoscalar factors, is developed for the derivation of the Coulomb energy averaged over the states, with a definite spin, arising from an atomic configuration $n \ell^N$.

atom-ph

Quantum Reservoir Engineering

We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. This will provide the basis for the experimental study of the process of decoherence in a quantum system. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to ``engineer'' the coupling and select the master equation describing the motion of the ion.

atom-ph

Some remarks on the two-electron atom

New, approximate, two-electron wavefunctions are introduced for the two-electron atoms (cations), which account remarkably well for the ground-state energies and the lowest-excxited states (where available). A new scheme of electronic configurations is also proposed for the multi-electron atoms.

atom-ph

Interaction of a slow monopole with a hydrogen atom

The electric dipole moment of the hydrogen-like atom induced by a monopole moving outside the electron shell is calculated. The correction to the energy of the ground state of the hydrogen atom due to this interaction is calculated.

atom-ph

Ionization of the hydrogen atom in strong magnetic fields: beyond the adiabatic approximation

High magnetic fields in neutron stars, B ~ 10^{11} - 10^{13} G, substantially modify the properties of atoms and their interaction with radiation. In particular, the photoionization cross section becomes anisotropic and strongly polarization dependent. In a number of previous works based on the adiabatic approximation the conclusion was drawn that the transverse cross section vanishes for frequencies smaller than the electron cyclotron frequency. In other works (which employed a different form of the interaction operator) appreciable finite values were obtained. An adequate interpretation of the neutron star thermal-like radiation requires a resolution of this controversy. In this work the atomic wave functions for both discrete and continuum states are calculated by solving the coupled channel equations allowing the admixture between different Landau levels, which provides much higher accuracy than the adiabatic approximation. This enables to resolve the above contradiction in favour of the finite transverse cross sections. The non-adiabatic treatment of the continuum includes coupling between closed and open channels, which leads to the autoionization of quasi-bound energy levels associated with the electron cyclotron excitations and gives rise to Beutler - Fano resonances of the photoionization cross section. Autoionization widths of these quasi-bound levels are calculated and compared with the radiative widths. The results are important for investigations of the radiation emergent from the surface layers of neutron stars.

atom-ph

Hyperfine interactions between electrons

The relativistic Breit Hamiltonian between electrons is transformed into an effective vector potential ${\bf A}_i$ for the $i.$th electron, ${\bf A}_i$ having the structure of a recoil--corrected hyperfine operator. Apart from a small three--body operator, the Dirac--Breit equation is now easier applied to relativistic magnetic properties of complex systems.

atom-ph

Single-Mode Cavity-QED of a Raman Interaction

We consider a single Rydberg atom having two degenerate levels interacting with the radiation field in a single-mode ideal cavity. The transition between the levels is carried out by a $Λ$-type degenerate two-photon process via a third level far away from single-photon resonance. At the start of interaction, the atom is considered to be in a coherent superposition of its two levels and the field in a coherent state. We study the dynamics of the atomic as well as the field states. The squeezing in the quadratures of atomic states can reach up to $100\%$. The cavity field evolves to a statistical mixture of two coherent fields with the phase difference between them decided by the interaction time. Analysis of entropies of the atom and the field shows that the two systems are dis-entangled periodically in certain cases.

atom-ph

Centrifugal Effects in a Bose-Einstein Condensate

Single particle states in the atomic trap employing the rotating magnetic field are found using the full time-dependent instantaneous trapping potential. These states are compared with those of the effective time-averaged potential. We show that the trapping is possible when the frequency of the rotations exceeds some threshold. Slightly above this threshold the weakly interacting gas of the trapped atoms acquires the properties of a quasi-1D system in the frame rotating together with the field. The role of the atom-atom interaction in changing the ideal gas solution is discussed. We show that in the limit of large numbers of particles the rotating field whose angular frequency is appropriately modulated can be utilized as a driving force principally for the center of mass motion as well as for the angular momentum $L = 2$ normal modes of the Bose condensate. A mechanism of quantum evaporation forced by the rotating field is analyzed.

atom-ph

Spin-rotation coupling in ferromagnetic clusters

We examine the magnetic response of free clusters considering the spin direction and the cluster orientation as the only active degrees of freedom. The average magnetization in small fields approaches the Langevin value for paramagnets, depending on the degree to which the Hamiltonian preserves symmetries. Superparamagnetic behavior is not achievable within models considering only these degrees of freedom.

atom-ph

Correlation Energy Estimators based on M{\o}ller-Plesset Perturbation Theory

Some methods for the convergence acceleration of the M{\o}ller-Plesset perturbation series for the correlation energy are discussed. The order-by-order summation is less effective than the Feenberg series. The latter is obtained by renormalizing the unperturbed Hamilton operator by a constant factor that is optimized for the third order energy. In the fifth order case, the Feenberg series can be improved by order-dependent optimization of the parameter. Alternatively, one may use Pad{\'e} approximants or a further method based on effective characteristic polynomials to accelerate the convergence of the perturbation series. Numerical evidence is presented that, besides the Feenberg-type approaches, suitable Pad{\'e} approximants, and also the effective second order characteristic polynomial, are excellent tools for correlation energy estimation.

chem-ph

On the Stability of Endohedral Rare Gas Fullerenes

The stability of Ne@C$_{60}$ and He@C$_{60}$ is discussed in the context of a spherical model where the carbon atoms are smeared out into a uniform shell. The electronic properties of the sixty $π$ electrons together with those of the central atom are treated in the Thomas-Fermi approximation. Simple electrostatic reasoning elucidates the nature of the radial stability of the complex. A method to include non-spherical corrections is outlined. Possible bonding topologies of the central atom and the C$_{60}$ cage are discussed, as well as the relevance of these topologies to incipient central atom distortions.

chem-ph