In electronic-structure calculations for finite systems using the local-spin-density (LSD) approximation, it is assumed that the eigenvalues of the Kohn-Sham equation should obey Fermi-Dirac (FD) statistics. In order to comply with this assumption for some of the transition-metal atoms, a nonintegral occupation number is used which also minimizes the total energy. It is shown here that for finite systems it is not necessary that the eigenvalues of the Kohn-Sham equation obey FD statistics. It is also shown that the Kohn-Sham exchange potential used in all LSD models is correct only for integer occupation number. With a noninteger occupation number the LSD exchange potential will be smaller than that given by the Kohn-Sham potential. Ab initio self-consistent spin-polarized calculations have been performed numerically for the total energy of an iron atom. It is found that the ground state belongs to the 3$d^6$4$s^2$ configuration. The ionization potentials of all the ${\mathrm{Fe}}^{\mathrm{n}+}$ ions are reported and are in agreement with experiment.

It is shown that in the low beam space-charge limit the small-signal gain for a proton maser, calculated from a dispersion relation, is proportional to (${\omega }_p$/${\omega }_0$${)}^2$, and agrees to this order with that derived from orbital velocity perturbations, to order (${\mathrm{qE}}_x$/m${\omega }_0$$U_0$${)}^2$. The rf current density in the interaction space is derived; ‘‘self-bunching’’ and the underlying physics of the gain (‘‘self-catching’’) are explored and a comparison is made between the collective formulation and that of single-particle orbits.

Multiconfiguration Hartree-Fock (MCHF) calculations recently predicted a positive binding energy for the p electron in the $s^2$$p^2$P state of ${\mathrm{Ca}}^{\mathrm{-}}$, in good agreement with experiment. The present paper explores the binding of electrons in several alkaline-earth elements. Fixed-core Hartree-Fock potentials demonstrate the angular momentum barrier. From a simple correlation study it is shown that the 3$d^2$4p configuration relative to the 3$s^2$3p configuration in ${\mathrm{Mg}}^{\mathrm{-}}$ lies much higher than the (n-1)$d^2$np configurations relative to ${\mathrm{ns}}^2$np in the heavier alkaline-earth elements. Accurate MCHF correlation studies are reported for two and three electrons outside a core from which binding energies are predicted for ${\mathrm{Ca}}^{\mathrm{-}}$, ${\mathrm{Sr}}^{\mathrm{-}}$, and ${\mathrm{Ba}}^{\mathrm{-}}$. Not included is correlation with the core (core polarization) and correlation within the core. The same procedures were also applied to Sc. Theoretical results with relativistic shift corrections are compared with experiment in the case of ${\mathrm{Ca}}^{\mathrm{-}}$ and Sc.

We use SU(1,1) coherent-state path integrals to describe the time evolution of systems driven by coherence-preserving Hamiltonians. Such Hamiltonians are composed of linear combinations of the group generators. The method described here is an alternative to the well-known Wei-Norman procedures. Application is made to the degenerate parametric amplifier of quantum optics.

An accurate method for variational calculations of atomic properties is constructed using the principle that the results must be invariant under gauge transformations. The technique is used with multiexponential basis sets and provides very fast convergence. The method is applied to the relativistic calculation of the dipole polarizability in hydrogenic ions. The results obtained with 21 relativistic Slater-type basis functions are accurate to 13 digits for nuclear charges from Z=1 to Z=115, therefore overcoming the large loss of accuracy for large values of Z, which is typical of single-exponential basis sets. The results are compared with previous calculations and the coefficients of a relativistic expansion of the polarizability in powers of (${\alpha }_{\mathrm{FS}\mathrm{Z}{)}^2}$ up to (${\alpha }_{\mathrm{FS}\mathrm{Z}{)}^8}$ are obtained, where ${\alpha }_{\mathrm{FS}}$ is the fine-structure constant.

In molecular Hartree-Fock instability problems (here restricted to the types of instabilities known as axial-spin-density waves and charge-density waves in Fukutome’s classification), attention is usually concentrated on the lowest solution of each type, and the one appearing at shortest interatomic distances. As shown, for instance, on the cyclic ${\mathrm{Li}}_6$ cluster problem, an asymptotic look at the symmetry-breaking problem enables one to generate a multiplicity of solutions which have generally been ignored. For ${\mathrm{N}}_2$ we find ten different types of triplet instabilities, dissociating into three different asymptotes and five different types of singlet instabilities, all having components in the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ ground state. At long interatomic distances all these solutions are true minima of the energy, some of them becoming saddle points at short interatomic distances. It is shown for the ${\mathrm{C}}_2$ problem that multiple symmetry-broken solutions may exist at short interatomic distances; these various solutions might be used in nonorthogonal valence configuration-interaction calculation for strongly correlated multiple bonds such as in ${\mathrm{C}}_2$ or ${\mathrm{Cr}}_2$.

We show that the exact Kohn-Sham wave functions and exact Kohn-Sham exchange potential $v_x^{\mathrm{KS}}$ may be calculated for any spherically symmetric system in which the electron states are described by orbitals having only two different radial wave functions. In this exchange-only theory the total energy, electron density, and maximum single-particle energy eigenvalue are all identical to the corresponding Hartree-Fock ground-state results. We present results for an external harmonic-oscillator potential with two filled subshells corresponding to a total of eight (unpolarized) electrons or a total of four (spin-polarized) electrons for a wide range of spring constants. Comparisons are made between the results obtained from the exact KS theory and those obtained from employing the local-spin-density (LSD) and Slater (SLA) exchange approximation and from the exact Hartree-Fock results with respect to wave functions, densities, single-particle eigenvalues, exchange energy, and the calculation of Hartree-Fock expectation values for total energy and single-particle energies employing single-particle density-functional wave functions. Of particular interest is the result that $v_x^{\mathrm{KS}}$ and $v_x^{\mathrm{LSD}}$ are similar in shape, but not in magnitude, which results in LSD orbitals which closely approximate the exact KS orbitals even though the single-particle eigenvalues are significantly in error and are in fact less accurate than those given by the SLA.

The two-electron Bethe-Salpeter equation is reviewed. The transition to a Hamiltonian form is discussed, and the criterion that the first-order energy shift vanish is used to determine the electron-electron potential that appears in the Hamiltonian. A similar program is carried through for the three-electron case. The fundamental idea of Feldman and Fulton [Nucl. Phys. B195, 61 (1982)] is used for the transition to the Hamiltonian form, although some changes are necessary. The optimum two-electron interaction is the same as that in the two-electron case. It is necessary to introduce a static three-electron interaction, which then can be determined from the vanishing of the first-order energy shift. It is extremely complicated and unlikely to prove useful in the near future.

The intensity of the $L_3$-$M_4$,5${\mathrm{M}}_4$,5 Auger line of ${}_{39}{}^{}{}_{}{}^{}\mathrm{Y}$ excited by photons with energies in the range of the $L_1$ edge has been measured. It exhibits a jump at the edge due to the onset of the Coster-Kronig vacancy transfer from the $L_1$ to the $L_3$ subshell. From the measured jump ratio 1.13±0.02 the Coster-Kronig yield $f_{13}$=0.49±0.09 is derived. This value agrees with a currently recommended value; however, it is significantly smaller than the prediction of recent relativistic calculations.

We have determined the transition probabilities for 23 lines of the Ar i 4s-5p array by emission spectroscopy utilizing a wall-stabilized arc. The seven remaining lines of this transition array were either very weak or overlapped strongly with other lines so that they could not be reliably measured. We placed our relative data on an absolute scale by applying the result of a recent critical analysis for the prominent 4s-5p line at 430.01 nm.

Semianalytic methods are developed to predict the alignment and orientation of excited helium ions produced in the photoionization of neutral helium in the low-energy limit. The ionic electron probability distribution is shown to align itself orthogonal to the direction of the incident light polarization axis in the same manner as the photoelectron angular distribution [C.H. Greene, Phys. Rev. Lett. 44, 869 (1980)]. In certain instances, propensity rules for the alignment and orientation of the ionic electron are violated. Coherent contributions from different degenerate orbital angular momenta are seen to be partially responsible for these ‘‘unfavored’’ trends. Explicit predictions of the time-unresolved fluorescence polarization are presented, including the effects of fine-structure depolarization.

We report computational results that show that the conical emission observed when a nearly resonant laser pulse propagates through an atomic vapor is the result of the breakup of the pulse into solitary waves. For an incident pulse with a radial as well as a temporal profile, the crests and troughs of the two-dimensional solitary waves are curved in a time-radius plane. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum, while the curvature of the solitary waves in the time-radius plane results in a transverse spatial modulation that leads to conical emission in the far field. These results were obtained by performing detailed numerical calculations of the time-dependent paraxial propagation of a cylindrically symmetric laser pulse through a vapor of two-level atoms under the rotating-wave and slowly-varying-envelope approximations in the limit of no collisional damping or Doppler broadening. Our results can be interpreted readily in terms of optical nutation on the Bloch sphere and in terms of noncollinear phase matching through the curvature of the solitary waves rather than through additional parametrically generated waves. We find that self-focusing is not required for the generation of conical emission, although it would be difficult to separate these effects experimentally.

Characteristic decay times for relaxation close to the marginal point of optical bistability are studied. A model-independent formula for the decay time is given which interpolates between Kramers time for activated decay and a deterministic relaxation time. This formula gives the decay time as a universal scaling function of the parameter which measures deviation from marginality. The standard deviation of the first-passage-time distribution is found to vary linearly with the decay time, close to marginality, with a slope independent of the noise intensity. Our results are substantiated by numerical simulations and their experimental relevance is pointed out.

Taking into account the vibronic-level structure in a laser medium, we study the influence of electron-vibration interaction on the field dynamics. Different vibronic transitions are coupled in the medium through this interaction and contribute to the emission from excited states, thus coupling different field modes in the cavity and influencing the field dynamics. A general model is presented and solved in a simple example of four coupled transitions. In particular, the effect of degenerate transitions is stressed.

We have studied the transient response of undamped two-level atoms to excitation by a classical bichromatic field consisting of a strong resonant component and a moderate-strength, tunable, ‘‘perturber’’ component. It is found that the strong field tends to stabilize the atom against the influence of the perturber field. Exceptions to this general result occur when the perturber is detuned from the strong field by the Rabi frequency of the latter or its subharmonics. We believe this stabilization phenomenon is a semiclassical analog of the effect that leads to the dynamical modification of spontaneous emission [M. Lewenstein and T. W. Mossberg, Phys. Rev. Lett. 59, 775 (1987)], and the presence of detunings at which the stabilization fails provides a simple motivation for the Rabi subharmonic resonances found in certain cw bichromatic spectra. Interestingly, when the perturber field is relatively weak, detuned from the atomic resonance by the strong-field Rabi frequency, and turned on with a specific initial phase relative to the strong field, one finds that the bichromatic field can be employed to dressed-state polarize initially ground-state atoms. In a related vein, we find that perturbations at the subharmonic detunings lead to interesting phase-dependent atomic dynamics. Results were obtained using both numerical and approximate analytical techniques entirely within the context of the rotating-wave approximation. The validity of the latter is ensured by demanding that all detunings and Rabi frequencies are vanishingly small compared to the atomic transition frequency.

Radiation effects from two-level atoms caused by the presence of a Fock-state field in a damped single-mode cavity are examined. An exact recurrence differential equation for density-matrix elements valid for any number of atoms or photons is derived. Numerical solutions for different cavity dampings (low- and high-Q cavities) and different photon numbers of the Fock-state field being present initially in the cavity are presented. Collective effects caused by the presence of many atoms are investigated. It is shown that new quasistationary states as well as collective radiation inhibition appear in the time behavior of the atomic energy expectation value. These effects arise from averaging over an ensemble of which each member consists of N identical two-level atoms placed into a resonant single-mode cavity. A comparison of the obtained results with those for an initial coherent or thermal field is also given.

The beam breakup instability caused by the interaction between beam and induction gaps in a steady-state free-electron laser in the microwave regime is considered. The large energy spread induced by free-electron laser performance is theoretically proved not to lead to Landau damping of the beam breakup instability when the synchrotron frequency is of order or larger than the betatron frequency.

A detailed exposition of explicit formulas used in the evaluation of raising-raising forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary-group distinct-row tabular-graphical representation of the many-particle basis. All matrix elements are expressible in the form of scalar and 2×2 matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors we develop a calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.

Based on the hydrodynamic theory of an electron gas, we have calculated the second-harmonic generation (SHG) from metal surfaces in various geometric configurations. The SHG of single-boundary surface plasmons coupled using the Kretschmann geometry is ten times larger for gold, copper, and silver, and 100 times larger for aluminum films than the SHG from the bare metal reflectors. The SHG due to long-range surface plasmons in a modified Kretschmann geometry with a very thin metal film sandwiched between two dielectric layers is typically over two orders of magnitude larger than that from the simple Kretschmann geometry. Enhanced SHG is presumed as the thickness of the index-matched liquid layer and the metal films are suitably adjusted because of the resonant interference.

The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.