The multiconfiguration Hartree-Fock method has been applied successfully to the calculation of oscillator strength for the transitions 2s2p ${}^1$P°→2$p^2$,2snd ${}^1$D (n=3–6) in beryllium. The effects of electron correlation, which are very important for these calculations, have been taken into account accurately through the configuration-interaction procedure. The length and velocity results of the oscillator strength as well as the calculated and experimental transition energies are in excellent agreement. The present results compare well with experiment and other available theoretical data.

The atomic Coulomb capture ratios for pions have been measured for boron carbide and boron tetraoxide. These results and previous ones for beryllium borides and boron nitrides are analyzed with a modified mesomolecular model, and the net atomic charges are deduced and compared with results by another method and with theoretical predictions. Qualitative agreement is obtained for the net atomic charges obtained with the present experiment and with theoretical predictions.

The result of the kinetic energy operator -(${ħ}^2$/2m) ${\nabla }_{\mathrm{r}}^2$, acting on the canonical density matrix C(r,${\mathrm{r}}_0$,β) and then evaluated on the diagonal ${\mathrm{r}}_0$=r, is expressed solely in terms of the so-called Slater sum C(r,r,β) and the same sum for s states only, for arbitrary central fields.

We consider the dispersion-interaction self-energy of two atoms or of a charge and an atom without imposing the Born-Oppenheimer approximation. We find compact expressions in terms of matrix elements of operators in the atomic displacement which are not limited by multipole expansions. The saturation effect of recoil causes the self-energy to be finite even at small separation. The relation to previously obtained results in terms of multipole expansions is discussed.

In this work we present a new scheme for coupling the different arrangement channels in a three-dimensional n-channel (where n>2) reactive system. Whereas the old scheme was found to yield a nonunitary S matrix when employed to a three-channel system, the new scheme yields a unitary S matrix and relevant results for the H+${\mathrm{H}}_2$ (J=0) reactive system.

A model-potential method has been employed to calculate the elastic $e^{\pm }$-Kr scattering at low incident energies. The potential due to Khan et al. [Phys. Rev. A 29, 3129 (1984)] contains one parameter to include the effect of short-range correlation. The same polarization potentials have been used for both the electron and positron cases, and the scattering parameters are presented. The results of $e^{\mathrm{-}}$-Kr are found to be in good agreement with those of other elaborate theoretical calculations and experimental values up to an incident energy of 30.0 eV. The results for positron scattering are found to be less satisfactory.

Cross sections for double-electron capture from helium atoms by fully stripped ions of lithium, carbon, and oxygen are calculated in the framework of the continuum distorted-wave (CDW) and continuum intermediate-state (CIS) approximations in the energy range of 0.125–2.5 MeV/amu. Cross sections are also calculated for α particles as the projectile in the CIS approximation. The results are compared with existing experimental findings. The present calculated results for symmetric and near-symmetric cases show good agreement with the experimental findings. The discrepancies between the calculated and observed values for the asymmetric cases are discussed.

Measurements of the double-electron-capture process in which a positive ion of iodine becomes a negative ion in a single collision with a magnesium atom are reported between 20 and 90 keV. The cross section is comparable to that for the rare gases and not as large as might be expected from a two-valence-electron atom. This process is probably insignificant in the production of negative ion beams using a magnesium-vapor target.

The recently observed anticorrelation between kinetic energy transfer to rotations and lattice vibrations in gas-surface collisions is investigated theoretically. Quantum effects for the rotational motion are taken into account in the sudden approximation. The lattice is treated in linear-response theory (valid both quantum mechanically and classically), and the translational motion is treated classically. The results agree well with exact quantum-mechanical coupled-channel calculations in simple cases. Experimental results for NO on oxidized Ge are described satisfactorily.

Number-phase minimum uncertainty states and number states are shown to be realized by quantum nondemolition measurements of the photon number. Interphase modulation in a Kerr medium establishes a quantum-mechanical correlation between the signal and probe waves initially in coherent states. State reduction is realized by homodyne detection of a probe quadrature-phase amplitude. The number uncertainty can be arbitrarily reduced by increasing the probe intensity. The minimum uncertainty relation between the number and sine operators approximately holds until a near-number state is realized.

The values of the characteristic frequencies in the Fourier spectrum for the semiclassical Jaynes-Cummings model in the case of a weak-coupling constant are found analytically and are also confirmed numerically. The rotating-wave approximation is not assumed. The sidebands of atomic and cavity modes occur at the characteristic frequencies and play an essential role in characterizing the Fourier spectra of chaotic behavior. The question of transition from nonchaotic to chaotic behavior is also studied.

The Golden-Kalman velocity-average approximation scheme for one-component plasmas is generalized to account for electronic screening effects. New formulas are established for the dispersion and damping of the ion-sound and ion-plasma modes at arbitrary coupling.

Experiments with free-surface cross-waves reveal that the wave field periodically decreases its transverse mode number in response to changes in geometry. This periodic adjustment limits the correlation dimension to a small value. The forcing parameters are changed by adjustments in geometry while leaving the forcing amplitude constant.

Existing formulas for the dispersion relation ω(k) of collective modes in liquids and amorphous solids are shown to have the often severe limitation that the velocity of sound is not correctly given. Therefore, a generalization to include wavelength dependence is made of the adiabatic compressibility, via the so-called thermodynamic fluctuation. The velocity of sound is thereby correctly related to the static structure (i.e., pair correlation function) and the ratio of the specific heats γ. This demonstrates that a fully quantitative expression for the dispersion relation ω(k) must involve three- and four-atom correlation functions in liquids and amorphous solids. Theories posed in terms of frequency moments of the dynamical structure factor would have to incorporate up to and including the eighth frequency moment in order to reproduce correctly the velocity of sound in the disordered systems considered here.

In stability analysis of nonlinear systems, the character of the eigenvalues of the Jacobian matrix (i.e., whether the real part is positive, negative, or zero) is needed, while the actual value of the eigenvalue is not required. We present a simple algebraic procedure, based on the Routh-Hurwitz criterion, for determining the character of the eigenvalues without the need for evaluating the eigenvalues explicitly. This procedure is illustrated for a system of nonlinear ordinary differential equations we have studied previously. This procedure is simple enough to be used in computer code, and, more importantly, makes the analysis possible even for those cases where the secular equation cannot be solved.

We point out that the results of Haake et al. [Phys. Rev. A 34, 3969 (1986)] on the mean and variance of the number of quanta are a classical effect, easily accounted for by classical statistical mechanics.

The integrability underlying the quantum mechanics of noninte- grable pulsed systems is examined along the line exploited by Nakamura and Lakshmanan [Phys. Rev. Lett. 57, 1661 (1986)]. Coupled dynamical equations for both quasienergies and quasieigenfunctions (rather than matrix elements) with a nonintegrability parameter λ taken as ‘‘time’’ are shown to be reduced to a classical Sutherland’s system with internal complex-vector space. Their complete integrability together with constants of motion are also exhibited.

A study is made of the quantum mechanics of a gas of spin-polarized (b-state) atomic hydrogen confined in a three-dimensional dynamic (ac) magnetic trap. A previous classical treatment indicated that evaporative cooling from such a trap could be used to attain conditions for Bose-Einstein condensation (BEC). An approximate solution is developed for the quantum mechanics of a single atom in an ac trap. This solution is then used to treat the statistical mechanics of the BEC in an ac trap. The ideal-gas limit is briefly considered, and this is compared with the more realistic approximation of a nonideal gas described by the finite-temperature Hartree-Fock equations with an s-wave scattering-length interaction. The threshold temperature for BEC differs only slightly from the value for an ideal gas. However, the nature of the condensate is strongly dependent on the scattering length.

We outline a systematic scheme for the derivation of relativistic energy density functionals on the basis of the Hartree-Fock limit of quantum electrodynamics. In particular, a relativistic analog of the nonrelativistic Thomas-Fermi-Dirac-Weizsäcker model is presented.