The frequency-dependent and wave-number-dependent dielectric properties of a condensate of a boson gas with static disorder are evaluated. For weak disorder the condensate is superfluid and the disorder induces a mass enchancement. For strong disorder the condensate is insulating and the static dielectric function is finite. Numerical solutions for the frequency dependence of the density relaxation function and the dynamical conductivity are given. The dielectric properties of a charged Bose gas with charged impurities and a repulsive Bose gas with neutral impurities are evaluated explicitly.

We study the fluctuations in a lattice model of the nematic-isotropic phase transition, whose mean-field approximation follows the Maier-Saupe theory. We show that fluctuations significantly change the order parameter, the transition entropy, and the precocity of the phase transition ($T_c$-$T^{\mathrm{*}}$)/$T_c$. A comparison with Monte Carlo simulation data shows that the fluctuation corrections remove most of the deficiencies of Maier-Saupe approximation.

We consider the dynamics of a quantum joint phase-space probability density in an exactly solvable model. The density is defined to be a true (i.e., positive) probability distribution for approximate (and thus simultaneously measurable) position and momentum variables. The dynamics of the quantum density is governed by a second-order partial-differential equation with non-positive-definite second-order coefficients. The quantum dynamics is contrasted with the dynamics of a similar joint density in a classical description. The non-positive-definite second-order terms in the quantum evolution equation, not present in the classical case, are responsible for quantum recurrences and prevent the appearance of fine-scale-structure ‘‘whorls’’ predicted in a classical description. The generation of ‘‘squeezing’’ in the model is also discussed.

We have used the theory presented by us in a recent paper to analyze a 1967 level-crossing experiment on the 2 ${}_{}{}^3{}_{}{}^{}P$ state of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ performed at the University of Michigan. Until now a consistent analysis of the experiment had not been possible because of inadequate development of the theory. The present analysis gives excellent agreement with the results of an atomic beam magnetic resonance experiment performed recently by us at Yale University. In fact we have used the combined data to give slightly improved results for four of the 11 relevant parameters. These four are the spin-antisymmetric contact hyperfine interaction constant [C’=-4327(69) MHz)], the 2 ${}_{}{}^3{}_{}{}^{}P$ dipole hyperfine interaction constant [D=-28.145(21) MHz], the 2 ${}_{}{}^3{}_{}{}^{}P$ tensor hyperfine interaction constant [E=-7.1353(38) MHz], and the orbital g factor [$g_L$=0.999 828 6(20)]. .AE

In this paper we present a new theoretical approach to the transient stimulated scattering of light. It was shown that a light-induced grating giving rise to stimulated scattering can be depicted in terms of nonlinear Volterra equations. Taking advantage of this approach we made a detailed study of the mechanism of transient stimulated Rayleigh scattering (SRLS), for which the pulse duration of laser light and the rise time of the isobaric modulations of the dielectric functions are of the same order. Assuming a small depletion of laser-light intensity only, we derive expressions describing the spatially and temporally resolved distributions of isobaric modulations of the dielectric function and of the optical field. From our analysis it follows that SRLS is generated only if a phase mismatch between the optical field and the light-induced isobaric grating occurs. Such a phase mismatch is due to the finite rise time of the grating. The calculations confirm that in absorbing liquids the appearing local heating determines the generation of isobaric gratings. Furthermore they put into evidence that in transparent liquids electrostriction and the optical Kerr effect become significant. The hitherto unexplained shift in the spectrum of SRLS in transparent liquids should now be related to the optical Kerr effect. It was also found that for some experimental conditions a significant part of SRLS reveals a wave front reversed to the incident laser field.

Hydrodynamic memory is known to induce long-time tails in the velocity and angular-velocity autocorrelation functions of Brownian particles and should affect dielectric response. In this paper we compute corrections to the linear dielectric response function due to hydrodynamic memory assuming only that the underlying stochastic process is Gaussian. Exact numerical results are obtained for a variety of fluid parameters. A new approximate expression for the dielectric response function is obtained, which gives better results than that obtained using a Fokker-Planck equation with a retarded kernel.

A phenomenological model has been devised for calculating the cold compression curves of metals up to the 10-TPa pressure region. The nuclear Grüneisen coefficient can also be correctly computed using this model. Shock Hugoniot curves were calculated for several metals using these cold compression curves to which the ion and electron thermal contributions were added. The results gave excellent agreement with experimental results for Pb, W, and Cd when the electron thermal portion is computed according to the Thomas-Fermi-Khirzhnits model. For Al, Cu, Fe, and Mo other electron thermal models must be used to give agreement with experimental results.

The two-dimensional random-parking limit is the area fraction of a plane covered by circles when the circles are added sequentially in a random way, without overlap, until no further circles can be added. As yet, no analytical solution exists for this limit. Several computer simulations and one experimental study have been carried out in the past, with results varying from 50% to 62% for the parking limit. In our work, we carry out an experimental determination of this parking limit, utilizing a spherical colloid that sticks irreversibly to a flat substrate. The experimental value obtained is 0.55±0.01, which agrees with two of the most recent, computer-generated values.

A closed-form expression is obtained for 〈r‖$G^j$V‖${\phi }_0$〉, where ${\phi }_0$ is the nonrelativistic hydrogenic ground state, V is a sum of static multipole perturbations of the form $A_{\mathrm{Ll}}$$r^L$$P_l$, L≥l, G=Q($E_0$-$H_0$${)}^{\mathrm{-}1}$Q is the projected static Green operator, and Q=1-‖${\phi }_0$〉〈${\phi }_0$‖ is the pro- jection operator. This method can be used iteratively to obtain the solution for &V &... &‖${\mathrm{\phi }}_0$〉, where {$V_m$,$V_{m\mathrm{-}1}$,...,$V_1$} is a set of static multipole perturbations. This quantity is of great interest in the computation of sum rules, high-order wave-function corrections due to multipole perturbations, and the adiabatic and nonadiabatic potentials in the scattering of a charged particle by a hydrogenic ion and in the interaction between a Rydberg electron and the core ion in high Rydberg states of heliumlike ions.

Estimates and critical stability thresholds characterizing the ground-state energies have been established with the help of a quasi- classical generalization of the virial theorem proposed previously. This enables us to evaluate ground-state energies in terms of the minima of corresponding Hamiltonian dispersions. Relativistic ($m_1$=$m_2$=$m_0$) and nonrelativistic two-body Hamiltonians with Coulomb and Yukawa potentials have been considered. For relativistic spin-(1/2) particles, as well as for the nonrelativistic ones, the calculations proceed by fixing to unity the underlying phase-space quantum.

A new method for accurately measuring the dispersion of the refractive index of gases is presented. The technique makes use of the phase-matching condition which applies to a sample subjected to a spatially periodic electric field in an electric-field-induced second-harmonic generation experiment. The attainable accuracy is comparable to that of interferometric methods, and this method may be extended to measure the refractive index in the vacuum-ultraviolet range. Results are given for the refractive index at λ≥229 nm for He, Ar, ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$.

A modified form of the Rayleigh-Schrödinger perturbation series which has been found very successful in the anharmonic-oscillator case is used for the screened-Coulomb-potential problem. It is shown that the solution of a cubic equation gives the range of the perturbation parameter for which one should expect a good approximation to the exact eigenvalue.

Convergence of the strong-potential Born (SPB) approximation as a function of the charges of the projectile and target is studied numerically. Time-reversal invariance (or detailed balance) is satisfied at sufficiently high velocities even when the charges are asymmetric. This demonstarates that the SPB approximation converges to the correct result even when the charge of the ‘‘weak’’ potential, which is kept to first order, is larger than the charge of the ‘‘strong’’ potential, which is retained to all orders. Consequently, the SPB approximation is valid for systems of arbitrary charge symmetry (including symmetric systems) at sufficiently high velocities.

The positron-impact excitation cross section for the n=2 level of helium has been calculated in the energy range 20–200 eV. A distorted wave obtained by solving an adiabatic equation has been used in the initial channel. The results are compared with the other existing theoretical predictions and measured values.

Three (1s,2s,2p) and five (1s,2s,2p,3s¯,3p¯) -state close-coupling methods have been employed to calculate the n=2 excitation cross sections of helium ion by positron impact. The effect of pseudostate is found to be very pronounced in the case of 1s-2s excitation.

Single-beam attenuation measurements of velocity-dependent total scattering cross sections are reported for metastable neon and argon on ground-state helium.

The recently formulated method of continued fractions for scattering problems is generalized (i) for the case of non-Hermitian potentials and Green functions and (ii) for the formulation through Volterra-type equations. A practically important possibility of potential scaling is also presented.

An atomic beam of H atoms was crossed by a pulsed beam of narrow bandwidth (Δν∼700 MHz) circularly polarized tunable vuv laser radiation at λ=121.6 nm. The atoms were excited into a single magnetic substate in the 2p ${\mathrm{}}^2$$P_{1/2}$ level and thus polarized. This polarization is transferred via hyperfine interaction to the nucleus. A second tunable uv laser served to ionize these atoms, thereby producing nuclear-spin-polarized protons with, theoretically, 100% degree of polarization. By changing the helicity of the circularly polarized vuv laser with a quarter-wave plate, the polarization direction of the protons is changed.

An exact solution for the collective spontaneous emission from an assembly of N identical two-level atoms, placed into a resonant damped cavity and excited to a symmetrical Dicke state with only one atom in the excited state, is derived.

Fully relativistic calculations are presented of the emission and absorption coefficients for synchrotron radiation propagating parallel to the magnetic field for loss-cone momentum distributions typical of magnetic-mirror-trapped electrons. Analytic results are obtained for step-function loss-cone distributions, while numerical results are provided for distributions with a smoother transition at the loss-cone boundary.