Experiments on two-dimensional systems of hard disks have been made in order to measure local fluctuations of thermodynamic quantities and long-range correlations in the presence of a temperature gradient.

Large-facetted monocrystals of blue phase I are grown and observed in coexistence with the isotropic liquid. Observations of this three-dimensional polyhedral habit, combined with a conjecture that facets perpendicular to screw axes are absent, are compatible with the $I\left(4_{1}32\right)$ space group for blue phase I. The (200) planes Bragg reflect approximately the same wavelength as the cholesteric spiral indicating that the blue phase I lattice constant is the cholesteric pitch even very close to the isotropic phase.

Sternheimer shielding factors are often obtained empirically by comparing nuclear electric quadrupole moment values derived from the hyperfine structure (hfs) of many-electron atoms with those determined by Coulomb-excitation or mesic-atom measurements. A large scatter in the resulting shielding factors arises from the lack of consistency in the approaches used in the analyses of the hfs. In the present work the radial hfs integrals are evaluated with a consistent configuration-average Dirac-Fock method. The scatter in the shielding factors obtained is reduced substantially and the results are in reasonable agreement with Sternheimer's original estimates.

We investigate the response of the electrons and the nucleus of an atom to a uniform electric field that oscillates in time. The standard calculation of the electric polarizability for a fixed-nucleus atom is generalized to the case that the nucleus is allowed to move. Our calculation provides a simple illustration of Ehrenfest's theorem and allows us to examine the validity of the Born-Oppenheimer approximation and the Feynman-Hellmann theory for nuclear dynamics. The dynamic form of the Feynman-Hellmann theorem is explicitly shown to describe correctly the dynamics of the nucleus to first order in the ratio of electron mass to nuclear mass. Explicit results are obtained to all orders in the electron- to nuclear-mass ratio in the case of the hydrogen atom. The concept of viscosity for a moving nucleus is also examined.

Using a coordinate transformation which regularizes the classical Kepler problem, we show that the hydrogen-atom case may be analytically solved via the phase-space formulation of nonrelativistic quantum mechanics. The problem is essentially reduced to that of a four-dimensional oscillator whose treatment in the phase-space formulation is developed. Furthermore, the method allows us to calculate the Green's function for the H atom in a surprisingly simple way.

The fine and hyperfine structures of the doubly excited, quintet states of the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{-}{}_{}{}^{}$ ion are of comparable magnitude. This leads to strong second-order hyperfine corrections and to significant distortion of the Landé interval rule. We discuss the results of our many-body calculations in this system, and also in the analogous lithium quartet systems for which experimental data exist. We find that the hyperfine matrix elements of these few-electron systems may be adequately computed without detailed consideration of the electron correlations. Fine structure is significantly affected by such correlations. Experimental verification of the ${\mathrm{Li}}^{-}$ structure is underway.

Relativistic equal-time wave equations obtained from field theory which describe bound states of $N$ Dirac particles inevitably involve Casimir-type positive-energy projection operators ${\Lambda }_{+}\mathrm{}\left(i\right)\mathrm{}$. For $N>\mathrm{}2\mathrm{}$, these operators are vital if the equations are to admit normalizable solutions. Such equations, which are of integro-differential form, have been used in the past to obtain relativistic corrections to, e.g., level shifts for a variety of simple atomic systems, and to provide a theoretical basis for the Dirac-Hartree-Fock type of equations for many-electron atoms. Here we initiate a study of such equations without making an expansion in powers of $\frac{v}{c}$. We work in momentum space, where the free-particle projection operators are simple functions of $\overrightarrow{\mathrm{p}}$ and the wave equation is essentially no more complicated than in the nonrelativistic case. In the present paper we describe techniques for finding the eigenvalues of $h_{+}\mathrm{}(1,2)=h_D\mathrm{}\left(1\right)+h_D\mathrm{}\left(2\right)+{\Lambda }_{++}V{\Lambda }_{++}$, where $h_D\mathrm{}\left(i\right)\mathrm{}$ is the free-particle Dirac Hamiltonian and $V$ is a local potential with a ${|{\overrightarrow{\mathrm{r}}}_1-{\overrightarrow{\mathrm{r}}}_2|}^{-1\mathrm{}}$ singularity. Numerical results are presented for the case of a pure Coulomb potential and a Coulomb-plus-Breit potential, for a wide range of mass ratios $\frac{m_1}{m_2}$ and coupling strength $\frac{e_1{e}_2}{4\pi }$. In the $m_2=\infty$ limit, comparison is made with the Dirac equation. The results are used to discuss the magnitude of level shifts associated with virtual-pair production in such two-body systems.

The hyperfine structure of the $4s$, $4p$, and $3d$ states in ${\mathrm{Ca}}^{+}$ has been evaluated with the use of many-body perturbation theory. Core-polarization and correlation effects have been included by solving inhomogeneous one- and two-particle differential equations. By solving these equations iteratively, these effects have been treated also to higher orders. Certain correlation effects have been accounted for by modifying the valence orbitals to approximate "Brueckner orbitals." Relativistic effects were estimated on the basis of relativistic calculations including core polarization. The final results for ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ca}$ are $A\left(4^2{S}_{\frac{1}{2}}\right)=-819\mathrm{}$ MHz, $A\left(4^2{P}_{\frac{1}{2}}\right)=-148\mathrm{}$ MHz, $A\left(4^2{P}_{\frac{3}{2}}\right)=-30.9\mathrm{}$ MHz, $\frac{B\left(4^2{P}_{\frac{3}{2}}\right)}{Q}=155\mathrm{}$ MHz/b, $A\left(3^2{D}_{\frac{3}{2}}\right)=-52\mathrm{}$ MHz, $\frac{B\left(3^2{D}_{\frac{3}{2}}\right)}{Q}=68\mathrm{}$ MHz/b, $A\left(3^2{D}_{\frac{5}{2}}\right)=-5.2\mathrm{}$ MHz, and $\frac{B\left(3^2{D}_{\frac{5}{2}}\right)}{Q}=97\mathrm{}$ MHz/b.

Electron-capture and electron-loss cross sections are reported for a large number of combinations of projectile species (C, Ar, Fe, Nb, and Pb), target gases (${\mathrm{H}}_2$, He, ${\mathrm{N}}_2$, Ne, Ar, and Xe), projectile charge states (6+ to 59+), and energies (310 keV/amu to 8.5 MeV/amu). These measured cross sections are compared with published theoretical calculations and scaling rules.

Experimentally and theoretically determined differential and total cross sections are reported for excitation of atomic hydrogen to its $n=2\mathrm{}$ level by 25-150-keV hydrogen molecular ions. The differential cross sections decrease 3-4 orders of magnitude over the measured center-of-mass scattering-angular range from 0 to 4.5 mrad. The results of a first Born approximation and two other theoretical calculations based upon the Glauber approximation are presented and compared with the experimental results. Both calculations based on the Glauber approximation agree fairly well with the experimental results. The Born approximation agrees moderately well with the experimental results at the very small scattering angles but is well below the experimental results at the larger scattering angles. None of the theoretical calculations presented agree well with the total cross section. However, the results for the total cross section of the two calculations based on the Glauber approximation agree with the experimental results in curve shape better than the Born-approximation results.

The total depopulation cross sections by ${\mathrm{N}}_2$ of high rubidium Rydberg states, $\mathrm{Rb}\mathrm{}\left(\mathrm{ns}\right)\mathrm{} \mathrm{}(n=25-46\mathrm{})\mathrm{}$ and $\mathrm{Rb}\mathrm{}\left(\mathrm{nd}\right)\mathrm{} \mathrm{}(n=23-44\mathrm{})\mathrm{}$, have been measured using time-resolved field ionization technique and compared to previous results obtained on the quenching of $\mathrm{Rb}\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ by CO. It is shown that the $\mathrm{Rb}\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ depopulation by ${\mathrm{N}}_2$ is much less efficient than the $\mathrm{Rb}\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ depopulation by CO and leads mainly to the quasielastic process of angular momentum mixing via the short-range interaction between the quasifree Rydberg-state electron and the molecule. It is clearly demonstrated that the presence of a permanent dipole in CO changes the collisional processes drastically. The agreement between experimental and theoretical predictions based on the impulse approximation is quite satisfactory.

Charge transfer from $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ to a fully-stripped ion projectile $X^{+Z}$ (of atomic number $Z$) occurs mainly to near-resonant levels ($n\lesssim Z$) of the captor, for low to intermediate energies ($E15-20$ keV/amu. To calculate capture cross sections for individual states, it is necessary to solve not only the molecular-state close-coupling problem for the primary charge transfer, but also to treat effects of long-range dipole and quadrupole couplings produced by the receding proton among the $n^2$ asymptotically degenerate levels of the captor with a given principal quantum number $n$. A simple and computationally efficient solution to this secondary coupling problem is given here, based on the exact solution for dipole couplings in a hydrogenic ion given previously by Demkov and co-workers. We show that the important effects of the quadrupole couplings are diagonal in the dipole interaction representation and that the residual effects are accurately computed with the first Magnus approximation. By this approach the entire secondary coupling problem (for any $n$) is reduced to computation of the $n\times n$ matrix for a single finite rotation, some simple numerical quadratures and a few matrix multiplications.

The eigenphase sum for electron—polar-molecule scattering admits separation into a part which is wholly dependent on the long-range field and a part which reflects other interactions. Closed-form expressions are given for the zero-energy eigenphase sum for diatomic molecules and simple polyatomic molecules in the fixed-nuclei approximation. A general framework for performing bodyframe scattering calculations is presented.

Differential cross sections have been measured for the electron-impact ionization of atomic hydrogen, using the ($e$, $2e$) technique with coplanar asymmetric kinematics. The experiments were performed at an incident energy of 250 eV with the slow outgoing electron being detected at energies of 5, 10, and 14 eV, for scattering angles of the fast outgoing electron of 3°, 5°, and 8°. The data are compared with differential cross sections calculated with use of the factorized distorted-wave impulse approximation, the plane-wave impulse approximation, and three recent Born-approximation calculations, consisting of first-order Born, second-order Born, and eikonal Born series treatments. In the distorted-wave impulse approximation calculations we investigate the effect of using different descriptions for the fast outgoing electron. Comparison of the data and the calculated cross sections indicates reasonable agreement with the distorted-wave impulse calculations, and good agreement with the second-order and eikonal Born series calculations.

The Lyman-α and adjacent dielectronic satellite lines have been observed with high spatial and spectral resolution from laser-irradiated aluminum tracer dot targets at 1.06, 0.53, and 0.27 μm wavelength. The $1s2p {}_{}{}^3{}_{}{}^{}P-{2p}^2{}_{}{}^3{}_{}{}^{}P$ to $1s2s {}_{}{}^3{}_{}{}^{}S-2s2p {}_{}{}^3{}_{}{}^{}P$ line-intensity ratio strongly increases for visible and uv laser wavelengths, indicating that time-integrated spectroscopic emissions from satellite lines probe higher electron densities under these laser-irradiation conditions. Numerical simulations including ground-state, singly excited and doubly excited levels of configurations $2l_{a}2l_b$ and $2l_{a}3l_b$ in a collisional-radiative equilibrium model including photon-pumping effects are in good agreement with experimental data. Plasma electric field broadening of satellite lines is also exhibited at high electron densities.

The construction of physical occupation and transition probabilities in non-Hermitian, effective-Hamiltonian models of coupled near-resonant discrete states which decay to a continuum is analyzed. We consider for definiteness the particular physical example of atomic multiphoton ionization. The possibility of finite duration and arbitrary modulation of this interaction, and of the subsequent ionization and/or decay, in such a system allows us to invoke "adiabatic switching" considerations in conventional $S$-matrix theory. The effective Hamiltonian $\hat{H}\mathrm{}\left(t\right)\mathrm{}$ is derived for both stationary and time-dependent Schrödinger equations. These derivations yield the same effective $\hat{H}\mathrm{}\left(t\right)\mathrm{}$, and further reveal that this operator is associated with discrete-state-projected "incoming" scattering states. The Hermitian conjugate operator ${\hat{H}}^{†}\mathrm{}\left(t\right)\mathrm{}$ is similarly shown to be associated with discrete-state "outgoing" scattering states. This shows that effective-Hamiltonian theories are intrinsically $S$-matrix theories. This fact, in turn, is employed to construct transition amplitudes. The possibility of resonance in the atom-field interaction requires that both the projected incoming states and projected outgoing states be employed in this construction. The projected incoming and outgoing states in the (discrete) bound space are quite conveniently described by effective time-dependent Schrödinger equations, supplemented by initial- and final-state boundary conditions. The fact of independent-exponential decay from each mode throughout the history of the interaction, for an arbitrary initial superposition state, in the adiabatic limit, suggests a practical construction for intermediate-time bound-state probabilities. This construction permits the formal definition of individual-state probabilities, which satisfy a generalized adiabatic theorem, and leads to the satisfying result that the total bound-state probability at all intermediate times is the sum of complex-mode probabilities. In marked contrast to the conventional norm-of-state definition of nonionization probability, this sum does not have oscillations at intermediate times, in the limit of adiabatic modulation of the interaction. Superposition-state probabilities, however, exhibit oscillations at intermediate times. The resulting non-Hermitian quantum dynamics is especially suited, and even essential, for an accurate description of near-resonance ionization. Precise matching of the time-dependent $\hat{H}\mathrm{}\left(t\right)\mathrm{}$ and ${\hat{H}}^{†}\mathrm{}\left(t\right)\mathrm{}$ with bases of their instantaneous eigenstates is required by approximate unitarity in the discrete decaying space, for a consistent theory. We illustrate these considerations in a general way in the context of resolvent-operator techniques. The implementation of the theory in both its time-dependent and stationary-state formulations is presented in an Appendix, for the completely general two-state non-Hermitian Hamiltonian. The results of these formulations are found to agree, in the adiabatic limit, to all orders in the non-Hermitian interaction. The utility of direct diagonalization of the effective $\hat{H}\mathrm{}\left(t\right)\mathrm{}$, advocated by Armstrong and Baker, is transparent. The overall context of interpretation of their earlier work is, however, significantly altered. Similar considerations apply for nonswitchable interactions, such as for $K$-meson decays. These results represent a practical generalization of quantum mechanics to non-Hermitian systems. The utility, and the necessity, of such a generalization has considerable theoretical interest, and direct experimental implications.

We have studied a special class of time-symmetric pulses interacting with a two-level system. These pulses are built out of a class of asymmetric functions for which the analytic description of the interaction was possible. The time behavior of these pulses is given. We have evaluated the transition probability in a closed form. These pulses can be used to simulate the familiar Lorentzian and Gaussian pulse shapes remarkably well. Therefore, they can be used in computing the overall features of the interaction process. Comparisons of the transition amplitudes are made between the closed-form solution and numerically calculated Lorentzian and Gaussian cases.

The parameters of adiabatic rapid passage (ARP) in the ground-state 0-0 hyperfine transition of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ have been investigated. These parameters relate to how adiabatic and how rapid the passage through resonance must be in order to maximize the degree of population reversal. We find both experimentally and theoretically that the adiabaticity requirement is rather weak; and that once satisfied, it is more important to pass through the resonance rapidly. Furthermore, interpreting our results in the Bloch-vector model of ARP, we find that the Bloch vector is only required to precess a half revolution about the effective field in order to follow a 90° change in the direction of that field. The applicability of the present results to ARP in general is discussed.

The Xe $5s$, $5p$ photoelectron satellite spectrum has been studied in the photon-energy range from 28 to 75 eV with the aid of synchrotron radiation. This range includes the Xe $5s$ Cooper minimum, and the cross sections and angular distribution data demonstrate the importance of the strong two-electron channels in the region where the $5s$ cross section is small. Although the behavior of the satellites was not recorded over the $4d$ maximum, the data near 75 eV show an enhancement in the cross section in that region. The data underline the need of including the two-electron channels explicitly in the theory over a wide photon-energy range.

Near-resonant four-wave light mixing in Na vapor with inert buffer gases reveals collision-induced coherences when the difference frequency between two incident light beams equals the hyperfine splitting or the Zeeman splitting between two states of the $3{}_{}{}^2{}_{}{}^{}S$ ground-state manifold. The Doppler broadening of the corresponding resonances decreases with increasing buffer-gas pressure. The width of the resonances becomes significantly narrower than the spontaneous linewidth of the near-resonant intermediate state and is determined by spin-exchange collisions between ground-state atoms. The dependence of the intensity of these collision-induced resonances on buffer-gas pressure and detuning from one-photon resonances is measured. Selection rules for various polarizations of the incident light fields and directions of an externally applied magnetic field are established.