An ac calorimetric technique has been used to investigate the nematic (N)–smectic-C (SmC) transition near the N-SmA-SmC multicritical point in a mixture of heptyloxypentylphenylthiolbenzoate and octyloxycyanobiphenyl (7¯S5+8OCB). The heat-capacity data are well described by a Landau model in which the first-order character is very weak. Thus there is a classical tricritical point along the SmC transition line at (or very close to) the N-SmA-SmC point. No calorimetric indications of a biaxial N’ phase were observed.

Asymptotically close to the Nth-order multicritical point of an N-phase system, there are N-1 sum rules involving the mean-field susceptibilities measured in each of the coexisting phases. These sum rules provide the experimentalist a convenient andn stringent test of the theory. In particular, they facilitate the detection of nonclassical effects, especially valuable for N>3 where the fluctuation effect is dominated by the classical contribution for three-dimensional systems.

Various approximations and models for Hartree-Fock kinetic energy T and Hartree-Fock exchange energy K are systematically derived with a minimum of assumptions and comparatively studied by testing on atoms. A Gaussian ansatz for the spherical average of the first-order density matrix and the uniform-gas ansatz are shown both to lead to the same formulas for T and K except for the values of certain numerical coefficients. Without any assumption one gets in all cases T=(3/2) F ρ(r)[1/β(r)]dr, where β(r) is the local temperature parameter of Ghosh, Berkowitz, and Parr [Proc. Natl. Acad. Sci. USA 81, 8028 (1984)]. The Gaussian ansatz gives K=(π/2) F ${\rho }^2$(r)β(r)dr, while the uniform-gas ansatz gives K=(9π/20) F ${\rho }^2$(r)β(r)dr. Assuming further only the existence of a local equation of state of the form β=β(ρ), one then gets, by imposing the exact normalization condition for the first-order density matrix, from the Gaussian ansatz T=(3π${/2\mathrm{}}^{5/3}$) F ${\rho }^{5/3}$(r)dr and K${=2\mathrm{}}^{\mathrm{-}1/3}$ F ${\rho }^{4/3}$(r)dr, respectively, 3.4% and 7.5% larger than the Thomas-Fermi-Dirac T and K which result from the uniform-gas ansatz. Numerical evidence is presented that shows preference for the Gaussian ansatz. A modified Gaussian ansatz also is examined.

We show that the physical quantities of an A-fermion system expressed by means of integrals of powers of the single-particle density ρ(r) are bounded by any kth moment around the origin 〈$r^k$〉 of ρ and A in a simple manner. As applications, the kinetic and semiclassical exchange energies of a neutral atom (A=Z) turn out to be bounded from below by 0.2184$Z^{5/3}$〈$r^{\mathrm{-}1}$${〉}^2$ and from above by 0.3046$Z^{4/3}$〈r〉, respectively. Comparison of these bounds with the microscopic values of the corresponding quantities is made. Similar bounds for the same quantities in nuclei are also given and analyzed.

The three-dimensional trajectories of a neutron in an average deformed potential are studied for two different potentials with prolate or oblate ellipsoidal deformations. The simplest one is a simple cavity which is shown to be integrable. The motion is studied and is found to be separable in spheroidal coordinates. It is shown that the phase space of an oblate cavity may contain a separatrix which is associated with the crossing of the focal circle while the prolate phase space does contain a separatrix only for the planar trajectories. By using arguments based on a uniform semiclassical approximation, it is shown that the quantum-energy-level spectra present indeed a difference between prolate and oblate shapes corresponding to the crossing of this separatrix. The second potential studied, the Buck-Pilt potential, has a diffuse surface. When it is deformed it becomes unintegrable. For this potential Poincaré surfaces of section are drawn. Large regular regions are shown in which the organization of the phase space is that of the cavity. Chaos and nonlinearities are also seen. Consequences of the existence of the regular regions similar to the cavity are drawn for the energy spectrum.

Evidence has been discovered for the violation of microscopic causality in the Compton scattering of light by protons. A calculation of the degree of acausality expected on the basis of a semiclassical model is found to be in quantitative agreement with the data.

Further evidence is presented for the violation of causality in the Compton scattering of light by protons for the energy region near the Δ(1232) resonance. A very simple precausal model has been found to reproduce both the photon absorption and scattering cross sections. Since dispersion relations are significantly violated in the same energy region, it is concluded that no causal model can fit the data as well as the precausal model.

The multiconfiguration Hartree-Fock theory and many-body perturbation theory are combined in a calculation of the correlation energy of the ground state of the neutral beryllium atom. For this purpose the two-component Be multiconfiguration Hartree-Fock wave function is treated as a reference state and perturbation theory is used to systematically improve upon the accuracy of this function. The correlation energy of each pair of occupied orbitals is determined by solving numerically a coupled set of two-particle inhomogeneous equations. A detailed comparison is made with other beryllium calculations.

The nonlinear response of an arbitrary electronic system to a time-dependent perturbation is treated within the density-functional formalism. Expressions for quadratic and cubic responses for a system of independent electrons are obtained in a form suitable for numerical calculations. The frequency dependence of the linear and cubic electric susceptibilities of rare-gas atoms are computed and compared with experiment.

A new version of perturbation theory is described. It extends the admissible class of Hamiltonians $H_0$ to nondiagonal matrices via use of the nondiagonal unperturbed propagators. Numerically, its efficiency is demonstrated on the standard anharmonic-oscillator example where it works as an effective resummation technique.

The formal quantum-mechanical treatment of rearrangement collisions in the presence of a strong laser field is developed. The analysis is restricted to structureless projectiles, hydrogenic target atoms, and a homogeneous, single-mode linearly polarized laser field, taken in the dipole approximation. The external field is found to interfere with the rearrangement process through several mechanisms, some of which are not present in field-assisted direct collisions. One new parameter comes from the difference of continuum Stark shifts. A second parameter relating to the transfer of the electron arises from a field-dependent shift of the particle momentum. The familiar notions of exothermic and endothermic reactions appear in a new perspective; namely, they transform into the reactions able to yield prevalently either emission or absorption of laser photons.

An electron spectroscopy study of ${\mathrm{H}}^{\mathrm{-}}$-Kr collisions in the 20–500-eV collision energy range revealed the excitation of (2$s^2$${)\mathrm{}}^1$S, (2$p^2$${)\mathrm{}}^1$D, and (2s2p${)\mathrm{}}^1$P states of ${\mathrm{H}}^{\mathrm{-}}$ and of the (5$s^2$${)\mathrm{}}^2$$P_{3/2}$,1/2 ${\mathrm{Kr}}^{\mathrm{-}}$ state. The angular distribution of electrons produced from the decay of these states is reported. An anisotropic distribution for the (2$s^2$${)\mathrm{}}^1$S state is observed at these energies as was previously reported for ${\mathrm{H}}^{\mathrm{-}}$ collisions with He, Ar, and ${\mathrm{H}}_2$ by Risley and co-workers [Phys. Rev. A 9, 1115 (1974) and IEEE Trans. Nuc. Sci. NS26, 1027 (1979)]. Relative cross sections for the excitation of these states are deduced from the angular distributions.

In this paper we report cross sections for electron-impact excitation of the X ${\mathrm{}}^1$${\Sigma }_g^{+}$→B ${\mathrm{}}^1$${\Sigma }_u^{+}$ transition in ${\mathrm{H}}_2$ for collision energies of 15, 20, and 30 eV. For this dipole-allowed transition with its associated long-range potential, the contributions of the more strongly scattered low-angular-momentum partial waves to the cross section were obtained from a two-state Schwinger multichannel calculation, and a modified Born-closure scheme was used to include the contributions from the remaining weakly scattered partial waves. Agreement between the calculated differential cross sections and available experimental data is encouraging.

Experimental cross sections for ionization of helium by projectile ions with charge Z up to Z=44 are presented at a fixed velocity v=7.48 a.u. corresponding to 1.4 MeV/amu. Total cross sections, summed over projectile charge states, for single ionization, ${\sigma }^{+}$, are compared to Born and Glauber calculations for point projectiles of charge Z. The Glauber calculations give a better fit to the Z dependence of the single-ionization cross sections than do the Born calculations. For double ionization, the ratio of ${\sigma }^{2+}$/${\sigma }^{+}$ increases as $Z^2$ for the smaller Z and less rapidly than $Z^2$ for larger Z projectiles, suggesting that the so called ‘‘direct’’ mechanism for double ionization is dominant, but that the first Born approximation is breaking down for the larger Z.

Within the framework of multichannel quantum-defect theory, Seaton’s scrR matrix is transformed to a modified reactance matrix with null submatrices for the open-open and degenerate closed-closed channel couplings. Using this coupling matrix, parametric expressions for the photoionization cross section in the autoionization region analogous to Fano’s resonance formula are derived for four cases: (i) many open channels and one closed channel, (ii) many open channels and many closed channels which do not interact either directly or through open channels, (iii) one open channel and many degenerate closed channels, and (iv) one open channel and two nondegenerate closed channels. The utility of the derived expressions in fitting experimental data is demonstrated using absorption spectra of Xe, Ge, Ca, and Sr.

The effects of the finite correlation time of the external modulation on the secondary-emission spectra are clarified emphasizing the deviation from the motional narrowing limit or the impact approximation in the case of large off-resonance excitation. The dependences of the excitation spectrum of the secondary emission on the modulation parameters and on the inhomogeneous broadening are studied systematically. It is found that the excitation spectrum of the luminescence shows a faster decrease than that of the Raman scattering as the off-resonance frequency increases. The present theory is relevant for explaining the recent experiment by Watanabe, Kinoshita, and Kushida [Chem. Phys. Lett. 126, 197 (1986)] on the β-carotene in solutions. A general theory of the time-resolved spectra of the secondary emission is formulated to incorporate the effect of the finite correlation time. The luminescence component shows a slow temporal decay with the longitudinal relaxation rate. It is found for the first time that the difference is unexpectedly large between the transient behavior of the luminescence intensity and that of the intermediate-state population for the slow-modulation regime and that the difference indicates the effect of finite correlation time of the frequency modulation. On the other hand, the transient behavior of the Raman scattering contains a fast component that follows the envelope of the excitation-pulse intensity and the same slow component as the luminescence. The ratio of the slow component to the total intensity depends sensitively on the modulation parameters and the off-resonance frequency. The modulation parameters of the system in question can be estimated from these dependences in combination with the spectral characteristics of the emission under stationary excitation.

We studied the $m_l$=0 photoionization channel of H(n=2, $m_l$=0) red and blue states in a dc electric field F theoretically and experimentally in the energy region between the two ionization thresholds: the Stark-induced classical threshold at E=-2 √F and the threshold of the field-free atom at E=0. We find that the ionization yield via the ‘‘rapidly’’ ionizing $m_l$=0 channels concentrates at the two thresholds. Such concentration has not been observed in similar experiments on complex atoms due to a large degree of electron scattering from the ion core that produces significant amounts of mixing among the excitation amplitudes and among the ionization channels. Our results show that the hydrogenic Stark levels of fixed principle quantum number n become sharper as their parabolic quantum number $n_1$ increases. On the other hand, the levels of fixed $n_1$ get wider as their quantum number n increases. Moreover, our results show a remarkable property: The ratio of the cross sections from the red and from the blue $m_l$=0 states of n=2 fall on a universal curve when plotted as a function of $Z_1$, the fraction of the nuclear charge that drives the bound motion. Also, the ratio is found to be larger than 1 in two regions where $Z_1$=0–(1/4) and (1/2)–(3/4), less than 1 in the rest of the $Z_1$ regions, $Z_1$=(1/4)–(1/2) and (3/4)–1, and is equal to unity at the common boundaries at $Z_1$=(1/4), (1/2), and (3/4), thus indicating special properties of these fractional charges.

Active and passive interferometers (as used, for example, for rotation-rate sensing or gravita- tional-wave detection) are known to have essentially the same ultimate sensitivity, although they appear to work differently, have signals of different sizes, and be limited by different kinds of noise (shot noise for the passive case, spontaneous emission for the active case). This paper explains this remarkable coincidence. The underlying physics common to both systems is brought forth and the role of the losses in limiting the sensitivity is clarified. The possibility of squeezing the field is explicitly considered; it is shown when it can or cannot help, and why.

Laser light is known to have a very small field linewidth (proportional to the inverse pump rate, far above threshold), while the photon intensity correlation decays quickly (intensity linewidth proportional to the pump rate). Here we study the polarization-symmetric laser as a device to provide a small photon linewidth, proportional to the inverse pump rate. The physical explanation is discussed, and the behavior throughout the whole nonlinear threshold range is reported.

Following a suggestion by Wheeler, we have performed delayed-choice experiments in both the spatial and time domains. For the first experiment we use a low-intensity Mach-Zehnder interferometer, and for the second the technique of quantum beats in time-resolved atomic fluorescence. The results obtained show no observable difference between normal and delayed-choice modes of operation, in agreement with the predictions of quantum mechanics.