A new kind of spontaneous mode splitting leading to an oscillatory instability in emission is predicted for optically pumped molecular lasers, resulting from pump-field-induced Rabi splitting of the emission line shape. General conditions are presented for the occurrence of mode splitting in homogeneously broadened resonantly pumped systems. Results of detailed analysis pertaining to specific mid- and far-infrared lasing transitions in ${\mathrm{NH}}_3$ show that such effects could occur under typical experimental conditions.

Self-pulsing and deterministic chaos is observed in a single-mode, homogeneous-line, ${\mathrm{CO}}_2$ laser with an overall negative feedback, when the damping constant of the feedback loop is of the same order as the population decay rate. This represents a fundamental limitation of the general use of feedback schemes in high-stability laser applications. A theoretical model is shown to yield results in good agreement with the experimental ones, thus confirming the simple structure of the associated phase space.

We study experimentally the detailed structure of resonances in forced Rayleigh-Bénard convection in mercury. The resonances appear as Arnold tongues in the phase diagram of the system. We follow a particular tongue beyond the critical line where tongues start to overlap and find a period-doubling curve stretching over the entire tongue. Above this line there is a symmetry breaking with period-doubling cascades at the two sides of the tongue. We also observe a multitude of other periodic windows in this regime together with hysteresis effects caused by overlap of other tongues. We follow one of the period-doubling cascades and study the full scaling structure of the attractor at the onset of chaos by means of an f(α) spectrum of scaling indices. The experimental spectrum is, within error, the same as the universal spectrum calculated theoretically.

A renormalization procedure is constructed for incommensurate self-dual lattices. The renormalization transformation has a trivial fixed point describing the behavior of systems near the unperturbed systems, and a nontrivial fixed point corresponding to the critical case.

Crises in the rf-driven resistively-shunted-junction model of a Josephson junction are studied with an analog simulator. The features of crises are discussed via a return map and spectral diagram. Two types of boundary crises in a strange attractor following the Feigenbaum route are found. The crucial difference between the hopping processes induced by crises and Pomeau-Manneville intermittency is also indicated.

The starting point of this paper is a recent extension by Theophilou of the Hohenberg-Kohn-Sham (HKS) density-functional theory to ensembles of systems consisting of the M lowest eigenstates, equally weighted. As in the HKS theory the key quantities are the exchange-correlation energy, $E_{\mathrm{xc}{}^M\left[\mathrm{n}\right(\mathrm{r}\left)\right]}$, and potential, $v_{\mathrm{xc}{}^M(\mathit{r};[\mathit{n}\left(\mathit{r}\mathcal{’}\right)\left]\right)}$. The present paper provides expressions for these quantities, valid for systems of slowly varying density. Even for such systems, however, there are essential nonlocal effects. Nevertheless both $E_{\mathrm{xc}{}^M}$ and $v_{\mathrm{xc}{}^M}$ can be calculated in terms of quantities characteristic of appropriate uniform thermal ensembles. This theory is the analog of the ground-state local-density approximation and allows calculation of excited-state energies and densities.

The formation of pion molecular orbitals is investigated theoretically for an isolated system consisting of a pion and two nuclei whose separation corresponds to typical molecular bond lengths. The validity of the Born-Oppenheimer approximation is investigated and confirmed. The effect, not previously studied, of the electrons which are associated with the chemical bond between the pair of nuclei in a molecule has been examined. Although it is standard practice to neglect the effect of the molecular electrons on the captured pion, except possibly for a constant screening factor, we find that this effect is of major importance. In particular, this effect illuminates the process in which a pion, initially captured in hydrogen, is transferred to a neighboring heavier atom.

New data on the pionic charge-exchange reaction on bound hydrogen in selected organic molecules have been analyzed using two alternative models. It appears that the model which describes both the charge-exchange reaction and the atomic capture probabilities with the same set of parameters is capable of giving the most consistent representation of the data. Transfer of pions initially captured in hydrogen to a neighboring heavy atom is an important feature of this model. The transfer parameter is very accurately determined from the pion charge-exchange data.

A self-interaction-corrected local-density approximation to the exchange part of the exchange-correlation functional is proposed. The method is based on the Rae exchange energy of an N-electron homogeneous gas and it gives rise to a one-electron equation where the exchange potential is a function of the number of electrons present in each shell. The results of the calculations of usual atomic properties, such as total and one-electron energies, electron affinities, and ionization potentials, are also presented, as well as the comparison with other approximations. In general, a very good agreement is found between the results of the method of this paper and the Hartree-Fock values and, when it is combined with a standard expression for correlation, with the experimental results.

The method of shifted large-N expansion, where N is the number of spatial dimensions, is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential (-A/r) and the Yukawa potential B exp(-Cr)/r of arbitrary strength B and screening parameter C. It emerges that although the analytic expressions for the energy eigenvalues $E_n$,l yield quite accurate results for a wide range of n,l in the limit of very weak screening, the results become gradually worse as the strength B and the screening coefficient C increase. This happens due to the fact that the effective large-N potential becomes quite shallow in comparison to the true potential and the expansion parameter is not sufficiently small enough to guarantee the convergence of the expansion series for the energy levels. Furthermore, the present analysis reveals an intrinsic limitation of the technique in case of specific superposition of potentials: For certain choices of B, C, n, and l, the structure of the effective potential becomes such that it does not possess a local minimum and consequently the method turns out to be inapplicable to determining the corresponding bound-state energies. However, such a limitation does not persist for a simple screened Coulomb potential and reasonably accurate energy eigenvalues and bound-state normalizations are obtained for the neutral atoms. It is expected that the normalized bound-state wave functions obtained through the shifted large-N formalism may be useful in calculating the oscillator strength, bound-bound dipole transition matrix elements, etc. which have significant importance in atomic processes.

The phase-space distribution function corresponding to a ground-state density of a many-electron system proposed earlier [S. K. Ghosh, M. Berkowitz, and R. G. Parr, Proc. Natl. Acad. Sci. USA 81, 8028 (1984)] is employed to obtain a new approximate exchange-energy functional. This is K[ρ]=(π/2) F ${\rho }^2$(r)β(r)dr, with β(r)=1/kT(r), where T(r) is the local temperature previously defined; (3/2)kT(r) is the kinetic energy per electron at r. In Thomas-Fermi theory, β=5(3${\pi }^2$ρ${)}^{\mathrm{-}2/3}$, and this formula gives (10/9) times the classical Dirac formula. This shows why the α parameter in Xα theory is normally close to ((10/9))((2/3))=0.74. Numerical calculations on atoms are performed, giving excellent results, and the exchange hole associated with the new formula is studied in detail.

We present a new measurement of parity nonconservation in cesium. In this experiment, a laser excited the 6S→7S transition in an atomic beam in a region of static electric and magnetic fields. The quantity measured was the component of the transition rate arising from the interference between the parity nonconserving amplitude, ${\mathrm{scrE}}_{\mathrm{PNC}}$, and the Stark amplitude, βE. Our results are Im${\mathrm{scrE}}_{\mathrm{PNC}/\mathrm{\beta }=\mathrm{-}1.65\pm 0.13}$ mV/cm and $C_{2p}$=-2±2, where $C_{2p}$ is the proton-axial-vector–electron-vector neutral-current coupling constant. These results are in agreement with previous less precise measurements in cesium and with the predictions of the electroweak standard model. We give a detailed discussion of the experiment with particular emphasis on the treatment and elimination of systematic errors. This experimental technique will allow future measurements of significantly higher precision.

A new formulation of the many-electron correlation problem is presented based on the use of parastatistics. It is shown that second-order para-Fermi creation and annihilation operators, which correspond to the creation and annihilation of spin-averaged paraparticles, occur naturally for the spin-independent many-electron problem. Moreover, the spin-independent many-electron Hamiltonian is directly expressible in terms of the parafield operators. The structure of the general para-Fermi algebra is also investigated from the viewpoint of the pseudo-orthogonal group O(2n+1, 1). Finally, an explicit matrix representation for the para-Fermi algebra of order 2, which enables one to handle even particle-number-nonconserving operators, is obtained in a canonical U(n)-adapted basis.

The electron holography technique was employed to make a crucial test of the existence of the Aharonov-Bohm (AB) effect. The relative phase shift was measured between two electron waves passing through spaces inside and outside a tiny toroidal ferromagnet, covered completely with a superconductor layer and a Cu layer. Below the transition temperature the relative phase shift was measured to be 0 or π due to the magnetic-flux quantization in units of h/2e. The results directly demonstrated the existence of the AB effect even when the magnetic field was confined by the surrounding superconductor due to the Meissner effect and an electron beam was prevented from penetrating the magnet.

The moleculelike normal modes formed by a pair of correlated electrons are examined through analysis of their wave functions in a body frame of the atom. The quantum numbers used by Lin for the classification of doubly excited states are reinterpreted from the body-frame viewpoint, and their connections with the rovibrator model of Herrick and Kellman are identified. This analysis also sheds light on the limitations of the rovibrator model of two correlated electrons. Because electrons are light and are not localized like atoms in a molecule, departure from the rovibrator picture grows rapidly as the rovibrational energy rises. Other limitations of the rovibrator model of doubly excited states stem from the following facts: (1) the dominant contribution to the rotational constant comes from the bielectronic repulsion instead of the kinetic energy; (2) the rotational contraction and T doubling result from atomic shell structure. We also include a brief discussion of the correspondence between the molecular stretching modes and the radial correlations of two electrons. The systematics of autoionization widths with respect to the correlation quantum numbers are also considered.

Asymptotic adiabatic hyperspherical potential curves and wave functions for two-electron atoms valid through order 1/$R^5$ are obtained. The wave functions and potentials include the polarization potential characteristic of the polarized orbital approximation. Terms specific to the separation in hyperspherical coordinates are identified. The ground state is discussed in detail to illustrate the general theory.

Recently a method for solving the Baer-Kouri-Levin-Tobocman integral equations was presented and applied to several collinear reactive systems. The method is based on using a distortion potential in the unperturbed Hamiltonian so that the translational part of the Green’s function involves distorted elastic wave functions. In this work we report on a solution of these equations without a distortion potential so that the Green’s function involves free (asymptotic) translational wave functions. The advantages of using these functions is that a certain amount of computer work is saved because some of the integrations can be carried out analytically. A disadvantage is that the rate of convergence with respect to both vibrational and translational basis functions is slower than when the smooth distortion potential is employed. Two diagnostics of the accuracy of the results are found to be the size of the determinant of coefficients of the simultaneous algebraic equations and symmetry of the R matrix. In addition, it is found that if a distortion potential is used, one should choose it so that the resulting perturbation is made small and of least extent possible. This accelerates convergence of the solution with respect to basis size.

We carry out a systematic study of the stability of the electron density in the ground state of neon upon adding well-defined improvements in the corresponding configuration-interaction (CI) wave functions. We describe a precise manner of obtaining a CI wave function which yields the electron density with an error no larger than 0.5% for a wide range of values of r. An accurate analytical density is obtained thereby, and a comparison with the Hartree-Fock density is made. Contrary to common belief, we find rather large discrepancies at r>2 bohrs between our accurate density and those obtained from two other CI wave functions, which account for more than 85% of the correlation energy.

Electric field mixing and ionization effects on the dielectronic recombination of ${\mathrm{Mg}}^{+}$ are studied within the context of the standard resonance cross-section expression. The eigenvectors for the doubly excited Rydberg states were determined by diagonalizing a Hamiltonian matrix which includes internal electrostatic, spin-orbit, and external field Stark elements. Rydberg-state ionization rates are determined using the hydrogenic formula of Damburg and Kolosov. A detailed comparison is made between theory and the recent variable-field crossed-beam measurements of Müller et al.

Absolute K-shell ionization cross sections have been measured for thin targets of Al, Ti, and Cu for protons in the energy range 0.3–2.0 MeV and for thin targets of Ti, V, Cr, Fe, Ni, Cu, and Ag for oxygen ions in the energy range 1.36–6.4 Mev. The experimental results are compared to the perturbed-stationary-state (PSS) approximation with energy-loss (E), Coulomb (C), and relativistic (R) corrections, i.e., the ECPSSR approximation (Brandt and Lapicki), to the semiclassical approximation (Laegsgaard, Andersen, and Lund), and to a theory for direct Coulomb ionization of the 1sσ molecular orbital [Montenegro and Sigaud (MS)]. The proton results agree within 3% with empirical reference cross sections. Also, the ECPSSR provides best overall agreement for protons. For oxygen ions, ECPSSR and MS predict experimental results satisfactorily for scaled velocities ξ≥0.4. For lower scaled velocities, the experimental cross sections become considerably higher than theoretical predictions for Coulomb ionization. This deviation increases with increasing $Z_1$/$Z_2$; it cannot be explained by electron transfer to the projectile or by ionization due to target recoil atoms.