The full effect of adiabatically varying Hamiltonians on systems prepared in eigenstates of the stationary Hamiltonian often includes geometric Berry’s phases. For degenerate systems these effects may result in transitions between distinct degenerate eigenstates that can be described in terms of a non-Abelian gauge potential. I demonstrate the explicit dynamic origin of such transitions between degenerate angular-momentum sublevels in an atom that is subject to collinear electric and magnetic fields that rotate adiabatically. The origin of the effects becomes clear when eigenstates of the total Hamiltonian, which includes the rotating fields, are calculated. The total Hamiltonian removes the degeneracy, and the eigenstates are in some cases linear combinations of the angular-momentum sublevels. Thus a system prepared in a specific sublevel may not remain in that sublevel, and the transition probability is exactly that given by an analysis of the geometric phase.

The perturbative-variational method is used with a nonorthogonal basis set whose elements are combinations of two harmonic-oscillator functions symmetrically shifted around the origin in order to approximate the eigenvalues and eigenfunctions of the two-well anharmonic-oscillator potential [V(x)=-${\mathit{Z}}^2$${\mathit{x}}^2$+${\mathit{x}}^4$ with ${\mathit{Z}}^2$>0]. This basis set is rather adequate for this potential and allows one to calculate not only the ground-state energy but also the energy of the excited states with very high precision.

Different neutron-interferometric setups for the joint detection of ‘‘path’’ and ‘‘interference’’ are investigated from the point of view of the theory of joint measurement. It is seen that this joint detection can only be done with limited quality. This substantiates Bohr’s insistence that the impossibility of jointly seeing interference and path is a consequence of the uncertainty principle. A connection between joint measurement and Wigner distributions is noted.

We have proposed a formal theory for the continuous measurement of relativistic quantum fields. We have also derived the corresponding scattering equations. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of our theory. A possible example of the relativistic continuous measurement has been outlined in standard quantum electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields.

We show that particle trajectories in the Wilson cloud chamber are straight and stable, using perturbation theory and generalized coherent states. The model consists of an incoming particle, many molecules, and the immediate environment of each molecule acting as a detector. Each such detector has many harmonic oscillators whose states are totally described by generalized coherent states, because of which particle trajectories are almost stable. That is, if a molecule is ionized through its interaction with the particle, the ionized excited state does not return to the lower states. Many molecules can be ionized when the line joining them is practically parallel to the direction of motion of the particle. However, when the molecules do not lie on a straight line, all of them cannot be ionized. The particle trajectory that is made up of the ionized molecules, therefore, is straight.

The nonadiabatic Berry’s phase is investigated for a quantum system with a dynamical semisimple Lie group within the framework of the generalized cranking approach. An expression for nonadiabatic Berry’s phase is given, which indicates that the nonadiabatic Berry’s phase is related to the expectation value of Cartan operators along the cranking direction in group space, and that it depends on (i) the geometry of the group space, (ii) the time evolution ray generated by the Hamiltonian (i.e., by the dynamics) in some irreducible representation Hilbert space, and (iii) the cranking rate. The expression also provides a simple algorithm for calculating the nonadiabatic Berry’s phase. The general formalism is illustrated by examples of SU(2) dynamic group.

The time-dependent Schrödinger equation for a spin particle in a rotating magnetic field is solved analytically by the cranking method, and the exact solutions are employed to study the nonadiabatic Berry’s phase. An alternative expression for Berry’s phase is given, which shows that Berry’s phase is related to the expectation value of spin along the rotating axis and gives Berry’s phase a physical explanation besides its gauge geometric interpretation. This expression also presents a simple algorithm for calculating the nonadiabatic Berry’s phase for Hamiltonians that are nonlinear functions of the SU(2) generators. It is shown that nonadiabaticity alters the time evolution ray and in turn changes its Berry’s phase. For the SU(2) dynamical group, the nonadiabatic effect on Berry’s phase manifests itself as spin alignment (a phenomenon in nuclear physics), and spin-alignment quantization (observed recently in high-spin nuclear physics) is related to Berry’s-phase quantization.

From Weinberg’s nonlinear wave equation we derive the nonlinear generalization of the optical Bloch equations with radiative damping. We compare these equations with Fermi’s nonlinear radiation-reaction theory and with Jaynes’s neoclassical theory. The nonlinear constant ε, which is small if compared to the binding energy per nucleon, can be comparable to the radiative lifetime of an excited state of an ion stored in an ion trap. We show that in such a case the nonlinear modification of the optical Bloch equations can lead to large-scale effects in coherent transients, in atomic quantum jumps, and in resonance fluorescence and can modify the emission line shape.

We reexamine certain reported resonances in atomic systems containing a positron (${\mathrm{Ps}}^{\mathrm{-}}$,${\mathit{e}}^{+}$H) using both the stabilization method and the complex-rotation method. The trial functions chosen are of the traditional Hylleraas type with two nonlinear parameters and up to 372 linear terms. Our results do not verify the existence of these resonances but hint at the existence of similar resonances in ${\mathit{e}}^{+}$${\mathrm{He}}^{+}$.

The Rayleigh-Ritz variational method is used with a multiconfiguration-interaction function to obtain the nonrelativistic energies and wave functions of the triply excited 2${\mathit{p}}^2$np ${}_{}{}^4{}_{}{}^{}$S° (n=2,3,4) and 2${\mathit{p}}^2$3p ${}_{}{}^2{}_{}{}^{}$S° states and also the doubly excited 1s2pmp ${}_{}{}^4{}_{}{}^{}$P (m=2,3,4), 1s2${\mathit{p}}^2$ ${}_{}{}^2{}_{}{}^{}$P, [(1s2p${)}^3$P,3p${]}^2$P, and [(1s2p${)}^1$P,3p${]}^2$P states for atomic systems with nuclear charges from Z=3 to 10. The relativistic and mass polarization corrections are evaluated via first-order perturbation theory, and the resulting relativistically corrected energies are used to compute transition wavelengths for 2${\mathit{p}}^2$np ${}_{}{}^{4,2}{}_{}{}^{}$S°→1s2pmp ${}_{}{}^{4,2}{}_{}{}^{}$P. The fine structure of the 1s2pnp ${}_{}{}^{4,2}{}_{}{}^{}$P states is also calculated with first-order perturbation theory. The nonrelativistic wave functions are used to compute the electric-dipole transition probabilities for 2${\mathit{p}}^2$np ${}_{}{}^{4,2}{}_{}{}^{}$S°→1s2pmp ${}_{}{}^{4,2}{}_{}{}^{}$P; this information is then used to compute the lifetimes for the 2${\mathit{p}}^2$np ${}_{}{}^{4,2}{}_{}{}^{}$S° states and the branching ratios for the transitions to the 1s2pmp ${}_{}{}^{4,2}{}_{}{}^{}$P levels. Intermediate-coupling effects for the 2${\mathit{p}}^3$ ${}_{}{}^4{}_{}{}^{}$S°${,}^2$D°${,}^2$P° and the 1s2${\mathit{p}}^2$ ${}_{}{}^4{}_{}{}^{}$P${,}^2$D${,}^2$P${,}^2$S states are investigated for the case of Z=10 and are shown to be small. Comparisons with experimental wavelength and lifetime measurements are made.

We demonstrate the utility of the close-coupling approximation, usually applied to scattering problems, for calculations of molecular bound states. Our primary test case is the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ state of ${\mathrm{H}}_2^{\mathrm{-}}$. While limited to Hartree-Fock accuracy, our analysis of this resonant state within the bound region parallels closely the results from more precise quantum-chemical calculations. Specifically, the crossing between the neutral and negative-ion curves occurs at an internuclear separation of 3.025 a.u. in our calculation, in good agreement with a multireference configuration-interaction approach of previous authors. The shape and total energy of the anion curve, when corrected for by the correlation energy of the target at the crossing, is also in good agreement with earlier results. The method is then extended into the unbound or resonant-state region by studying the shape-resonance behavior of scattering eigenphase sums.

We present accurate calculations of the 1${\mathit{s}}^2$2s and 1${\mathit{s}}^2$2p energy levels of lithiumlike ions for 15≤2Z≤92. The multiconfiguration Dirac-Fock method has been used to calculate relativistic effects. One-electron radiative corrections and estimated screening corrections have been calculated. These results are in good agreement with relativistic many-body calculations. General agreement with experimental transition energies (available up to Z=92) is very good.

The static electric dipole polarizabilities of the aluminum atom and dimer have been measured by deflecting a molecular beam in an inhomogeneous electric field. Collimated aluminum-cluster beams are produced by a pulsed laser vaporization source. Deflections are determined by means of a novel position-sensitive time-of-flight mass spectrometer. The measured polarizabilities are 6.8±0.3 and 19±2 A${\mathrm{̊}}^3$ for the atom and dimer, respectively, in good agreement with the ab initio calculations presented here. The experimental techniques described here allow precise determination of the mean deflections and velocities of the particles in the beam and are generally applicable for beams produced by laser vaporization sources.

The optimized-inner-projection (OIP) method is implemented and applied to determine the lower bounds to the ground-state correlation energy for the Pariser-Parr-Pople and Hubbard models of cyclic polyenes ${\mathrm{C}}_{\mathit{N}}$${\mathrm{H}}_{\mathit{N}}$, N=4ν+2, ν=3–5, in the whole range of the coupling constant. In actual calculations, the orthogonally spin-adapted form of the OIP equations is used, and full advantage is taken of the high symmetry of the cyclic polyene model, so that systems with N≥14 can be explored. Comparison is made with the results of both full and limited configuration-interaction calculations and with the correlation energies obtained with certain approximate coupled-cluster schemes. Contrary to the six- and ten-membered rings, the OIP lower bounds to the ground-state correlation energy of cyclic polyenes with larger number of sites are very poor and cannot serve as a meaningful source of information. Since the eigenvalues of the intermediate Hamiltonian, in terms of which the OIP technique is defined, are highly degenerate even in the weakly correlated region, and in view of the random behavior of the OIP bracketing function, the OIP method becomes computationally very demanding for N≥14 rings. Moreover, simple iterative schemes usually diverge and sophisticated root searching procedures have to be applied. The usefulness of the OIP technique for the determination of lower bounds to energy eigenvalues in larger systems is thus questioned.

Multiconfiguration self-consistent-field followed by multireference-configuration-interaction calculations using localized molecular orbitals were performed to obtain zeroth- and first-order perturbed Möller-Plesset (MP) wave functions and transition dipole moments for the X${\mathrm{}}^1$${\mathrm{\Sigma }}^{+}$ (ground), ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$, and ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$ states to calculate the radiative lifetimes of these excited states. In order to improve the quality of the transition dipole moment between the initial and final states using orthogonal basis sets, an alternative approach based on state-averaged G¯ ${}_{}{}^{\mathrm{}\left(0\right)\mathrm{}}{}_{}{}^{}$ and G¯ ${}_{}{}^{\mathrm{}\left(1\right)\mathrm{}}{}_{}{}^{}$ (zeroth-order and MP perturbed) spinless one-particle reduced matrices to obtain mean adapted orbitals (MAO’s) is proposed. This method is tested on the spin-allowed ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$${\leftarrow }^1$${\mathrm{\Sigma }}^{+}$${,}^1$Π transitions, where excellent agreement with the experimental lifetimes is obtained. It was found that the difference in convergence, as far as the transition dipole moments are concerned, when using the MAO’s obtained through G¯ ${}_{}{}^{\mathrm{}\left(0\right)\mathrm{}}{}_{}{}^{}$ or G¯ ${}_{}{}^{\mathrm{}\left(1\right)\mathrm{}}{}_{}{}^{}$ is very small, and therefore the additional effort to obtain the first-order MAO’s is no longer justified.

We have developed a simple model that yields an approximate analytical expression for the Coulomb-barrier penetration factor in terms of the reduced mass M of the nucleon pair, the mass m of the particle that binds together the nuclei, the inner turning point ${\mathit{r}}_{\mathit{i}}$ for the state under consideration, and the variation in the electronic or muonic contribution ${\mathit{E}}_{\mathit{e}}$(r) to the total energy between r=0 and ${\mathit{r}}_{\mathit{i}}$. In the case of muon-catalyzed d+t→α+n fusion, our model yields fusion rates within 25% of those obtained from much more elaborate calculations. The remarkable accuracy of our simple model results from the fact that it is highly accurate for small r, the region that we demonstrate makes the predominant contribution to Coulomb-barrier penetration factors. Furthermore, we use this observation to explain the old puzzle of why the adiabatic approximation yields such accurate fusion rates.

We compare the standard Zener tunneling problem with one in which the unperturbed states do not intersect. We find that even when their adiabatic energy spectra are identical, the two cases have dramatically different asymptotic tunneling probabilities. The time of Zener tunneling, a measure of the duration of the transition, is also different for the two. The latter is determined by calculating the transition probability as a function of time, for both the sudden and adiabatic limits. We also develop analytic asymptotic expansions for the tunneling probability for these limits. The results are discussed in terms suitable for comparison with experiment.

The ${\mathit{M}}_{4,5}$NO and ${\mathit{M}}_{4,5}$NN Auger spectra in Rb have been studied both experimentally and theoretically in order to understand the effect of the outermost 5s electron on the valence-shell hole states in Rb. Transition energies were obtained from extensive multiconfiguration Dirac-Fock calculations and the line intensities from our relativistic single-channel Auger-rate code. The ${\mathit{M}}_{4,5}$NO transitions were reproduced by intermediate-coupling calculations quite well indicating that the initial-state correlation with the 5s electron present is weak. For the ${\mathit{M}}_{4,5}$NN transitions our single-channel calculations revealed dramatic effects of the 5s electron on the configuration interaction in the final ionic states. Even the most elaborate calculations failed, however, to give a basis for complete identification of the observed spectral features.

Electron scattering by diatomic molecules involving the formation of a single resonance is treated within the configuration-interaction formalism. A technique is presented for solving the resulting nonlocal integro-differential equation for the nuclear motion in the resonant state. This technique is applied to the scattering of electrons by molecular hydrogen (and its isotopes) via the formation of X${\mathrm{}}^2$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ resonance, using a semiempirical model for the resonant state. Numerical cross sections for dissociative attachment, to ${\mathrm{H}}_2$, of electrons with energies below 5 eV are presented and compared both with available experimental data and with those obtained using the local approximation for the complete integro-differential equation. In contrast to the local theory, the nonlocal theory predicts cross sections that exhibit discontinuities at energies at which a new vibrational channel opens up. We also give an upper bound for attachment cross sections that holds for all isotopes of molecular hydrogen for all values of the incident electron energies.

We have measured doubly differential K-shell ionization cross sections in neon by electron impact. Incident energies ranged from 2 to 7 keV and detection angles varied between 20° and 130°. The coincidence technique with Auger electrons has been employed to identify K-shell ionization events; the data were brought to an absolute scale by use of previously measured total K-shell ionization cross sections. The results are compared with calculations using the first-order Born and Born-Ochkur approximations. The agreement between theory and experiment is satisfactory if either the energy or the detection angle of the secondary electron is small. The experimental cross sections have been transformed into generalized oscillator strengths, which turned out to be independent of the incident energy, even in those kinematical regions where the first-order Born approximation clearly failed.