Recently we showed that quantum cyclic evolution occurs, provided the initial wave function was one of the eigenfunctions of the evolution operator, whatever the concrete form of the Hamiltonian [Phys. Rev. A 50, 5317 (1994)]. This paper will show that, for some specific Hamiltonians, cyclic evolution may occur, even if the initial wave function is not one of the eigenfunctions of the evolution operator. The general conditions for the occurrence of cyclic evolution is derived. Several interesting examples of quantum evolution, also including noncyclic evolution, and some specific geometric phases are given. © 1996 The American Physical Society.

Despite the dynamical stability and absence of chaos in quantum wave functions, it is demonstrated that the quantal trajectories of the de Broglie–Bohm quantum theory of motion are capable of showing linear and exponential divergences of neighboring particle orbits for a general nonintegrable system. A quantal trajectory is influenced by the whole phase space and can be associated with a set of Lyapunov-like exponents which separate time scales of different stability © 1996 The American Physical Society.

We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the nonexistence of absolute time, i.e., of simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum theory: the quantum equilibrium distribution ρ=‖ψ${\mathrm{\Vert }}^2$ cannot simultaneously be realized in all Lorentz frames of reference. © 1996 The American Physical Society.

The electromagnetic field inside an isotropic optically active medium is quantized on the base of Fedorov’s model for optical activity. The modified photon propagator is derived. Using this result it is shown that the QED correction to the electron mass contains chiral terms which nevertheless are parity invariant. The spontaneous emission rate of a two-level atom is shown to increase in the medium. The spontaneously emitted radiation is partially polarized. © 1996 The American Physical Society.

The problem of reconstructing a pure quantum state ‖ψ〉 from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ‖ψ(x,t)${\mathrm{\Vert }}^2$ has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval Δt later, ‖ψ(x,t+Δt)${\mathrm{\Vert }}^2$, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, ${\mathcal{T}}^{\mathit{M}}$. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system. © 1996 The American Physical Society.

The functional of uncertainty J[ψ] assigns to each state ‖ψ〉 the product of the variances of the momentum and position operators. Its first and second variations are investigated. Each stationary point is located on one of a countable set of three-dimensional manifolds in Hilbert space. For a harmonic oscillator with given mass and frequency the extremals are identified as displaced squeezed energy eigenstates. The neighborhood of the stationary states is found to have the structure of a saddle, thus completing the picture of the landscape of uncertainty in Hilbert space. This result follows from the diagonalization of the second variation of the uncertainty functional, which is not straightforward since J[ψ] depends nonlinearly on the state ‖ψ〉. © 1996 The American Physical Society.

It is shown that transitions between the 2s and 2p states of the ${\mathit{A}}_{2\mathrm{\pi }}$ atoms consisting of pairs of ${\mathrm{\pi }}^{+}$,${\mathrm{\pi }}^{\mathrm{-}}$ mesons can be induced by the scattering of an incident relativistic beam of ${\mathit{A}}_{2\mathrm{\pi }}$ atoms by a thin magnetic layer. We calculate the transition probability as a function of the thickness of the magnetic layer. For a relativistic factor γ=(1-${\mathit{v}}^2$/${\mathit{c}}^2$${)}^{\mathrm{-}1/2}$=20 of the incident ${\mathit{A}}_{2\mathrm{\pi }}$ atoms and a magnetic field B=2 T we find a probability of the 2s→2p transition of 0.0013. © 1996 The American Physical Society.

Muonic hydrogen (μH) is a unique tool to study the low-energy properties of the proton form factors. The energy levels of μH are very sensitive to QED, recoil, and proton finite-size effects. We calculate the corrections to the Lamb shift and also to the fine and hyperfine structures that contribute at the 0.01-meV precision level. This result may allow for the precise determination of the proton charge radius from measurements of the 2P-2S transition energy in μH. A more accurate value for the proton radius is necessary for further improvements of QED tests based on the hydrogen atom. © 1996 The American Physical Society.

Experiments measuring the decay of positrons and orthopositronium in gases show a complicated dependence of the annihilation rate on the gas density. Theoretical and experimental studies indicate that the nonlinear dependence of the decay rate on gas density is the result of local alterations in the gas density surrounding the decaying particle. In this paper the virial expansion of the decay rate of both free positrons and positronium atoms in powers of the gas density is developed. The temperature-dependent coefficients in the density expansion of the decay rate are expressed in terms of modified cluster integrals that are determined by the interaction of the free positron or positronium atom with the host gas. Explicit expressions are given for the decay rate through terms of order ${\mathrm{\rho }}^2$ in the gas density. The term linear in the gas density is investigated analytically for the specific case of a hard-sphere interaction and its relevance to the decay of orthopositronium is demonstrated. Both the low- and high-temperature limits of the decay rate are determined analytically and the lack of temperature dependence observed in most experimental measurements of the decay rate at low density is explained. Finally, the results of path-integral Monte Carlo calculations for the decay rate over a wide temperature range are presented. © 1996 The American Physical Society.

The delayed annihilation time spectra (DATS) of antiprotonic helium atoms have been studied in isotopically pure low-temperature ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ gas at various densities. The DATS taken at 5.8 K and 400 mbar are very similar in shape except for (i) a small difference in the time scale and (ii) the presence of a distinct fast decay component in the case of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The ratio of overall trapping times (mean lifetimes against annihilation), R=${\mathit{T}}_{\mathrm{trap}}$${(}^4$He)/${\mathit{T}}_{\mathrm{trap}}$${(}^3$He), has been determined to be 1.144 ± 0.009, which is in good agreement with a theoretical estimate yielding R=[${\mathit{M}}^{\mathrm{*}}$(p¯${\mathrm{}}^4$He)/ ${\mathit{M}}^{\mathrm{*}}$(p¯${\mathrm{}}^3$He)${]}^2$=1.14, where ${\mathit{M}}^{\mathrm{*}}$ denotes the reduced mass of the p¯${\mathrm{He}}^{2+}$system. The presence of a short-lived component with a lifetime of 0.154±0.007 μs in the case of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ suggests that the p¯${\mathrm{}}^3$${\mathrm{He}}^{+}$atom has a state of intermediate lifetime on the border between a metastable zone and an Auger-dominated short-lived zone. The fraction of antiprotons trapped in metastable states at 5.8 K and 400 mbar is lower by 22.2(4)% for ${}_{}{}^3{}_{}{}^{}\mathrm{than}$ for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. All the data can be fitted fairly well with simple three-level and four-level cascade models. © 1996 The American Physical Society.

The outer valence double-ionization spectrum of ${\mathrm{SiF}}_4$ is investigated by performing accurate ab initio Green’s-function calculations based on a newly implemented block-Lanczos algorithm. An analysis of the double-hole density in the correlated states of ${\mathrm{SiF}}_4^{2+}$ proves that pronounced hole-localization phenomena at the fluorine atoms take place in all the final dicationic states of the Auger decay. We discuss how these phenomena are at the origin of the observed fluorine and silicon Auger spectral profiles and, in particular, how they provide a complete and conclusive account of all the peaks appearing in the Si LVV spectrum. Confirming this, a simple convolution of appropriate intra-atomic components of the computed two-hole density distribution is shown to reproduce the measured spectra in every detail. The recently introduced foreign-imaging phenomenon is fully confirmed by the present extended calculations. © 1996 The American Physical Society.

Using the collinear beam-laser method, we have measured the spontaneous emission lifetime of the 1s2p${\mathrm{}}^3$${\mathit{P}}_2^{\mathit{o}}$ level in Be III to be 29.1±0.2 ns, in good agreement with many mutually consistent theoretical values. This resolves the discrepancy between theory and the previous experimental value. We also obtain a value of 0.214±0.002 for the multiplet oscillator strength of the 1s2s${\mathrm{}}^3$S→1s2p${\mathrm{}}^3$${\mathit{P}}^{\mathit{o}}$ transition. © 1996 The American Physical Society.

We solved the three-dimensional Schrödinger equation for a hydrogen atom in strong magnetic and electric fields of arbitrary mutual orientation, obtaining accurate values for the wavelengths and oscillator strengths of some low-lying bound-bound transitions. The influence of the electric-field strength and its relative orientation to the magnetic field on the calculated spectra is compared with the diamagnetic hydrogen atom. We therefore focus on field strengths relevant to the interpretation of spectra of magnetic white dwarf stars—one of the major applications of these calculations. © 1996 The American Physical Society.

As a general common concept, underlying diverse methods used to compute generalized electronic excitations in atoms and molecules, intermediate-state representations (ISR’s), are considered and analyzed. Essentially, an ISR results by representing the excitation energy operator in terms of so-called correlated excited states (CES’s) or states derived thereof. Three different ISR schemes are compared, namely the biorthogonal coupled-cluster (BCC) representation used in both the coupled-cluster linear response and equation-of-motion coupled-cluster methods, a unitary coupled-cluster (UCC) representation, and the excitation class orthogonalized (ECO) representation resulting from a Gram-Schmidt orthogonalization procedure for the CES. Moreover, the relationship between the BCC scheme and the symmetry-adapted-cluster–configuration-interaction method is discussed. The relevance of the ISR schemes, as opposed to the much simpler configuration-interaction (CI) expansions, arises from two basic properties referred to as separability and compactness. The former property is a sufficient condition for size-consistent results, while the latter allows one to use smaller explicit configuration spaces than in comparable CI treatments. We show that the ECO and UCC representations are both separable and compact, whereas a somewhat restricted compactness property applies in the BCC case. © 1996 The American Physical Society.

The equation-of-motion (EOM) method and the equivalent superoperator propagator approach, used in studies of (generalized) electronic excitations, are analyzed with respect to two basic properties referred to as separability and compactness. The separability property ensures that the computed excitation energies and transition moments are size consistent; compactness means that the secular configuration spaces used in the EOM and propagator schemes can be systematically smaller than those of comparable configuration-interaction (CI) expansions. The validity of these properties depends critically on an appropriate orthonormalization of the operator manifolds used in the EOM and propagator schemes. Separable and compact EOM versions are obtained by generalizing the excitation class orthogonalization procedure discussed in the preceding paper [Phys. Rev. A 53, 2140 (1996)] to the basis operators. Moreover, it is shown that the EOM secular equations for N±1,N±2,..., electron systems can be formulated as state representations of a generalized Hamiltonian in terms of ‘‘intermediate’’ Fock space states. These intermediate-state representations (ISR’s) give some interesting insight complementing the usual operator based derivation of the EOM propagator schemes. In particular, the ISR formulation allows for a transparent discussion of the relationship between the (N±1)-electron EOM scheme and the Dyson equation for the electron propagator. Some potentially useful EOM variants are proposed. © 1996 The American Physical Society.

We describe the influence of radiation trapping on the spatial distribution of the excited-state population in sodium vapor, interacting with a linearly polarized Gaussian laser beam. Counterintuitively the excitation volume experiences a strong spatial shrinking at high optical depth. The interpretation of this nonlocal effect is based on the numerical solution of the stationary Holstein equation, which takes into account the full frequency dependence of the reabsorption probability within the process of diffusion of radiation. The calculations performed are in good qualitative agreement with the spatial effects observed experimentally. © 1996 The American Physical Society.

An algebraic model of boson realization is proposed to study the vibrational spectra of a tetrahedral molecule, where ten sets of boson creation and annihilation operators are used to construct the Hamiltonian with ${\mathit{T}}_{\mathit{d}}$ symmetry. There are two schemes in our model. The first scheme provides an eight-parameter fit to the published experimental vibrational eigenvalues of methane with a root-mean-square deviation 11.61 ${\mathrm{cm}}^{\mathrm{-}1}$. The second scheme, where the bending oscillators are assumed to be harmonic and the interactions between the bending vibrations are neglected, provides a five-parameter fit with a root-mean-square deviation 12.42 ${\mathrm{cm}}^{\mathrm{-}1}$. ©1996 The American Physical Society.

The hyperfine constants for the ground and two lowest excited states of lithium are calculated in a multiconfiguration Dirac-Fock model. Convergence of the calculated magnetic dipole and electric quadrupole constants is studied as the active set of orbitals is systematically increased. The final results are compared with experimental data and theoretical values obtained from other methods. © 1996 The American Physical Society.

Eleven lithium resonances, eight below the ${\mathrm{Li}}^{+}$ 2s2s${\mathrm{}}^1$S threshold and three above the ${\mathrm{Li}}^{+}$ 2s2p${\mathrm{}}^3$${\mathit{P}}^{\mathit{o}}$ threshold, are studied with the saddle-point complex-rotation method. These are the triply excited ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ resonances above the 2s2s2p${\mathrm{}}^2$${\mathit{P}}^{\mathit{o}}$ and 2p2p2p${\mathrm{}}^2$${\mathit{P}}^{\mathit{o}}$ states. They are classified based on the energy, the relative contribution of the different angular-spin components to the normalization, and by inspecting the relativistic corrections. The partial Auger widths are obtained for the individual channels and the total Auger widths are obtained by coupling the important open channels and summing over the other channels. These results are compared with the recent experimental data. © 1996 The American Physical Society.

The dynamics of the first capture and decay processes occurring during the interaction of slow highly charged ions below a surface has been studied in looking at the x rays emitted directly, or in coincidence, by impinging bare or hydrogenlike ions of various atomic numbers on solid targets. Some results on the decay processes of these hollow atoms, mainly formed below the surface, for argon, iron, and krypton ions are presented. By measuring the changes of the number of electrons in the L and M shells of the ions, compared to the lifetime of the K shell, it has been possible to evaluate the mean time for the filling of the L and M shells. These measurements are compared with a model of interaction of the ions with the surface. © 1996 The American Physical Society.