A specific model of quantum measurement [D. F. Walls, M. J. Collet, and G. J. Milburn, Phys. Rev. D 32, 3208 (1985)] based on a generic system-meter-environment measurement scheme is investigated in terms of probability distributions on projective Hilbert space. Starting from the unitary evolution of the total system a stochastic process for the wave function of the reduced system-meter system is derived by elimination of the degrees of freedom of the environment. The stochastic process is interpreted in terms of the direct detection of the photoelectrons created by the meter quanta in the environment. Two general variances are introduced which represent, respectively, the average intrinsic quantum fluctuations and the statistical fluctuations of the quantum expectation of the measured observable. Involving fourth moments of the wave function, these variances allow to monitor the transformation from quantum to classical probabilities during the process of measurement. © 1996 The American Physical Society.

A universal approach is developed to study revivals of wave packets made of bound states with an arbitrary spectrum ${\mathit{E}}_{\mathit{n}}$ exhibiting hierarchical time scales. An analytic expression in form of a recursion formula is derived, which allows for a given wave packet the prediction of all revival times in any time scale. The theory is applied to metallic Rydberg clusters, i.e., two oppositely charged metallic clusters in a bound state with high angular momentum, taking into account their mutual polarization connected with a complicated n dependence of the spectrum ${\mathit{E}}_{\mathit{n}}$. The theoretical predictions are compared with numerical results using a stroboscopic picture of the autocorrelation function. © 1996 The American Physical Society.

A method for studying the generalized center-of-mass coordinate and relative momentum operators is provided. This method is based on unitary transformations. The eigenvectors of these operators can be easily obtained. Their properties and relationship with one-body system eigenvectors are also discussed. © 1996 The American Physical Society.

The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar curvature term in the quantum Hamiltonian. The coefficient of the latter term is known to be related to the factor-ordering problem in curved-space quantization. Hence, in principle, the scattering data may be used to provide an experimental resolution of the theoretical factor-ordering ambiguity. To demonstrate the sensitivity required of such an experimental setup, the effect of a localized magnetic field in the scattering process is also analyzed. © 1996 The American Physical Society.

The formation process of metastable $\mathrm{dt}\mu$ molecules in $D_2-T_2$ mixtures in investigated. The $\mathrm{dt}\mu$ molecule exhibits a series of three-body resonances embedded in the $t\mu +d$ scattering continuum just below the $t\mu \mathrm{}\left(2s\right)+d$ threshold. These states can be formed in collisions of excited $t\mu \mathrm{}\left(2s\right)\mathrm{}$ atoms with $D_2$ molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of $D_2$. We present a scattering-theoretic model for this process, and perform a numerical calculation of its cross section. The essential transition amplitudes are obtained from three-body wave functions for the $\mathrm{dt}\mu$ subcluster, and adiabatic wave functions for the entire hybrid system in the final channel. It is found that the effective formation rate is limited by the Auger-transition rates of the molecular complex formed. The calculated cross sections exhibit broad "peaks," with magnitudes large enough for the formation process to favorably compete with deexcitation of $t\mu \mathrm{}(n=2\mathrm{})\mathrm{}$ atoms via radiative and collisional processes. The formation of metastable $\mathrm{dt}\mu$ can therefore be one of the fastest processes depleting the $n=2\mathrm{}$ levels of the $t\mu$ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.

The stationary variant of direct perturbation theory of relativistic effects is presented. In this variant neither the unperturbed (nonrelativistic) equation nor the equations for the relativistic corrections are solved exactly, but each of them is replaced by the condition that a certain functional becomes stationary. Let ${\mathrm{\psi }}_0$=(${\mathrm{\Phi }}_0$,${\mathrm{\chi }}_0$) be the four-component spinor with modified metric in the nonrelativistic limit and ψ${\mathrm{¯}}_2$=(${\mathrm{\Phi }}_2$,${\mathrm{\chi }}_2$) the leading relativistic correction of O(${\mathit{c}}^{\mathrm{-}2}$), then one can define functionals ${\mathit{F}}_0$(${\mathrm{\Phi }}_0$,${\mathrm{\chi }}_0$) and ${\mathit{F}}_4$(${\mathrm{\Phi }}_2$,${\mathrm{\chi }}_2$) called respectively the Lévy-Leblond and the Rutkowski-Hylleraas functional, such that stationarity of ${\mathit{F}}_0$ with respect to variation of ${\mathrm{\Phi }}_0$ and ${\mathrm{\chi }}_0$ determines ${\mathrm{\Phi }}_0$ and ${\mathrm{\chi }}_0$, and stationarity of ${\mathit{F}}_4$ with respect to variation of ${\mathrm{\Phi }}_2$ and ${\mathrm{\chi }}_2$ determines ${\mathrm{\Phi }}_2$ and ${\mathrm{\chi }}_2$. The unperturbed (i.e., nonrelativistic) energy ${\mathit{E}}_0$ as well as the leading relativistic correction ${\mathit{c}}^{\mathrm{-}2}$${\mathit{E}}_2$ are expressible through ${\mathrm{\Phi }}_0$ and ${\mathrm{\chi }}_0$ while for the next higher corrections ${\mathit{c}}^{\mathrm{-}4}$${\mathit{E}}_4$ and ${\mathit{c}}^{\mathrm{-}6}$${\mathit{E}}_6$, ${\mathrm{\Phi }}_2$ and ${\mathrm{\chi }}_2$ are also needed. Either of the two functionals ${\mathit{F}}_0$ and ${\mathit{F}}_4$ can be decomposed into two contributions, the error of one of which is ≥0 while that of the other is ≤0. An upper-bound property is obtained if the error of the second part vanishes. A strict variation perturbation theory requires that the approximate Φ${\mathrm{̃}}_2$ and χ${\mathrm{̃}}_2$ reproduce the behavior of the exact ${\mathrm{\Phi }}_2$ and ${\mathrm{\chi }}_2$ near a nucleus, which implies terms in ln r. If one regularizes Φ${\mathrm{̃}}_2$ one must also regularize χ${\mathrm{̃}}_2$; otherwise ${\mathit{E}}_6$ diverges. If one regularizes both ${\mathrm{\Phi }}_2$ and ${\mathrm{\chi }}_2$ in the sense of a kinetic balance, one gets regular results for ${\mathit{E}}_4$ and ${\mathit{E}}_6$, but one loses the strict upper-bound property. The Breit-Pauli expression for ${\mathit{E}}_2$ is shown to be correct only if the nonrelativistic wave equation has been solved exactly. Otherwise there is an extra term. Finally the question as to which extent some of the singularities in the perturbation theory of relativistic effects might be artifacts due to the unphysical assumption of a point nucleus is discussed. It is shown, however, that these singularities are not removed if one uses realistic extended nuclei. For all atoms, the critical radius ${\mathit{r}}_{\mathit{c}}$ inside of which the nuclear attraction energy is larger than the rest energy of the electron is larger than the extension of the nucleus. © 1996 The American Physical Society.

The Zeeman splitting of the metastable 5${\mathit{D}}_{3/2}$ level of ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{+}{}_{}{}^{}$ in a magnetic field of 6 T has been measured in a laser-microwave double resonance experiment in a Penning ion trap. The magnetic field at the ion’s position is determined by the cyclotron frequency of electrons stored in the same trap. From the ratio of both transition frequencies we obtain a ${\mathit{g}}_{\mathit{J}}$ value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6${\mathit{S}}_{1/2}$ ground-state ${\mathit{g}}_{\mathit{J}}$ factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. © 1996 The American Physical Society.

We propose an alternative way of calculating the resonances of the Stark effect in hydrogen. The method is based on a rational approximation of the logarithmic derivative of the eigenfunction, and leads to a quantization condition for the complex energies of the metastable states. We present accurate results for the ground and some excited states for several field intensities. © 1996 The American Physical Society.

Extension of the applicability of the closed-shell coupled-cluster (CC) theory with doubly (CCD) or singly and doubly (CCSD) excited clusters to quasidegenerate situations requires the inclusion of the connected triply and quadruply excited cluster components ${\mathit{T}}_3$ and ${\mathit{T}}_4$. Since an explicit consideration of these clusters for larger systems is computationally very demanding, we explore the possibility of estimating the ${\mathit{T}}_4$ contribution using the projected unrestricted Hartree-Fock (PUHF) wave function. The resulting CCDQ′ and CCSDQ′ approaches are shown to correctly approximate the effect of the quadruply (Q′) excited ${\mathit{T}}_4$ clusters, even when the PUHF wave function itself cannot serve as a good source of the lower-order pair-cluster components. It is important that the results of the cluster analysis of the PUHF solution are used directly and no further approximations are made. Only when both pair-cluster and ${\mathit{T}}_4$ cluster components are reasonably well approximated by the PUHF wave function, the ${\mathit{T}}_4$ cluster contributions cancel out certain CCSD diagrams, and good CC results can be obtained with the approximate coupled-pair approaches. It is also demonstrated that it may be more difficult to balance ${\mathit{T}}_3$ and ${\mathit{T}}_4$ clusters relying on simple perturbative approaches, such as CCSDQ′+T(CCSDQ′). The results of formal considerations, including a thorough investigation of the cluster structure of the PUHF wave function, are illustrated on several examples. These include a few model systems composed of four and eight hydrogen atoms in various geometrical arrangements, as described using minimum and double zeta plus polarization basis sets, for which the exact full configuration interaction data are available. The orthogonally spin-adapted formulation of CC theory is used throughout. © 1996 The American Physical Society.

The reaction rate of the nuclear fusion d${\mathrm{}}^6$Li${\to }^8$${\mathrm{Be}}^{\mathrm{*}}$($2^{+}$,0) is estimated in the case where the nuclei are confined to each other by a muon. For the description of nuclear transitions, a method that is analogous to the linear combination of atomic orbitals has been used. Using the complex coordinate rotation method, we found that a molecular d-μ${\mathrm{-}}^6$Li state exists with energy (-20.3084-i0.0066) eV and |${\mathrm{\Psi }}_{\mathit{m}}$(0)|=0.44 ${10}^{\mathrm{-}7}$ ${\mathrm{fm}}^{\mathrm{-}3/2}$. The nuclear wave functions needed were constructed in the form of antisymmetrized products of harmonic-oscillator functions for the three-cluster approximation (ddα) to the five-body (NNNNα) problem. It was found that the reaction rate λ is strongly dependent on the energy gap between the ${\mathit{d}}^{\mathrm{}6}$Li threshold and the energy of the final ${}_{}{}^8{}_{}{}^{}\mathrm{Be}_{}^{\mathrm{*}}{}_{}{}^{}$ resonant state. The value of λ obtained by averaging over the width of this resonance is 0.183×${10}^{10}$ ${\sec }^{\mathrm{-}1}$. © 1996 The American Physical Society.

Fully relativistic formulas for the energy-level shifts arising from no-pair exchange diagrams of two transverse photons plus an arbitrary number of Coulomb photons are derived in closed form within the external potential Bethe-Salpeter formalism. O(${\mathrm{\alpha }}^7$(lnα)${\mathit{mc}}^2$) corrections to the fine-structure splittings of helium are obtained and expressed in terms of expectation values of nonrelativistic operators. O(${\mathrm{\alpha }}^7$${\mathit{mc}}^2$) operators from exchange diagrams are found in nonrelativistic approximation. O(${\mathrm{\alpha }}^6$${\mathit{m}}^2$${\mathit{c}}^2$/M) nucleus-electron operators contributing to the fine-structure splittings are derived. Nonrelativistic operators of O(${\mathrm{\alpha }}^6$${\mathit{mc}}^2$) corrections to the triplet levels of helium are presented. Nonrelativistic operators of O(${\mathrm{\alpha }}^6$(lnα)${\mathit{mc}}^2$) corrections to the helium singlet levels and to positronium S levels are derived. O(${\mathrm{\alpha }}^6$${\mathit{m}}^2$${\mathit{c}}^2$/M) hydrogen and O(${\mathrm{\alpha }}^6$${\mathit{mc}}^2$) positronium P levels, and O(${\mathrm{\alpha }}^6$(lnα)${\mathit{mc}}^2$) corrections of first order to positronium S levels, are calculated using the derived operators for helium, in agreement with those obtained previously by others, except for one term in corrections to positronium P levels. In addition, the O(${\mathrm{\alpha }}^6$${\mathit{mc}}^2$) Dirac energies for hydrogenic non-S levels are exactly reproduced in a perturbative calculation. © 1996 The American Physical Society.

We investigate the topology of the adiabatic potential-energy surfaces of the $4_{\mathit{g}\mathrm{}\left(\mathit{u}\right)}$,$5_{\mathit{g}\mathrm{}\left(\mathit{u}\right)}$,$6_{\mathit{g}\mathrm{}\left(\mathit{u}\right)}$ electronic states of the hydrogen molecular ion in a strong magnetic field. The increasing complexity of the surfaces with increasing degree of electronic excitation is demonstrated. Stable local as well as global molecular equilibrium configurations are found for the parallel, perpendicular, as well as intermediate configurations. © 1996 The American Physical Society.

We have observed the second-order, field-induced Zeeman effects of the Doppler-free two-photon transitions 5${\mathrm{}}^2$S–3${\mathrm{}}^2$S and 4${\mathrm{}}^2$D–3${\mathrm{}}^2$S of atomic sodium using fields up to 5 T. Using a suitable experimental configuration it was possible to avoid the appearance of first-order effects in the high-field limit. The remaining small field-induced shifts are of the order of magnitude of a few linewidths. They yield the differences of the diamagnetic susceptibilities of the connected atomic states. The method is therefore capable of providing data related to atomic electronic structure. © 1996 The American Physical Society.

The Fermi contact term for the 2${\mathrm{}}^2$S, 2${\mathrm{}}^2$P, and 3${\mathrm{}}^2$S states of Li and the 2${\mathrm{}}^2$S state of ${\mathrm{Be}}^{+}$ are calculated using high-precision variational wave functions in Hylleraas coordinates. The nonrelativistic Fermi contact terms obtained for these states are 2.905 922(50), -0.214 783(50), 0.673 405(50), and 12.497 57(30) a.u., respectively. Estimates of corrections for finite nuclear size, relativistic effects, and QED effects are shown to yield satisfactory agreement with experiment for the 2${\mathrm{}}^2$S state of Li and ${\mathrm{Be}}^{+}$, but there remains a substantial disagreement with experiment for the 3${\mathrm{}}^2$S state of Li. © 1996 The American Physical Society.

Identities and approximations are proposed for the current-density-functional theory. Based on the virial theorem and the scaling properties of the kinetic and exchange energy density functionals, when local and variable-separation assumptions are made, local formulas for these functionals are obtained. One also obtains hierarchies of equations, which combine to give series expansions of the functionals in terms of their functional derivatives with respect to both the density and the paramagnetic current density. In addition, a general formulation is investigated in the form of the constrained search of a coupled Hamiltonian. Subject to the validity of a Taylor series, both the correlation energy density functional and its kinetic component can be expanded into series, each of which, if locality density approximations are assumed, consists of homogeneous functionals of degree (4-n)/3 in density scaling, (4-n)/2 with respect to v(r), a gauge-invariant variable. © 1996 The American Physical Society.

The intensity distributions of some transitions belonging to the iron-group elements have been analyzed in the framework of unresolved transition array theory. More specifically, the transitions of the types ${\mathit{l}}^{\mathit{N}}$(${\mathrm{\alpha }}_{\mathit{cL}\mathit{cS}\mathit{c}}$)l′-${\mathit{l}}^{\mathit{N}}$(${\mathrm{\alpha }}_{\mathit{cL}\mathit{cS}}$c)l″ and ${\mathit{l}}^{\mathit{N}}$(${\mathrm{\alpha }}_{\mathit{cL}\mathit{cS}\mathit{c}}$)s(${\mathrm{\alpha }}_{\mathit{cL}\mathit{c}}$${\mathrm{\Sigma }}_{\mathit{c}}$)l′-${\mathit{l}}^{}$N(${\mathrm{\alpha }}_{\mathit{cL}\mathit{cS}\mathit{c}}$)s(${\mathrm{\alpha }}_{\mathit{cL}\mathit{c}}$${\mathrm{\Sigma }}_{\mathit{c}}$)l″ (l′,l″≥4) have been considered. The possibility to characterize these transitions by the first weighted moments of their wave-number distributions is clearly demonstrated. © 1996 The American Physical Society.

We have measured the absolute polarization of the 2${\mathit{p}}^{61}$${\mathit{S}}_0$-2${\mathit{p}}^5$${(}^2$${\mathit{P}}_{3/2}^{\mathit{o}}$)3s[3/2${]}_2^{\mathit{o}}$ magnetic quadrupole transition in Ne-like barium, excited in an electron-beam ion trap at a variety of energies. We find strong evidence for the existence of resonant excitation processes that are not explained by our collisional-radiative calculations even when the polarization arising from impact excitation is included. At energies well away from where the resonances occur, the agreement between experiment and theory is good. © 1996 The American Physical Society.

Energies of the [2${\mathit{p}}^5$3d${]}_{\mathit{J}=1\mathrm{}}$ excited states of neonlike ions with nuclear charges in the range Z=10-92 are evaluated using an all-orders method based on relativistic many-body perturbation theory. The calculation starts from a multiconfiguration Hartee-Fock (HF) wave function, and includes correlation corrections from both the Coulomb and Breit interactions. The dominant correlation corrections, which are those associated with the 2p hole state, are treated to all orders. Reduced-mass and mass-polarization corrections are computed up to first order. The electron self-energy, the vacuum polarization, and the frequency-dependent Breit interaction are also included in first order, using a local potential that approximates the ${\mathit{V}}^{\left(\mathit{N}\mathrm{-}1\right)}$ (HF) potential. Comparisons are made with existing measurements and with other calculations. © 1996 The American Physical Society.

The cross section σ for the positron-impact ionization of the hydrogen atom near threshold has been evaluated analytically with the final-state wave function involving three Coulomb functions. Contrary to the earlier result that σ vanishes exponentially, we find the threshold law as σ∼${\mathit{E}}^{3/2}$. © 1996 The American Physical Society.

The requirements that the scattering functions for quantal scattering at energies below the first inelastic threshold be unitary and analytic have been used to establish a process that gives the complex scattering amplitudes from differential cross sections. From those amplitudes, scattering phase shifts have been deduced by Legendre integration. The effects of the natural ambiguity of the phase of the scattering amplitude, under conditions for which uniqueness and (numerical) stability of solutions are not assured, also have been studied to show that the process we have developed to specify the scattering phase shifts can give stable nonspurious results. The scattering of electrons from He atoms for incident energies ranging from 1.5 to 19 eV are considered as an example of this procedure. Phase-shift analyses of those data have been made with a variety of other techniques to allow a comparative study of our results and of sets with which are associated fits to cross sections that are statistically significant. © 1996 The American Physical Society.