Consequences of relativistic causality for measurements of nonlocal characteristics of composite quantum systems are investigated. It is proved that verification measurements of entangled states necessarily erase local information. A complete analysis of measurability of nondegenerate spin operators of a system of two spin-1/2 particles is presented. It is shown that measurability of certain projection operators which play an important role in axiomatic quantum theory contradicts the causality principle.

A time-varying Hamiltonian in a two-level system with different relaxation rates is studied using an effective-Hamiltonian model. Energy sheets are featured. A suited adiabatic basis is provided in which equations of evolution are given for arbitrary paths. Phase factors are discussed for adiabatic loops. The influence of relaxation on the criterion for adiabatic evolution is pointed out.

A complementary electric Aharonov-Bohm (AB) effect is proposed and investigated where one branch of a chopped and split electron beam traverses a region with an electric field and upon interference with the other branch no phase shift would be observed. The analysis of the proposed experiment is carried out (1) in a semiclassical (SC) eikonal approximation and (2) in a complete quantum-mechanical (QM) calculation with a plane-wave approximation similar to AB’s original paper. The QM phase shift is the sum of the SC phase shift plus an AB-like phase shift for a constant potential. While the SC analysis predicts that there must be a phase shift, the full QM indicates that a null phase shift is possible.

Multichannel quantum-defect theory is applied to the highly accurate ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ ab initio excited-state potential-energy curves calculated by Wolniewicz and Dressler [J. Chem. Phys. 82, 3262 (1985); and (private communication)]. We show that the three double-minimum states, EF, GK, and HH¯, can be represented to within 8 ${\mathrm{cm}}^{\mathrm{-}1}$ by a smooth R-dependent 3×3 nondiagonal quantum-defect matrix. This quantum-defect matrix corresponds to a collision of the Rydberg electron with the ${\mathrm{H}}_2^{+}$ target, which may be in either the 1${\mathrm{\sigma }}_{\mathit{g}}$ or 1${\mathrm{\sigma }}_{\mathit{u}}$ state. Also discussed is the use of this quantum-defect matrix to calculate diabatic states, more highly excited Born-Oppenheimer states, and the electronic ionization width of the superexcited (1${\mathrm{\sigma }}_{\mathit{u}}$${)}^2$ doubly excited state.

In the preceding paper [Phys. Rev. A 49, 3888 (1994)] we obtained the quantum-defect matrix of the strongly interacting double-minimum states of ${\mathrm{H}}_2$ by fitting to the ab initio clamped-nuclei electronic energies of Wolniewicz and Dressler [J. Chem. Phys. 82, 3292 (1985), and private communication]. Yu, Dressler, and Wolniewicz have calculated the vibronic energies of the corresponding states using an approach involving the state-by-state evaluation of vibronic coupling, and the solution of a set of coupled equations. Here we calculate the vibronic energies using our quantum-defect matrix in a version of scattering theory known as multichannel quantum-defect theory (MQDT). This less traditional treatment involves both singly and doubly excited channels and reproduces the vibronic energies to almost the same precision as the coupled-equations approach. In addition, several refinements have been made to MQDT.

We present a theoretical formulation of resonant inelastic x-ray scattering (RIXS) of molecules with an element of symmetry, and study the consequences of this formulation both with respect to short and long lifetimes of the intermediate core-excited scattering states and with respect to localized versus delocalized descriptions for these states. Strong polarization and excitation energy dependencies are predicted. The ‘‘core-hole localization’’ problem is explored also from the point of view of diffractional scattering of an x-ray photon showing that x-ray photons distinguish core holes in the short-wavelength limit only. By analyzing the properties of the x-ray scattering tensor, strict selection rules for the RIXS process are derived. The local decomposition model (one-center approximation) frequently employed in ordinary x-ray emission is generalized for the calculation of intensities and polarization dependence of the RIXS process, assuming either localized or delocalized core holes. It is argued that Stokes doubling should be a commonly observable feature in RIXS spectra. By means of model calculations we demonstrate the crucial role of RIXS selection rules, of channel interferences, of Stokes doubling, and of the form of the excitation frequency function for the appearance of RIXS spectra.

We have measured the vacuum-ultraviolet 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_{1–}$1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{2,0}$ transition wavelengths in heliumlike silicon by photographic spectroscopy of a beam-foil source. The results are 814.71±0.02 Å and 878.68±0.03 Å, respectively, and represent a sensitive test of present relativistic and quantum electrodynamic calculations. Comparisons are made between our results, previous measurements of these transitions, and the current theories. Good agreement is obtained, particularly with recent relativistic many-body perturbation calculations. A discussion of future measurements of this interval is also presented.

Isotope shifts and hyperfine structures of twelve transitions from the high-lying metastable ${}_{}{}^9{}_{}{}^{}$${\mathit{H}}_{\mathit{J}}$ (J=1–7) states of the 4${\mathit{f}}^6$5d6s configuration in Sm i have been measured for the stable isotopes by means of atomic-beam laser spectroscopy. Hyperfine constants A and B for the odd-mass isotopes ${}_{}{}^{147}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{149}{}_{}{}^{}\mathrm{Sm}$ are determined for the ${}_{}{}^9{}_{}{}^{}$${\mathit{H}}_{\mathit{J}}$ (J=1–7) states and six upper levels of the transitions in Sm i. $J— dependences of the isotope shifts are observed for the 4${\mathit{f}}^6$5d6s ${}_{}{}^9{}_{}{}^{}$H term. Parameters ${\mathit{z}}_{5\mathit{d}}$ of the crossed-second-order effect are derived for the 4${\mathit{f}}^6$5d6s configuration, and ${\mathit{z}}_{5\mathit{d}}$/λ is found to be 165(10) MHz/${\mathrm{fm}}^2$. It has been verified that the field shift is dominant in the crossed-second-order effect.

Perturbation energies ${\mathit{E}}_2$, ${\mathit{E}}_3$, and ${\mathit{E}}_4$ in the 1/Z expansion for the ground-state two-electron atom are calculated using accurate representations of the partial waves L=0,1,2,. . . of the first- and second-order eigenfunctions. These are obtained by combining L-Hylleraas basis functions with a one-dimensional finite-element procedure. The contribution to ${\mathit{E}}_2$, ${\mathit{E}}_3$, and ${\mathit{E}}_4$, made by partial waves L≫1, can, with a surprising accuracy, be covered by numerical extrapolation with the help of a Schwartz-type expression in powers of 1/(L+1/2).

Variational and fixed-node diffusion Monte Carlo calculations for several states of the iron atom are presented. The Ne-core electrons are eliminated by accurate scalar relativistic pseudopotentials. Variational valence correlation energies are the largest obtained so far by any variational method including the most extensive quantum chemistry calculations. The average difference between experiment and diffusion Monte Carlo results for the s→d excitation energies, the ionization potential, and the electron affinity is 0.15 eV.

We perform a gauge-independent pseudoseparation of the center-of-mass motion for neutral two-body systems in crossed fields. The resulting Hamiltonian is investigated for two different cases of the interaction. First, we reduce the Hamiltonian for a two-particle system with anisotropic harmonic interaction in a magnetic field to the Hamiltonian of a charged anisotropic harmonic oscillator in a magnetic field. For the latter we derive closed-form analytical expressions of its eigenenergies and wave functions. Second, we investigate the hydrogen atom in crossed fields. The potential for the relative motion of electron and proton exhibits an outer potential well at large distances. We perform extensive numerical calculations of a large number of eigenvalues and wave functions and compare these to the analytical results of a harmonic approximation of the potential well.

The 3${\mathit{p}}^{\mathrm{-}1}$→5${\mathit{s}}^1$ resonant excitation energy and decay width of the Zn atom are calculated by an ab initio Green’s-function method. The agreement with experiment is reasonably good. The decay width and the dipolar relaxation energy shift of the 3${\mathit{p}}^{\mathrm{-}1}$→5${\mathit{s}}^1$ resonantly excited state of the Zn atom is predominantly due to the 3${\mathit{p}}^{\mathrm{-}1}$5${\mathit{s}}^1$→3${\mathit{d}}^{\mathrm{-}2}$5${\mathit{s}}^1$ɛf(p) super-Coster-Kronig spectator decay and the corresponding virtual process. The calculated decay width is larger than the experimental one but smaller than that of the 3${\mathit{p}}^{\mathrm{-}1}$ core-ionized state. It appears that the discrepancy is due to the overestimate of the 3${\mathit{p}}^{\mathrm{-}1}$5${\mathit{s}}^1$→3${\mathit{d}}^{\mathrm{-}1}$4${\mathit{s}}^{\mathrm{-}1}$5${\mathit{s}}^1$ɛp Coster-Kronig decay by the present calculation.

The three-body contribution to resonant dtμ formation, coming from the configuration mixing of the angular momentum states of the [(dtμ)d2e]* complex caused by colliding ${\mathrm{D}}_2$ molecules, is calculated in a classical-trajectory model. The collisions bring about significant broadening of the transition energies and an important contribution to three-body molecular formation. Results are presented in terms of a universal “width function” ${\lambda }_{\mathrm{ff}\prime }$ for states f and f′, and indicate that neither the impact approximation nor a recent quasistatic calculation of this process can be considered reliable. Furthermore, the calculated three-body molecular formation rate has the experimentally correct magnitude and temperature dependence.

Landé ${\mathit{g}}_{\mathit{J}}$ factors in the 6${\mathit{snp}}^{1,3}$${\mathit{P}}_1$ sequences and their perturbers were investigated using an extended multichannel quantum-defect theory (MQDT). Improved MQDT wave functions have been obtained. The agreement between experiment and theory is good.

We present a two-step method to calculate the vibrational-rotational spectrum of diatomic molecules in general. The aim of the method is to solve the radial part of the Schrödinger equation with the effective potential in the general form of V=${\mathit{tsum}}_{\mathit{n}}$ ${\mathit{a}}_{\mathit{n}}$${\mathit{r}}^{\mathit{n}}$, where n may be a positive or negative number. The flexibility of the form of the prototype potential used enables us to describe accurately the interatomic potential in general. The method of solution is composed mainly of two steps. In the first step, we introduce a transformation so that the domain of the wave function is the whole real axis. The operator formalism is used to carry through the variational conditions analytically for the ground state of the system. In the second step, we improve the ground-state energy by a standard diagonalization procedure around the ground state using the harmonic oscillator basis obtained from the first step. In this way, we also obtain the low-lying excited states accurately. The method is applied to the following systems explicitly: (1) the lower-energy levels of the H atom or Kratzer’s potential in molecular problems, (2) the vibrational-rotational spectrum of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{}{}_{}{}^{}$ state of the ${\mathrm{H}}_2^{+}$ ion, and (3) the so-called spiked oscillator harmonic system. The results of all these calculations demonstrate that the two-step method is very powerful in the solution of one-dimensional problems, in particular for cases where the effective potential has only one minimum.

The delayed annihilation of antiprotons, which was recently discovered in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at KEK, has been studied at CERN in gas-phase ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The annihilation time spectra in gaseous ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at various pressures were found to be similar to that for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The observed average lifetime in the region t>1 μsec for 3 atm ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ was about 3.2 μsec, while for 3 atm ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ gas it was 2.8 μsec, i.e., shorter by 15%. The time spectra show a growth-decay-type function, which is indicative of the presence of a series of metastable states. For ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ they have nearly identical shapes, differing only in the time scale by (14 ±3)%. These observations are qualitatively consistent with the atomic model of p¯${\mathit{e}}^{\mathrm{-}}$${\mathrm{He}}^{2+}$ proposed by Condo [Phys. Lett. 9, 65 (1964)]. The time spectra were found to be sensitive to the presence of small amounts (as small as 20 ppm) of ${\mathrm{H}}_2$. No evidence was seen for delayed annihilation in gaseous Ne.

The term energies of the lowest ten doubly excited ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ terms of neutral lithium are calculated by using the restricted variational method with a full core plus correlation. Relativistic and mass-polarization effects are included as the first-order perturbation to the nonrelativistic energy. Our results support the assignments for the observed lines at 3619 Å and at 4885 Å as the decay from the term 1s2p3s ${}_{}{}^4{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$. This term is identified as the seventh member in the ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ series, and its energy is almost degnerate with that of the eighth member, being only 24 ${\mathrm{cm}}^{\mathrm{-}1}$ apart. To facilitate unambiguous closed loop analyses in comparisons with experiment, precision calculations are also carried out to determine the relative term values for 1s2p2p ${}_{}{}^4{}_{}{}^{}\mathrm{P}$ at 26 915.7(5) ${\mathrm{cm}}^{\mathrm{-}1}$ and for 1s2s3d ${}_{}{}^4{}_{}{}^{}\mathrm{D}$ at 42 778.4(4) ${\mathrm{cm}}^{\mathrm{-}1}$, which agree well with the experimental data of 26 915.16(6) ${\mathrm{cm}}^{\mathrm{-}1}$ and 42 778.3 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively. Our results suggest that the transition 1s2s3 ${}_{}{}^4{}_{}{}^{}1\mathrm{s}2\mathrm{p}3\mathrm{s}$ ${}_{}{}^4{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$ should be at 8500.5 Å.

Doubly excited states in helium are calculated with many-body perturbation theory to all orders in the electron-electron interaction. A finite and numerical basis set, rotated out into the complex plane, is used. Results, for energies and widths, are presented for states with electrons in the n=2 and n=3 states. The possiblity of an accuracy of a few parts in ${10}^6$ is demonstrated. The method is equally applicable to the study of doubly excited states of many-electron systems and the extension to the corresponding relativistic procedure is straightforward.

We investigate the effects of nuclear forces on the eigenvalues and sticking fractions of the ground and excited J=0 states of the dtμ molecule using a variational R-matrix approach. The nuclear boundary condition is imposed on the entire variational wave function, rather than on the individual elements of the basis, by means of the Bloch operator. This formulation results in rigorously symmetric variational matrix elements and improved flexibility of the basis at small d-t separations. Our results for the fusion rates and initial sticking fractions are ${\lambda }_{\mathit{f}}$=1.25×${10}^{12}$ ${\sec }^{\mathrm{-}1}$ and ${\mathrm{\omega }}_{\mathit{s}}^0$=0.912% for the v=0 state and ${\lambda }_{\mathit{f}}$=1.05×${10}^{12}$ ${\sec }^{\mathrm{-}1}$ and ${\mathrm{\omega }}_{\mathit{s}}^0$=0.912% for the v=1 state.

A simple method for deriving the energy level shifts in the QED of multicharged ions is considered. Calculation formulas for the reducible part of the two-photon-exchange diagrams in both the Feynman and the Coulomb gauges are derived for arbitrary states of two-electron multicharged ions. The final expressions for this contribution have a form that is convenient enough for numerical calculations.