The total-electron-capture cross section for collisions of C${}^{4+}$ with ground-state hydrogen (deuterium) is measured in the energy range 6–1000 eV/u using the merged-beam technique. The fraction of C${}^{4+}$ metastable ions present in the ion beam is measured to be 5%, which results in a correction to the cross section of only a few percent. The independently absolute measurements are generally in good agreement with previous measurements for total electron capture; however, the reduced uncertainties of these measurements allow a more detailed comparison with theory. Our observations show that existing fully quantal molecular-orbital calculations that include rotational coupling overestimate the cross section by approximately 25%. Better agreement is found with a recent semiclassical impact-parameter coupled-channel calculation. While all available theoretical data predict that the cross section varies smoothly with energy around the maximum, a sharp structure is observed around 400 eV/u.

The threshold behavior of the cross section of an endothermic energy pooling reaction is investigated. In a vapor cell experiment, pulsed excitation followed by delayed fluorescence detection narrows the transverse velocity distribution of colliding pairs of laser-excited strontium atoms in the ${5s5p}^3{P}_1$ level, and laser detuning establishes the collision velocity in the direction of counterpropagating laser beams. A probe laser detects the excited-state collision product of the endothermic ${5s5p}^3{P}_1{+5s5p}^3{P}_1\to {5s6s}^1{S}_0{+5s}^{21}{S}_0$ reaction. The cross section rises steeply at threshold and is nearly flat for 1.2–2 times the threshold energy. This behavior can be partly explained by the shape of the molecular potential curve of the collisionally produced state. From the measured $1.1\times {10}^{-12}{\mathrm{cm}}^3{\mathrm{}\mathrm{s}}^{\mathrm{-}1}$ thermally averaged rate coefficient, the above-threshold cross section is found to be approximately $6\times {10}^{-17}{\mathrm{cm}}^2.$ The thermally averaged rate coefficient for the highly exothermic energy pooling reaction ${5s5p}^3{P}_1{+5s5p}^3{P}_1\to {5s5p}^1{P}_1{+5s}^{21}{S}_0$ is also reported and measured to be $1.1\times {10}^{-10}{\mathrm{cm}}^3{\mathrm{}\mathrm{s}}^{\mathrm{-}1}.$ The cross section for this exothermic reaction is found to be nearly independent of collision velocity.

A continuous measurement of energy that is sharp (perfect) leads to the quantum Zeno effect (freezing of the state). Only if the quantum measurement is fuzzy (unsharp), continuous monitoring gives a readout $E\left(t\right)\mathrm{}$ from which information about the dynamical development of the state vector of the system may be obtained in certain cases. This is studied in detail. Fuzziness is thereby introduced with the help of restricted path integrals equivalent to non-Hermitian Hamiltonians. For an otherwise undisturbed multilevel system it is shown that this measurement represents a model of decoherence. If it lasts long enough, the measurement readout discriminates between the energy levels and the von Neumann state reduction is obtained. For a two-level system under resonance influence (which undergoes, in the absence of measurement, Rabi oscillations between the levels) different regimes of measurement are specified depending on its duration and fuzziness: (i) the Zeno regime, where the measurement results in a freezing of the transitions between the levels, and (ii) the Rabi regime, where the transitions are maintained. It is shown that in the Rabi regime at the border to the Zeno regime a correlation exists between the time-dependent measurement readout and the modified Rabi oscillations of the state of the measured system. Possible realizations of continuous fuzzy measurements of energy are sketched.

The dissociative recombination (DR) of vibrationally excited H${}_2^{+}$ ions to form products in high Rydberg states has been investigated experimentally and theoretically for small $(0.01\mathrm{}-0.1$ eV) center-of-mass energies of the projectile electron. The merged beam method was used in the experiment and very large cross sections were found for DR from highly vibrationally excited states. The Rydberg states population was analyzed by the application of an electric field ionizer with an axial electric field in excess of 70 kV/cm, which is sufficient to ionize Rydberg states with $n>~10$. Experiments with and without the ionizer were performed and cross sections $\sigma (0<n<~21)$, $\sigma \mathrm{}(n<\mathrm{}10\mathrm{})\mathrm{}$, and $\sigma (10\mathrm{}<~n<~21)$ were measured. The dipole approximation was used for the interpretation of the experimental results. Molecular rovibrational transitions were considered quantum mechanically. At low collision energy (0.01 eV), DR cross sections with high $n=10\mathrm{}-21$ Rydberg products arise from initial vibrational states $v>~15$. Absolute values of these cross sections are found to be of the order of magnitude of ${10}^{-12}-{10}^{-13}$ cm${}^2$. Comparison of theoretical and experimental results has shown that the modified back autoionization (involving transitions to the continuum and to very high $n$; that is the “indirect” mechanism of DR) plays a significant role for all cross sections.

We present cross sections for the direct charge-transfer process ${\mathrm{N}}^{4+}\mathrm{}\left(2s\right)+\mathrm{H}\to {\mathrm{N}}^{3+}{(nl;n}^{\prime }{l}^{\prime })+{\mathrm{H}}^{+}$ for center-of-mass collision energies between 0.1 eV/amu and 8 keV/amu. The results are in good agreement, at low energies, with merged-beams measurements for the total electron-capture cross sections in collisions of ${\mathrm{N}}^{4+}$ with hydrogen and deuterium targets. We also compare the calculated final-state cross sections with the results of recent translational energy spectroscopy measurements. The calculated final-state cross sections show good agreement with the experiment for ion projectile energies up to 8 keV. Our calculations suggest that the total electron-capture cross sections display Langevin behavior for collision energies below 0.4 eV/amu.

A method is proposed for investigating muon transfer from excited muonic hydrogen atoms to an element $Z>\mathrm{}2\mathrm{}$, and is applied to argon measurements. It makes use of a comparison between the muonic x-ray intensity patterns of the Lyman series of this element measured in mixtures with and without hydrogen. The analysis of the data taken in two gas mixtures H${}_2$ + Ar at 15 bar with argon concentrations of 2% (0.3%), yields consistent results. In both mixtures, two thirds of the prompt argon x rays proceed from transfer from excited $\mu p^{*}$ states. The Coulomb capture ratio determined in both mixtures yields a mean value of $A$(H${}_2$,Ar) = 0.21(2), and agrees with the corresponding pionic ratio.

It is well known that the effective potential describing the interaction of a charged particle with a charged or neutral system at large distances, but in the nonretardation region, is given by the sum of the Coulomb term, if the net charge of the system is not zero, a static dipole polarization potential $-a/2\mathrm{}{\rho }^4$, a term $\sim 1/{\rho }^6$ plus higher-order terms. In the retardation region a term $\sim 1/{\rho }^5$ appears which is a correction to the static dipole polarization potential. It is shown here within the three-body approach that the dynamic polarization of the bound state through the continuum causes a long-range nonretardated term $\sim 1/{\rho }^5$ which can also be considered as a correction to the static dipole polarization potential and which exists in the nonretardation region.

The Auger decay of the C $1s\to 3p$ excitation in CO has been studied by means of vibrationally selective angle-resolved electron spectroscopy. It is shown that for these highly excited Rydberg states the strict spectator model works excellently in describing the Auger decay. Consequently, all the spectral features have been identified by comparison to previous normal Auger studies. Intense lines belonging to $3p\to 4p$ shakeup also accompany the main lines; together with the total absence of any participator contribution, this reveals the atomiclike nature of the $3p$ Rydberg orbital. Remarkably large differences between the decay spectra recorded on the $3p({\upsilon }^{\prime }=0)$ and the $3p({\upsilon }^{\prime }=1)$ resonance reveal the spatial differences in the decay paths. For transitions to the final state with the lowest binding energy in the spectator region, an angular anisotropy dependent upon the vibrational quantum number of the final state is observed. We observe different angular anisotropy for transitions to different vibrational levels of the same electronic final state in resonant Auger spectroscopy.

A procedure discussed by Bates for calculating ion-atom excitation and ionization cross sections and energy loss in the plane-wave Born approximation has been programmed. The procedure involves integration over the product of elastic scattering factors or generalized oscillator strengths for excitation or ionization from both projectile and target. The calculations are done in the center-of-mass system where the distinction between projectile and target is lost. Thus the cross sections and energy loss in the laboratory frames of both target and projectile emerge from a center-of-mass calculation symmetrical in nuclear and net charges. The traditional simple modeling of energy loss, using scaled proton stopping power (SP) and an effective projectile charge, is unsymmetrical, and therefore dubious as a guide for extrapolating to ion-ion energy loss. Because the energy loss includes processes that cannot be uniquely allocated to one ion or the other, e.g., mutual ionization, one does not expect, in general, a simple SP picture to suffice. However, it is found at intermediate and high center-of-mass energies that the energy loss is dominated by elastic scattering of one ion and ionization of the other. From this observation, and the requirement that hydrogenic ion results be recovered in the appropriate limit, a simple extension of the Bethe formula is obtained. Explicit subshell and total ionization cross sections are presented for Li ions interacting with neutral Zn and Au, and the calculated energy loss is compared with experiment. It is found that the simple extension of the Bethe formula is in surprisingly good agreement with the explicit calculations, suggesting that an improved extension of the Bethe formula may exist.

Angle-resolved measurements of the Ar ${2p}_{1/2}^{-1}4s,3d,4d$ and ${2p}_{3/2}^{-1}4s,3d,4d$ resonant Auger transitions have been carried out using photons from an undulator beamline at the Advanced Light Source. The intensity distributions and angular distribution anisotropy (β) parameters have been reported for nearly all of the possible ${3p}^4\mathrm{nl}$ final ionic states. Our results further verify the predictions of the spectator model for the ${2p}_{1/2,3/2}^{-1}4s$ resonances and the subsequent breakdown of this model for the ${2p}_{1/2,3/2}^{-1}3d$ and ${2p}_{1/2,3/2}^{-1}4d$ relative intensities. No prior measurement of the resonant Auger β parameters of the ${2p}_{1/2,3/2}^{-1}3d$ and ${2p}_{1/2,3/2}^{-1}4d$ resonances, and the intensity distribution for the ${2p}_{1/2}^{-1}4d$ resonance has been reported, to the best of our knowledge. Our results have been compared with previous experimental and theoretical results wherever possible.

We report experimental rate coefficients for the energy-pooling collisions $\mathrm{K}{(4P}_J)+\mathrm{K}{(4P}_J)\to \mathrm{K}\mathrm{}\left(4S\right)+\mathrm{K}\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ with product states $nl=5P,$ $6S,$ and $4D.$ The experimental procedure and analysis are similar to those used in a recent study of energy-pooling collisions in cesium. In potassium, it was found that ${4P}_{1/2}{+4P}_{1/2}$ collisions are more efficient than ${4P}_{3/2}{+4P}_{3/2}$ collisions for populating $5P,$ while the opposite is true for populating $6S.$ Since fluorescence from $4D$ was not seen, we can only report an upper limit for that rate coefficient.

We present the asymptotic solution of the Schrödinger equation for three charged particles in the region ${\Omega }_{\alpha }$ in which ${\rho }_{\alpha }\to \infty$ and $r_{\beta \gamma }/{\rho }_{\alpha }\to 0,$ where $r_{\beta \gamma }$ is the distance between particles β and γ, and ${\rho }_{\alpha }$ is the distance between particle α and the center of mass of the pair (β,γ) $\left(\alpha \ne \beta \ne \gamma \right).\mathrm{}$ Our asymptotic wave function in ${\Omega }_{\alpha }$ satisfies the Schrödinger equation up to terms of order $O(1/{\rho }_{\alpha }^2)$ and contains the zeroth-order terms and all of the first-order $O(1/{\rho }_{\alpha })$ terms. The new wave function contains additional terms which are absent in previous wave functions derived recently by others. The additional terms can be expressed in terms of solutions of a two-body problem with boundary conditions which do not correspond to the conventional boundary conditions for two-body states. We also prove that the leading term of our asymptotic wave function in ${\Omega }_{\alpha }$ is equal to the leading term of the Redmond-Merkuriev (RM) wave function in ${\Omega }_{\alpha },$ and hence the RM wave function is applicable in regions of ${\Omega }_{\alpha }(\alpha =1,2,3)$ up to terms of order $O(1/{\rho }_{\alpha }).\mathrm{}$

Dirac wave functions for high-energy electrons channeled in crystals are obtained for crystal string potentials. Specifically, we study partial cylindrical wave expansions for “cylindrical constant and $1/\rho$ potentials. The periodicity along the crystal axis is taken into account as a perturbation to the cylindrical wave functions. We also find a Sommerfeld-Maue-like solution for the $1/\rho$ potential. The cross section for channeling electron-positron pair production in continuum states is obtained for the crystal string potential. For two-dimensional Sommerfeld-Maue-like electron and positron wave functions, matrix elements and cross section are obtained for unpolarized photons. The fact that channeling continuum pair production can only occur when the photon is hitting the crystal string at a small, finite angle is taken into account.

We have measured the experimental final average charge states for ${\mathrm{C}}^{q+}$ $\mathrm{}(q=2,4,6+),$ ${\mathrm{Ar}}^{q+}$ $\mathrm{}(q=8,16,17+),$ and ${\mathrm{Fe}}^{q+}$ $\mathrm{}(q=5,10,15,22+)\mathrm{}$ ions grazingly reflected from a smooth graphite surface as a function of the initial charge state, impact angle, and impact velocity $(v<\mathrm{}1\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}).\mathrm{}$ The final charge state is almost independent of the initial charge state of the ion and of the impact angle for all investigated ions and impact velocities, which indicates that the projectile experiences a charge-state equilibration during the grazing-angle collision. The velocity dependences of the average charge state after a grazing-angle collision and after foil penetration were found to be similar. However, the grazing-angle collision yields the lower average charge state. The three kinds of projectiles used in this work show similar properties during the scattering, despite their different electronic structures or masses, which suggests that our results can be generalized for any kind of highly charged ion.

The electronic self-energy of hydrogenic ions interacting with a jellium metal surface is studied within the fixed-ion approximation. A model framework is introduced that allows for the efficient computation of the complex (non-Hermitian) self-energy matrix in a large space of (bound) hydrogenic states. For the specific case of protons interacting with an aluminum surface, resonance energies and widths of dressed ionic states are obtained by diagonalizing the self-energy matrix. The hybridization properties of the dressed ionic states are analyzed. The self-energy of individual dressed states is found to converge rapidly with increasing dimension of the space of unperturbed hydrogen states. The resonance energies are compared to (1) energies obtained by diagonalizing only the direct couplings among the hydrogen states and (2) the real part of the diabatic (diagonal) self-energy. This comparison demonstrates the pronounced effect that indirect couplings between hydrogen states via conduction band states have on the resonance energies at intermediate and small ion-surface distances. Our results for incident protons are confronted with the results of other (perturbative and nonperturbative) calculations of level shifts and widths in proton-surface interactions. Although we use a simplified electronic potential, we find good agreement with calculations employing more refined potentials.

A “which-path” (welcher Weg) measurement necessarily destroys the fringes in a double-slit interference experiment. We show that in all instances one may attribute this destruction to a disturbance of the particle’s momentum by an amount equal to at least $\pi ħ/2d$, where $d$ is the slit separation, in accordance with the uncertainty principle. However, this momentum transfer need not be local; that is, it need not act at either of the slits through which the particle passes. For well-known welcher Weg measurements such as Einstein’s recoiling slit and Feynman’s light microscope, the disturbance can be understood in terms of random classical momentum kicks that act locally. In some recent proposals, including that by Scully, Englert, and Walther [Nature (London) 351, 111 (1991)], the momentum transfer is of a peculiarly quantum, nonlocal nature. In this paper we introduce a formalism based on the Wigner function, as this describes both the local and nonlocal momentum transfer caused by any welcher Weg measurement. We show that for some examples, such as that of Scully, Englert, and Walther, there is no momentum disturbance at the slits even though the nonlocal momentum disturbance is sufficient to destroy the interference pattern. Finally, we discuss the experimental signatures of nonlocal versus local momentum transfer and demonstrate a strong similarity to the nonlocality of the Aharonov-Bohm effect.

We investigate theoretically the use of time-varying magnetic fields to selectively create and manipulate quasiparticles in magnetically trapped Bose condensates. To maximize the transition matrix element connecting two desired quasiparticle states, the spatial symmetry of the applied magnetic field must be tailored to exploit the different spatial distributions of magnetization in the two quasiparticle states. This “spatial magnetic resonance” effect is analogous to the Franck-Condon factor in electric dipole transitions in diatomic molecules. Experimentally, the spatial magnetic resonance technique may allow the creation of coherences between quasiparticle states, the inversion of quasiparticle state populations, the measurement of quasiparticle lifetimes ($T_1$) and decoherence times ($T_2$), the creation of quasiparticle echoes, etc., in analogy with conventional spin magnetic resonance.

We have simulated the evaporative cooling of a dilute gas of Bose particles including quantum statistics using a Monte Carlo method. This approach can model situations which are far away from quasiequilibrium such as occur during forced evaporative cooling. We have also simulated the dynamical formation of Bose-Einstein condensate for homogeneous and inhomogeneous Bose gases under the random-phase approximation. It was found that the rate of accumulation of Bose particles into low-energy states through collisions is increased by forced evaporation; and a macroscopic population at ground state can be reached at a time scale characterized by classical collision time for an inhomogeneous gas in a harmonic potential. We present the results of simulations for the evaporative cooling and formation of a Bose-Einstein condensate in one-, two-, and three-dimensional position cuts and energy cuts.

An analytic expression is presented for the elementary excitation spectrum of the Bose-Einstein condensate of a trapped boson system in the weakly interacting, low-density limit. Explicit analytic formulas for the elementary excitation spectrum are obtained for harmonic-oscillator traps. These formulas provide information about the behavior of the elementary excitation levels as a function of the number of atoms and their interaction strength for a given trap geometry. They also provide a low-density benchmark for results of fully numerical calculations.

We present results of simulations of a quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation. The QBME is the simplest version of a quantum kinetic master equation derived in previous work. We consider two cases of trapping potentials: a three-dimensional square-well potential with periodic boundary conditions and an isotropic harmonic oscillator. We discuss the stationary solutions and relaxation to equilibrium. In particular, we calculate particle distribution functions, fluctuations in the occupation numbers, the time between collisions, and the mean occupation numbers of the one-particle states in the regime of onset of Bose condensation.