In high-energy atomic collisions between bare high-Z projectiles and low-Z target atoms, an electron may be captured radiatively into the projectile [radiative electron capture (REC)]. The photon angular distributions can be very well represented by radiative recombination (RR) of the projectile with free electrons. This process is the inverse of the photoelectric effect. In this paper, we present exact differential RR cross sections for ${\mathrm{Au}}^{79+}$ and ${\mathrm{U}}^{92+}$ at projectile energies of 0.2, 0.5, 1, 2, 5, and 10 GeV/u. We also show the differential cross sections for the photoelectric effect at x-ray energies corresponding to the former projectile energies. It is seen that because of the dramatic forward-peaking of the cross sections at high energies, measurements of REC from low-Z targets are the most practical way to study the photoelectric effect. In one particular example, 10.8 GeV/u ${\mathrm{Au}}^{79+}$ on Au targets, we show that the RR cross section multiplied with the number of target electrons is very close to the REC cross section calculated within the impulse approximation. © 1996 The American Physical Society.

Using a first-order distorted-wave Born approximation we examine the creation of bound-free electron-positron pairs in relativistic heavy-ion collisions. We consider this process as the transfer of a negative-energy electron in the Coulomb field of one of the colliding ions to a bound state of the other. We calculate differential and integral cross sections for various collision systems by employing exact relativistic single-electron wave functions in momentum space. Our results confirm the experimentally reported increase of cross sections with increasing collision energy and their unexpected strong dependence on the charge number of the ion which captures the electron. The calculated dependence on the charge number of the other colliding partner is, however, weaker than experimentally reported. A major conclusion of this investigation is that at least at moderate relativistic collision energies distortions of electronic states due to both Coulomb centers are important for this process. © 1996 The American Physical Society.

Measurements of the triple differential cross sections in coplanar symmetric energy sharing geometry for the two isoelectronic molecules ${\mathrm{N}}_2$ and CO are presented between 90 and 400 eV incident energy. At 400 eV, our results are compared to those of previous (e,2e) experiments done in other geometries and to photoionization data. At this incident energy, a comparison is also made with the plane wave impulse approximation (PWIA). Our calculations show that this does not perfectly describe the measured cross sections. Measurements made over an extended angular range, 30°–120°, present two maxima: that at large angle results from backscattering of the projectile prior to ionization of the target and is not explained by the PWIA. As energy is decreased, as for atoms, the relative importance of the low angle peak diminishes and that of the large angle peak increases: we then lack an adequate theoretical model and only comparison with data obtained for atomic targets under similar kinematical conditions is possible. Our high energy resolution permits the observation of several satellite structures for both target molecules, in particular for CO. At 400 eV, the assignment of these to different residual ion primary hole states correlates with the forms of the angular distributions. © 1996 The American Physical Society.

Levinson’s theorem relates the zero-energy phase shift δ for potential scattering in a given partial wave l, by a spherically symmetric potential that falls off sufficiently rapidly, to the number of bound states of that l supported by the potential. An extension of this theorem is presented that applies to single-channel scattering by a compound system initially in its ground state. As suggested by Swan [Proc. R. Soc. London Ser. A 228, 10 (1955)], the extended theorem differs from that derived for potential scattering; even in the absence of composite bound states δ may differ from zero as a consequence of the Pauli principle. The derivation given here is based on the introduction of a continuous auxiliary ‘‘length phase’’ η, defined modulo π for l=0 by expressing the scattering length as A=a cotη, where a is a characteristic length of the target. Application of the minimum principle for the scattering length determines the branch of the cotangent curve on which η lies and, by relating η to δ, an absolute determination of δ is made. The theorem is applicable, in principle, to single-channel scattering in any partial wave for ${\mathit{e}}^{\pm }$-atom and nucleon-nucleus systems. In addition to a knowledge of the number of composite bound states, information (which can be rather incomplete) concerning the structure of the target ground-state wave function is required for an explicit, absolute, determination of the phase shift δ. As for Levinson’s original theorem for potential scattering, no additional information concerning the scattering wave function or scattering dynamics is required. © 1996 The American Physical Society.

A recent formulation provides an absolute definition of the zero-energy phase shift δ for multiparticle single-channel scattering of a particle by a neutral compound target in a given partial wave l. This formulation, along with the minimum principle for the scattering length, leads to a determination of δ that represents a generalization of Levinson’s theorem. In its original form that theorem is applicable only to potential scattering of a particle and relates δ/π to the number of bound states of that l. The generalized Levinson theorem relates δ/π for scattering in a state of given angular momentum to the number of composite bound states of that angular momentum plus a calculable number that, for a system described in the Hartree-Fock approximation, is the number of states of that angular momentum excluded by the Pauli principle. Thus, for example, for electron scattering by Na, with its (1s${)}^2$(2s${)}^2$(2p${)}^6$3s configuration and with one L=0 singlet composite bound state, δ would be π+2π for s-wave singlet scattering, 0+3π for s-wave triplet scattering, and 0+π for both triplet and singlet p-wave scattering; the Pauli contribution has been listed first. The method is applicable to a number of ${\mathit{e}}^{\pm }$-atom and nucleon-nucleus scattering processes, but only applications of the former type are described here. We obtain the absolute zero-energy phase shifts for ${\mathit{e}}^{\mathrm{-}}$-H and ${\mathit{e}}^{\mathrm{-}}$-He scattering and, in the Hartree-Fock approximation for the target, for atoms that include the noble gases, the alkali-metal atoms, and, as examples, B, C, N, O, and F, which have one, two, three, four, and five p electrons, respectively, outside of closed shells. In all cases, the applications provide results in agreement with expectations. © 1996 The American Physical Society.

A mechanism for dissociative excitation (DE) of molecular ions via autoionizing resonances is discussed. This mechanism produces dissociation at collision energies below the excitation threshold for the ion’s dissociative states and can alter the dissociation products. Calculated DE cross sections for ${}_{}{}^4{}_{}{}^{}\mathrm{HeH}_{}^{+}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{HeD}_{}^{+}{}_{}{}^{}$ between 5 and 25 eV contain contributions from several resonances and agree well with the recent measurements by Strömholm et al. [Phys. Rev. A (to be published)]. In this completely ab initio study the electronic scattering parameters came from complex Kohn variational calculations and a quantum wave-packet treatment was used for the dissociation dynamics. © 1996 The American Physical Society.

The rate of the radiative decay of the ${\mathrm{HeH}}^{+}$(b${\mathrm{}}^3$${\mathrm{\Sigma }}^{+}$) molecular ion has been investigated. At infinite internuclear separation the b${\mathrm{}}^3$${\mathrm{\Sigma }}^{+}$ electronic state dissociates to form metastable atomic helium He(2${\mathrm{}}^3$S) and a proton ${\mathrm{H}}^{+}$. The optically allowed electronic transition to the lowest triplet ${\mathrm{HeH}}^{+}$(a${\mathrm{}}^3$${\mathrm{\Sigma }}^{+}$) state which dissociates to ${\mathrm{He}}^{+}$(1s) and H(1s) was considered. This transition can lead to the population of metastable triplet (a${\mathrm{}}^3$${\mathrm{\Sigma }}^{+}$) states in beams of ${\mathrm{HeH}}^{+}$ ions. © 1996 The American Physical Society.

The hyperspherical coupled-channel method is applied to the positron-helium scatterings in a low-energy region below 54.4 eV. An independent electron model is used for the helium atom under the approximation that the active electron is bound by a central model potential. All the hyperspherical adiabatic states associated with Ps(n,l; n=1-4, l=0-2) and He(1snl; n=1-5, l=0-3) in the separated-atom limit are coupled for the expansion of the scattering equation, which is solved by means of a hybrid procedure of the diabatic-by-sector and the conventional adiabatic-basis-expansion methods. Excellent agreement is obtained with experiment for the positronium formation. © 1996 The American Physical Society.

We report experiments on dissociative recombination (DR) of ${\mathrm{HD}}^{+}$ and ${\mathrm{H}}_2^{\mathrm{}+}$. Product state information has been obtained over a wide range of electron energies with a position sensitive detector consisting of a graded absorber in combination with a surface-barrier detector. At low electron energies (<3 eV) hydrogen atoms are formed preferentially in highly excited states (n>2); at high electron energies (>12 eV) both hydrogen fragments are excited. The dissociative recombination rate of ${\mathrm{H}}_2^{\mathrm{}+}$ has been measured also as a function of storage time in the energy range of 0 eV to 20 eV. We show that the ${\mathrm{H}}_2^{+}$ beam is still vibrationally excited after 20 s at our experimental conditions. The ${\mathrm{H}}_2^{\mathrm{}+}$ ions relax vibrationally through interaction with electrons in the electron cooler. Vibrationally excited levels (v≥5) have DR rates that exceed the DR rate of the lower vibrational levels by two orders of magnitude. The latter observation has important consequences for the interpretation of previous DR experiments on ${\mathrm{H}}_2^{\mathrm{}+}$. © 1996 The American Physical Society.

Electron capture and direct elastic scattering in collisions of ${\mathrm{H}}^{+}$ ions with ${\mathrm{C}}_2$${\mathrm{H}}_2$ molecules are studied by using a molecular representation within a fully quantum-mechanical approach below 1.5 keV. Calculations are carried out at two different molecular configurations: (i) ${\mathit{C}}_{00\mathit{v}}$ symmetry, in which ${\mathrm{H}}^{+}$ approaches the H atom along a C—H bond in the acetylene (${\mathrm{C}}_2$${\mathrm{H}}_2$), and (ii) ${\mathit{C}}_{2\mathit{v}}$ symmetry, in which ${\mathrm{H}}^{+}$ approaches perpendicularly toward the midpoint between two carbon atoms. We find that electron capture in the ${\mathit{C}}_{00\mathit{v}}$ symmetry configuration takes place preferentially over that in the ${\mathit{C}}_{2\mathit{v}}$ symmetry configuration at scattering angles above 15°. The results for the ${\mathit{C}}_{2\mathit{v}}$ and ${\mathit{C}}_{00\mathit{v}}$ symmetries are comparable in magnitude below 10°, although the ${\mathit{C}}_{2\mathit{v}}$ symmetry dominates slightly at still smaller angles. Hence, interferences arising from these molecular configurations in differential cross sections for electron capture and elastic scattering processes are strongly present at angles smaller than a few degrees. Accordingly, the total cross section for the ${\mathit{C}}_{2\mathit{v}}$ symmetry is larger by a factor of 3 at 1 keV, and the difference widens as the energy decreases to the eV regime. This is because in ${\mathit{C}}_{2\mathit{v}}$ symmetry, ${\mathrm{H}}^{+}$ can have a larger overlap with the charge distribution of the ${\mathrm{C}}_2$${\mathrm{H}}_2$ molecule, thus causing a stronger interaction. © 1996 The American Physical Society.

Mean energy losses of 10.4-MeV neutral hydrogen atoms penetrated through thin carbon foils of 3.7–13.4 μg/${\mathrm{cm}}^2$ were measured using a high-resolution magnetic spectrograph. The measured particles are those entered into the carbon foil as ${\mathrm{H}}^0$ and emerged from it as ${\mathrm{H}}^0$. From the attenuation measurement of ${\mathrm{H}}^0$ in the foils, we can regard the energy losses as those of ${\mathrm{H}}^0$ in a frozen charge state. The measured stopping power of carbon for 10.4-MeV ${\mathrm{H}}^0$ is 21.3±1.8 eV/(μg/${\mathrm{cm}}^2$) and is about one-half that for ${\mathrm{H}}^{+}$ at the same speed. This result agrees well with the theoretical predictions based on the first-order Born approximation. © 1996 The American Physical Society.

We calculated the mean energy loss as a function of the exit angle for 100 and 400 keV/amu ${\mathrm{H}}_2^{\mathrm{}+}$ ions transmitted through thin carbon foils. The results showed that at 100 keV the energy loss exhibited a maximum in the forward direction as opposed to that of protons, which had a minimum at zero degree ejection angle. Our studies demonstrate that such a difference stems from the wake or polarization forces acting upon the trailing ion in the cluster. © 1996 The American Physical Society.

We study the approach to equilibrium of a Bose gas to a superfluid state. We point out that dynamic scaling, characteristic of far from equilibrium phase-ordering systems, should hold. We stress the importance of a nondissipative Josephson precession term in driving the system to a new universality class. A model of coarsening in dimension d=2, involving a quench between two temperatures below the equilibrium superfluid transition temperature (${\mathit{T}}_{\mathit{c}}$), is exactly solved and demonstrates the relevance of the Josephson term. Numerical results on quenches from above ${\mathit{T}}_{\mathit{c}}$ in d=2,3 provide evidence for the scaling picture postulated. © 1996 The American Physical Society.

Delayed-choice experiments have been performed using an atomic Stern-Gerlach interferometer operating with a low-intensity beam of metastable hydrogen atoms. By use of a fast-commutable analyzer, it is possible to modify the operating mode of the interferometer while the atom has already entered the device. Various types of delayed-choice experiments have been carried out to check the standard interpretation of quantum-mechanics. Within the experimental accuracy, our results do not show any discrepancy between permanent and delayed-choice operating modes of the interferometer. © 1996 The American Physical Society.

For a non-self-interacting Bose gas with a fixed, large number of particles confined to a trap, as the ground-state occupation becomes macroscopic, the condensate number fluctuations remain microscopic. However, this is the only significant aspect in which the grand canonical description differs from canonical or microcanonical in the thermodynamic limit. General arguments and estimates including some of the vanishingly small quantities are compared to explicit, fixed-number calculations for ${10}^2$–${10}^6$ particles. © 1996 The American Physical Society.

We study the stability of a Bose condensate of atomic ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ in a (harmonic oscillator) magnetic trap at nonzero temperatures. In analogy to the stability criterion for a neutron star, we conjecture that the gas becomes unstable if the free energy as a function of the central density of the cloud has a local extremum which conserves the number of particles. Moreover, we show that the number of condensate particles at the point of instability decreases with increasing temperature, and that for the temperature interval considered, the normal part of the gas is stable against density fluctuations at this point. © 1996 The American Physical Society.

With strong rare-earth permanent magnets we have built highly refractive atom-optical components for laser-cooled atoms. We have studied the influence of axially symmetric multipole components on a cesium atomic beam. In analogy to traditional optics the action of a quadrupole ring parallels a conical prism, or axicon. Hexapole lenses were applied for focusing with a more than 1000-fold increase in atomic flux density at the focal spot and for imaging with the atomic beam. Two hexapole lenses were combined to form a telescope, which was operated off axis in order to separate fast thermal and slowed atoms. The experiments can approximately be described in terms of geometrical optics. © 1996 The American Physical Society.

A cylindrical light lens for atoms is studied in the limit of high detuning. The dynamics of atomic motion in a quantized electromagnetic field is shown to be separable into strictly classical and purely quantum-mechanical aspects when an ideal lens of arbitrary thickness is assumed. New insight is gained in the thick-lens regime, both in the classical and quantal domain. Different sources of aberration in nonideal lenses are studied. Their inclusion in a subsequent feasibility discussion for the observation of focal structures caused by field quantization sets experimental tolerances for an eventual measuring apparatus. © 1996 The American Physical Society.

We study the three-dimensional atomic Bose gas using renormalization group techniques. Using our knowledge of the microscopic details of the interatomic interaction, we determine the correct initial values of our renormalization group equations and thus obtain also information on nonuniversal properties. As a result, we can predict, for instance, the critical temperature of the gas and the superfluid and condensate density of the Bose-Einstein condensed phase in the regime na${\mathrm{\Lambda }}_{\mathit{th}}^2$≪1, where the average interaction energy is small compared to the average kinetic energy. © 1996 The American Physical Society.

We examine the magnetic response of free clusters considering the spin direction and the cluster orientation as the only active degrees of freedom. The average magnetization in small fields approaches the Langevin value for paramagnets, depending on the degree to which the Hamiltonian preserves symmetries. Superparamagnetic behavior is not achievable within models considering only these degrees of freedom. © 1996 The American Physical Society.