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The measurements of the M- and N-shell ionization probabilities in gold bombarded by highly charged S q+ (q = 4–14) ions of energy 0.4–3.8 MeV/amu are reported. The ionization probabilities were extracted from the measured L-X-ray spectra which were substantially modified by the multiple ionization effects. The observed L-X-ray line shifts and broadening allowed us (Banaś et al., 2002) to extract both the M- and N-shell ionization probabilities for the zero impact parameter. These ionization probabilities, which correspond to the moment of X-ray emission , were correlated with the ionization probabilities for the moment of ion impact ionization by using the vacancy rearrangement procedure developed here. In this way the ionization probabilities for the moment of ion impact multiple ionization were obtained. By comparing to the theoretical predictions of the semiclassical approximation (SCA) (Trautmann and Kauer, 1989) and the “geometrical model” (GM) (Sulik et al., 1987) based on the binary encounter approximation (BEA), the role of the electronic wave functions and the binding effect is discussed. Generally, the calculations using the hydrogenic wave functions reproduce the measured ionization probabilities.

Particle-induced X-ray emission (PIXE) technique is usually applied using typically 1 MeV to 3 MeV protons or helium ions, for which the ion-atom interaction is dominated by the single ionization process. For heavier ions the multiple ionization plays an increasingly important role and this process can influence substantially both the X-ray spectra and atomic decay rates. Additionally, the subshell coupling effects are important for the L- and M-shells ionized by heavy ions. Here we discuss the main features of the X-ray emission induced by heavy ions which are important for PIXE applications, namely, the effects of X-ray line shifts and broadening, vacancy rearrangement and change of the fluorescence and Coster–Kronig yields in multiple ionized atoms. These effects are illustrated here by the results of the measurements of L X-ray emission from heavy atoms bombarded by 6 MeV to 36 MeV Si ions, which were reported earlier. The strong L-subshell coupling effects are observed, in particular L 2 -subshell, which can be accounted for within the coupling subshell model (CSM) developed within the semiclassical approximation. Finally, the prospects to use heavy ions in PIXE analysis are discussed.

The L-shell X-ray production cross sections have been measured for sulphur ions in the energy range of 12.8–120 MeV for Au and Bi elements. The experimental L X-ray spectra were analyzed using the method that takes into account the multiple ionization in outer shells. The L-subshell ionization cross sections have been obtained from measured X-ray production cross sections for resolved Lα 1,2 Lγ 1 and Lγ 2,3 transitions using the L-shell fluorescence and Coster–Kronig yields modified by the multiple ionization effects in the M and N shells. The results are compared with the predictions of ECUSAR theory, which is the modified ECPSSR approach describing both direct ionization and electron-capture processes and the semiclassical approximation (SCA) calculations for direct ionization. These approaches were modified by the L-subshell coupling effects within the “coupled-subshell model” (CSM). Both modified approaches are in good agreement with the data. Remaining discrepancies are discussed in terms of the L-shell decay rates modified for the multiple ionization effects.

In recent years, a large number of papers have appeared that dealt with $\EPEM$ pair production in heavy ion collisions at high energies. To a large extent these studies were motivated by the existence of relativistic heavy ion accelerators all over the world. There pair production can be studied in so called ``ultra-peripheral collisions'', where the ions do not come close enough to interact strongly with each other. Various different methods have been used and it is the purpose of this review to present a unified picture of the present status of the field., 51 pages, 16 figures, submitted to Physics Reports

Analysing (e,e'p) experimental data involves corrections for radiative effects which change the interaction kinematics and which have to be carefully considered in order to obtain the desired accuracy. Missing momentum and energy due to bremsstrahlung have so far always been calculated using the peaking approximation which assumes that all bremsstrahlung is emitted in the direction of the radiating particle. In this article we introduce a full angular Monte Carlo simulation method which overcomes this approximation. The angular distribution of the bremsstrahlung photons is reconstructed from H(e,e'p) data. Its width is found to be underestimated by the peaking approximation and described much better by the approach developed in this work., Comment: 11 pages, 13 figures

We calculate the inelastic electron- and muon-pair production in peripheral relativistic heavy ion collisions in the region of large Q 2 of one of the photons. This offers a possibility to study the quark distribution functions in ions in "ultraperipheral heavy ion collisions". The calculations are compared with those making use of the equivalent photon and the equivalent lepton approximation. We compare the results for Pb-Pb and Pb-p collisions at RHIC (γ ≈ 100) and LHC (γ ≈ 3000) energies. Furthermore we include nuclear modifications to the parton distribution functions in our calculations to study their effect on the cross sections.

The coupling and binding effects in ionization of L-shell electrons by heavy ions have been studied by measuring the L γ (L–N,O) X-ray transitions in gold excited by an impact of O, Si and S ions in the energy range 0.3–5 MeV/amu. The L-subshell ionization cross sections were extracted from measured X-ray spectra taking into account their substantial modifications due to the multiple ionization effects, which also change the fluorescence and Coster–Kronig yields. In order to interpret the data the L-subshell couplings were incorporated in the theoretical calculations based on the semiclassical approximation (SCA) within the “coupled subshell model” (CSM). Resulting SCA–CSM calculations, which describe the data for oxygen ions quite satisfactory, are further modified to include the saturation of the binding effect in order to describe the data for heavier Si and S ions. We find that the semiclassical SCA–CSM calculations of L-shell ionization by heavy ions ( Z 1 ≫ 1), which include corrections both for coupling and binding saturation effects, agree reasonably well with the measured data.

Virtual radiative corrections due to the long range Coulomb forces of heavy nuclei with charge Z may lead to sizeable corrections to the Born cross section usually used for lepton-nucleus scattering processes. An introduction and presentation of the most important issues of the eikonal approximation is given. We present calculations for forward electroproduction production of rho mesons in a framework suggested by the VDM (vector dominance model), using the eikonal approximation. It turns out that Coulomb corrections may become relatively large. Some minor errors in the literature are corrected., Comment: 14 pages, 6 figures, published version

Due to coherence, there are strong electromagnetic fields of short duration in very peripheral collisions. They give rise to photon-photon and photon-nucleus collisions with a high flux up to an invariant mass region hitherto unexplored experimentally. After a general survey of the field equivalent photon numbers and photon-photon luminosities, especially for relativistic heavy ion collisions, are discussed. Special care needs to be taken to include the effects of the strong interaction and nuclear size in this case. Photon-photon and photon-hadron physics at various invariant mass scales are then discussed. The maximum equivalent photon energy in the lab-system (collider frame) are typically of the order of 3 GeV for RHIC and 100 GeV for LHC. Diffractive processes are an important background process. Lepton-pair, especially electron-positron pair production is copious. Due to the strong fields there will be new phenomena, like multiple e+e- pair production. The experimental techniques to select gamma-gamma-processes are finally discussed together with important background processes.

The experiment DIRAC at CERN aims to measure the lifetime of relativistic π+π- atoms (pionium) with an accuracy of 10%, requiring cross sections for the interaction of pionium with the target material with an accuracy of 1% as theoretical input. We calculate the excitation cross sections for the Coulomb interaction with the target atoms in the Glauber approximation which takes into account all multi-photon exchange processes. We find that they decrease the excitation cross sections, calculated to first order in the Born approximation, by more than 2-15% for target materials with increasing Z and all initial states, much worse than the desired accuracy of 1%.

The results concerning the $e^+e^-$ production in peripheral highly relativistic heavy-ion collisions presented in a recent paper by Baltz {\em{et al.}} are rederived in a very straightforward manner. It is shown that the solution of the Dirac equation directly leads to the multiplicity, i.e. to the total number of electron-positron pairs produced by the electromagnetic field of the ions, whereas the calculation of the single pair production probability is much more involved. A critical observation concerns the unsolved problem of seemingly absent Coulomb corrections (Bethe-Maximon corrections) in pair production cross sections. It is shown that neither the inclusion of the vacuum-vacuum amplitude nor the correct interpretation of the solution of the Dirac equation concerning the pair multiplicity is able the explain (from a fundamental point of view) the absence of Coulomb corrections. Therefore the contradiction has to be accounted to the treatment of the high energy limit., 6 pages, 4 Postscript figures, uses svjour.cls/svepj.clo

The standard procedure of extracting the proton root-mean-square radii from models for the Sachs form factors $G_e (q)$ and $G_m (q)$ fitted to elastic electron-proton scattering data %has a serious flaw. is more uncertain than traditionally assumed. The extrapolation of $G(q)$, from the region $q_{min} < q < q_{max}$ covered by data to momentum transfer $q=0$ where the $rms$-radius is obtained, often depends on uncontrolled properties of the parameterization used. Only when ensuring that the corresponding densities have a physical behavior at large radii $r$ can reliable $rms$-radii be determined.

Magnetic contributions to the interaction of ordinary matter with pionium, i.e. exotic atoms formed from oppositely charged pions, are calculated explicitly in the context of the experiment DIRAC at CERN. These contributions have previously been estimated to amount to about 1% of the complete cross sections. Since this experiment requires the cross sections for electromagnetic processes at the 1% level as an input, a justification by explicit calculation of the previous estimations is necessary. We also estimate the magnitude of relativistic effects particularly for the electromagnetic coupling of the pionium system to the target system. These effects turn out to be negligible.

Multiple ionization in outer M- and N-shells in Ta, Os, Au, Bi, Th and U targets was studied for O, Si and S ion impact at energies of 0.3-2.2 MeV amu-1. Excited Lγ(L-N, O) x-rays measured with a semiconductor Si(Li) detector were resolved by using a newly developed method accounting for simultaneous x-ray energy shift and line broadening due to the multiple ionization. The measured ionization probabilities, corrected for the effect of the vacancy rearrangement up to the moment of L x-ray emission, are interpreted as the ionization probabilities for M- and N-shells for the zero impact parameter. The ionization probabilities for the N-shell are found to be substantially increased by the super-Coster-Kronig transitions. Derived ionization probabilities for M- and N-shells are compared with the predictions of the geometrical model (GM) and the semiclassical (SCA) calculations in the united-atom limit. The universal scaling of the measured ionization probabilities for the M- and N-shells is discussed within the GM and SCA approaches.

Due to the coherence of all the protons in a nucleus, there are very strong electromagnetic fields of short duration in relativistic heavy ion collisions. They give rise to quasireal photon-photon and photon-nucleus collisions with a large flux. RHIC will begin its experimental program this year and such types of collisions will be studied experimentally at the STAR detector. RHIC will have the highest flux of (quasireal) photons up to now in the GeV region. At the LHC the invariant mass range available in gamma-gamma-interactions will be of the order of 100 GeV, i.e., in the range currently available at LEP2, but with a higher gamma-gamma-luminosity. Therefore one has there also the potential to study new physics. (Quasireal) photon-hadron (i.e., photon-nucleus) interactions can be studied as well, similar to HERA, at higher invariant masses. Vector mesons can be produced coherently through photon-Pomeron and photon-meson interactions in exclusive reactions such as A+A -> A+A+V, where A is the heavy ion and V=rho,omega,phi or J/Psi., 6 pages, to be published in the proceedings of the Photon'99 conference

K-shell ionization by slow, heavy projectiles has been studied for moderately asymmetric ( Z 1 / Z 2 ∼ 0.3) collisions by measuring K-X-ray production cross sections in Ca, Sc, Ti, Cr, Fe and Cu excited by 14 N ions of energy 1.75–3.15 MeV. The influence of multiple ionization in L- and M-shells on measured data was estimated by analyzing K-X-ray energy shifts and K β /K α intensity ratios. The results are compared with the predictions of K-shell ionization theories, based on the plane-wave Born approximation (PWBA), semiclassical approximation (SCA), binary-encounter approximation (BEA), and adiabatic molecular orbital (MO) approach. Different corrections to these approaches, to account for the higher-order effects, are discussed. The data are not satisfactorily described in detail by discussed theories over the whole energy range, but the SCA calculations reproduce the present, low-energy data quite reasonably. The need for a more realistic description of the electron binding effect is discussed.

Lα1,2, Lβ1,3,4, Lβ2,15, Lγ1(5) and Lγ2,3(4,4′) X-ray production cross-sections have been measured on selected medium-Z elements using 16O ions with energies from 0.19 to 0.75 MeV u−1. Calculated L-subshell ionization cross-sections were compared with the predictions of the direct ionization theories: the ECPSSR theory, the semiclassical approximation (SCA) in the united atom limit (SCA-UA) and SCA coupled-channel calculations (SCA-CC) involving a few lowest lying states. For the ECPSSR theory, large discrepancies were found for all three subshells. Better overall agreement between the experiment and theory was found for the SCA-UA theory. SCA-CC calculations improved the agreement between experiment and theory for the L2-subshell in the very adiabatic region. By measuring the Lα X-ray production cross-sections on W targets of different thickness, possible contribution of electron capture (EC) to the X-ray production cross-section was estimated to be less than 20%. The degree of multiple ionization of outer shells caused by heavy ion bombardment was estimated from the X-ray line energy shifts and by comparing the X-ray intensity ratios for heavy ions and protons.

We present a calculation of higher order effects for the impact parameter dependent probability for single and multiple electron-positron pairs in (peripheral) relativistic heavy ion collisions. Also total cross sections are given for SPS and RHIC energies. We make use of the expression derived recently by several groups where the summation of all higher orders can be done analytically in the high energy limit. An astonishing result is that the cross section, that is, integrating over all impact parameters, is found to be identical to the lowest-order Born result for symmetric collisions. For the probability itself on the other hand we find rather large effects at small impact parameters compared to the lowest order results, which translate to large effects for the cross section for multiple pair production., 9 pages, 4 figures

We calculate the cross sections for the production of one and more electron-positron pairs due to the strong electromagnetic fields in relativistic heavy ion collisions. Using the generating functional of fermions in an external field we derive the N-pair amplitude. Neglecting the antisymmetrisation in the final state we find that the total probability to produce N pairs is a Poisson distribution. We calculate total cross sections for the production of one pair in lowest order and also include higher-order corrections from the Poisson distribution up to third order. Furthermore we calculate cross sections for the production of up to five pairs including corrections from the Poisson distribution., 13 pages REVTeX, 4 Postscript figures, This and related papers may also be obtained from http://www.phys.washington.edu/~hencken/

{ital L} x-ray production and subshell ionization cross sections of Au and Bi have been measured for the bombardment of {sup 19}F and {sup 28}Si ions in the energy range 30{endash}57 MeV and 36{endash}84 MeV, respectively. Comparison of the {ital L}{alpha} x-ray production cross sections of Au with the earlier data by Malhi and Gray [Phys. Rev. A {bold 44}, 7199 (1991)] shows reasonable agreement for {sup 19}F impact and their data are consistently higher for {sup 28}Si at all energies. The measured {ital L}{alpha} line energy shows a shift towards higher energy, which appears to be proportional to the square of the projectile atomic number at all impact energies. This shift suggests the presence of multiple ionization in the {ital L} and {ital M} shells with a simultaneous production of four {ital M} holes in Au at the impact energy of 3 MeVu{sup {minus}1} of {sup 28}Si. The {ital L}-subshell ionization cross sections obtained from the measured x-ray production cross sections have been compared with the semiclassical approximation and perturbed stationary state theory with energy loss, Coulomb deflection, and relativistic correction for the electron motion calculations, which show large deviations for the {ital L}{sub 1} subshell. The {ital L}{submore » 2}- and {ital L}{sub 3}-subshell ionization cross sections are underestimated by both the theories by a factor of 1.2{endash}4.0 for {sup 28}Si impact whereas for the {sup 19}F case there is reasonable agreement for the {ital L}{sub 3} cross section but the {ital L}{sub 2} cross section is underestimated by 20{endash}30{percent}. {copyright} {ital 1996 The American Physical Society.}« less

We use the world data on electron-deuteron elastic scattering to determine the deuteron structure functions and the charge rms radius. Coulomb distortion is included using second-Born approximation. We find a radius of 2.130 ± 0.003 ± 0.009 fm (±stat., ±syst.), which agrees with the information obtained from nucleon-nucleon scattering and from optical isotope shifts.

L-subshell ionization of Au has been investigated for alpha -particle and lithium-ion bombardments with energies 0.54-1.74 MeV u-1 and 0.65-1.44 MeV u-1, respectively. Comparison of experimental X-ray production cross sections with the predictions of the ECPSSR and SCA theories shows reasonably good agreement for Lalpha and Lbeta X-rays, whereas for Lgamma and Lgamma 1+5 the ECPSSR theory underestimates the cross sections by about 60% for both alpha -particle and lithium-ion impact, and the SCA theory agrees reasonably well. The ECPSSR theory underestimates the L1- and L2-subshell ionization cross sections and gives good agreement for the L3-subshell, whereas the SCA theory overestimates the L3-subshell ionization cross sections and gives good agreement for L1 and L2. The experimental data for the total-ionization cross sections are within 25% of the predictions of both the theories.

In order to study the contribution of a possible colour Van der Waals potential to 208 Pb 208 Pb elastic scattering we discuss the influence of small additional potentials to the pure Coulomb interaction. The study shows, that - besides relativistic effects, vacuum polarisation and nuclear polarisability - the formation of quasimolecules during the scattering process gives the dominant contribution. Perfect agreement with the data would require a colour Van der Waals contribution, but the uncertainty in the quasimolecular effect is considerable.

An approximation based on the WKB method to describe inner-shell ionization processes induced by heavy charged particles is presented. It is shown that this semiquantal approximation agrees, in general, fairly well with the well known semiclassical approximation except in the region of large impact parameters where considerable discrepancies were found.

L-subshell ionization of Au and Bi induced by boron impact has been investigated for impact energies ranging from 0.48 to 0.88 MeV/u. The energy dependence of the measured ionization cross section shows, for the first time, a plateau structure for all three subshells. The plateau structure revealed by previous data for proton and helium impact was for the L1 subshell only and this had been attributed to the bimodal nature of the 2s electron density. The observed plateau structure for all the three subshells and its occurrence at a somewhat lower energy signifies a considerable amount of Stark mixing of target 2s and 2p atomic wavefunctions. Fresh calculations incorporating the Stark mixing effect in target atomic wavefunctions are necessary to improve agreement with the present data. The existing theories, however, are found to be inadequate.

Proton-induced differential and total alignment is reviewed and some calculations presented. A density matrix formalism is employed as the theoretical framework and a more efficient expansion into state multipoles used. The collision T-matrix elements entering the expression for the alignment tensor are calculated in the semiclassical approximation to first order. A coordinate space formulation including classical hyperbolic trajectories for the projectile path is adopted here, to take proper account of deflection. Relativistic Hartree-Fock orbital wavefunctions for bound and continuum electronic states in the partial-wave expansion cover both screening and relativistic effects in the atom in a unifying scheme. The continuum orbitals are calculated iteratively until the frozen core VN-1 potential converges.

The accuracy of the first and second order WKB approximation in describing sub-Coulomb elastic scattering of ions is investigated. Thereby the scattering of non-identical as well as of identical particles is taken into consideration. It is shown that in cases where the behaviour of the scattered ions is not quasi-classical and therefore the first order WKB approximation fails, the second order WKB will be in most cases still a quite good approximation.

The theory of inner shell ionization for arbitrary atomic shells is reviewed. Emphasis is onL- andM-shells in order to show how the proper screening formalism entering the electronic form factor affects the ionization probabilities. The radial wavefunctions in the form factor are computed as relativistic Hartree-Fock orbitals for both bound and continuum states. The continuum orbitals were evaluated in theV(N−1) potential with correct exchange. These results are then compared with the previous ones using screened hydrogen-like wavefunctions and also with the experimental data in some cases.

Measurements of L-shell X-ray production cross sections and corresponding L-subshell ionization cross sections for selected rare earth elements (57

The electronion scattering experiment ELISe is part of the installations envisaged at the new experimental storage ring at the International Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany. It offers an unique opportunity to use electrons as probe in investigations of the structure of exotic nuclei. The conceptual design and the scientific challenges of ELISe are presented. © 2011 Elsevier B.V. All rights reserved., The authors acknowledge financial support from the EC via the INTAS pro- gramme, grants No. 03-54-6545 and 05-1000008-8272. This work was partially supported by the Hessian LOEWE initiative Helmholtz International Center for FAIR

A fully numerical Hartree-Fock approach is outlined in order to calculate atomic states in the field of a magnetic monopole. The exchange potentials are obtained by evaluating directly the non-local definition integrals and by solving local Poisson-like equations, respectively. Using these results, the excitation of helium by slow magnetic monopoles is examined. An improved excitation cross section is reported.

The properties and the observational implications of degenerate heavy neutrino matter that is gravitationally bound by baryonic stars is investigated with special emphasis on the 17 keV neutrino. As a test of our ideas we propose a new experiment aimed at observing the radiative decay of this controversial neutrino.

L X-ray line production cross sections for Eu, Tb and Er elements have been measured as a result of 73Li ion bombardment at energies from 4.2 to 19.6 MeV. The corresponding L1-, L2- and L3-subshell ionization cross sections have been calculated and have been compared to the predictions of the ECPSSR and SCA theories. Possible reasons for observed disagreements between experiment and theory are discussed.

TheKβ spectra of molybdenum, palladium and lanthanum bombarded by 6.7 MeV/amu4He ions were measured with a transmission curved crystal spectrometer.L andM satellite lines were observed and resolved. Experimental energies are compared with those calculated with a MCDF program.M -shell ionization probabilities are deduced from the measured satellite intensity ratios and compared with theoretical (SCA) predictions. The experimental values are found to be higher than the calculated ones (by a factor of 2 for La and a factor of about 4 for Mo and Pd). The influence of coupling effects, electron wave functions, electron capture, electron correlation and target activation is discussed.

Radiative processes lead to important corrections to (e,e{sup '}p) experiments. While radiative corrections can be calculated exactly in QED and to a good accuracy also including hadronic corrections, these corrections cannot be included into data analyses to arbitrary orders exactly. Nevertheless consideration of multiphoton bremsstrahlung above the low-energy cutoff is important for many (e,e{sup '}p) experiments. To date, higher-order bremsstrahlung effects concerning electron scattering experiments have been implemented approximately by employing the soft-photon approximation (SPA). In this paper we propose a novel approach to multiphoton emission which partially removes the SPA from (e,e{sup '}p) experiments. In this combined approach one hard photon is treated exactly; and additional (softer) bremsstrahlung photons are taken into account resorting to the soft-photon approximation. This partial removal of the soft-photon approximation is shown to be relevant for the missing-energy distribution for several kinematic settings at MAMI and TJNAF energies.

We investigate whether the apparent discrepancy between proton electric form factor from measurements using the Rosenbluth separation technique and polarization transfer method is due to the standard approximations employed in radiative correction procedures. Inaccuracies due to both the peaking approximation and the soft-photon approximation have been removed in our simulation approach. In contrast to results from (e,e'p) experiments, we find them in this case to be too small to explain the discrepancy., 6 pages, 3 figures

For many years QED-effects have been investigated in atomic and particle physics mainly in leptonic systems. Little information only is available on QED-effects in Coulomb-interaction between hadrons.1,2) Experiments performed on the proton-proton system1) yield results which disagree with theoretical predictions by an amount of about 50% of the vacuumpolarization effect.

In order to extract the effect of vacuum polarization from 12 C- 12 C elastic scattering data, a detailed theoretical study of the low-energy Mott cross section is performed. It is shown that the contributions of nuclear interaction, Coulomb excitation, bremsstrahlung can be neglected, while radiative corrections and nuclear polarizability can be described by a small additional potential. Screening by atomic electrons is corrected by a screening function, which acts on all potentials. Relativistic effects are accounted for using the “Todorov equation”. In order to overcome numerical difficulties for very long range potentials a WKB approximation and a semiquantal approach are discussed and compared. The study shows that the first-order vacuum-polarization potential contributes most to the correction of the cross section. All other contributions are at least one order of magnitude smaller.

The coupling and binding effects have been studied in $L$-subshell ionization of heavy Au, Bi, Th, and U atoms by an impact of ${^{28}\text{S}\text{i}}^{q+}$ ions in the energy range of 8.5--36.0 MeV. The measured $\mathit{L}$ x-ray spectra were analyzed taking into account the multiple ionization effects in outer $M$ and $N$ shells. The $L$-subshell ionization cross sections have been obtained from measured x-ray production cross sections using the $L$-shell fluorescence and Coster-Kronig yields which were modified for a reduced number of electrons and closed Coster-Kronig transitions in the multiply ionized atoms. The results are compared with the available calculations, which are based on the semiclassical approximation (SCA) as well as the plane-wave Born approximation (PWBA). We demonstrate that for silicon ion impact these theoretical approaches have to be modified to include the $L$-subshell coupling effect using the ``coupled subshell model'' (CSM) as well as the saturation of the binding effect at the united atom limit. The calculations modified for both effects are in much better agreement with the data. In particular, an order-of-magnitude improvement of agreement between the data and the SCA-CSM calculations including the binding-saturation effect is reported for low-energy Si ions for the ${L}_{2}$-subshell. The results are also compared with the predictions of the PWBA based ECPSSR and ECUSAR theories accounting for the energy-loss (E), Coulomb-deflection (C), and relativistic (R) effects treating the binding effect within the perturbed stationary state (PSS) approximation with correction for the binding-saturation effect introduced to describe the united-atom and separated-atom (USA) limits.

The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasi-elastic (e,e') scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which takes the twofold effect of the attractive nucleus on initial and final state electrons into account, namely the modification of the electron momentum in the vicinity of the nucleus, and the focusing of electrons towards the nuclear region leading to an enhancement of the corresponding wave function amplitudes. The focusing effect due to the attractive Coulomb field of a homogeneously charged sphere on a classical ensemble of charged particles incident on the field is calculated in the highly relativistic limit and compared to results obtained from exact solutions of the Dirac equation. The result is relevant for the theoretical foundation of the effective momentum approximation and describes the high energy behavior of the amplitude of continuum Dirac waves in the potential of a homogeneously charged sphere. Our findings indicate that the effective momentum approximation is a useful approximation for the calculation of Coulomb corrections in (e,e') scattering off heavy nuclei for sufficiently high electron energies and momentum transfer., Comment: 16 pages, 9 figures, LATEX, some references added

Absolute $K$-shell ionization cross sections of Sb, Au, and Bi have been measured in collisions with highly charged C, O, and S ions having energies between 2 and $6.25\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕u$. The data are presented along with the earlier results with F and Si ions as projectiles. The measured data have been compared with theoretical models based on the semiclassical approximation including relativistic effect and perturbed stationary state approximation including the corrections for energy loss, Coulomb deflection, and relativistic effects. The data were analyzed in term of relativistic effect on $K$-ionization: its dependence on the projectile atomic number, target atomic number and projectile energy. The present data set along with our recently measured similar data for F and Si ions show that the relativistic effect increases with projectile atomic number and decreases with projectile velocity. A comparison of the experimental data and relativistic calculations, both normalized to nonrelativistic model, show the inadequacy of the theoretical models in describing the relativistic correction on $K$-shell ionization. For example, the theoretical predictions agree with experimental findings for O ions on Bi while the same theoretical predictions deviate from the experimental results by about a factor of 2 for Si and S on Bi, the theory being higher.

The $M$-shell ionization in high-$Z$ atoms by low-energy light $_{1}^{1}\mathrm{H}$, $_{1}^{2}\mathrm{H}$, $_{2}^{3}\mathrm{He}$, and $_{2}^{4}\mathrm{He}$ ions have been studied systematically in the energy range $0.1--1.0\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{amu}$ in order to verify the available theoretical approaches describing the $M$-shell ionization by charged particles in asymmetric collisions. The present low-energy data, combined with our earlier results reported for $M$-shell ionization by hydrogen and helium ions for higher energies, form a systematic experimental basis to test the theoretical predictions of $M$-shell ionization based on the plane-wave Born approximation (PWBA), the semiclassical approximation (SCA), and the binary-encounter approximation (BEA). In the PWBA based approaches the energy loss (E), Coulomb deflection (C), perturbed stationary state (PSS), and relativistic (R) effects were considered within the ECPSSR theory and its recent modification, called the ECUSAR theory, in which a description of the PSS effect was corrected to account for the united- and separated-atom (USA) electron binding energy limits. In the SCA calculations with relativistic wave functions the binding effect was included only in the limiting cases of separated-atom and united-atom limits. Possible contribution of the electron capture, multiple ionization, and recoil ionization to the $M$-shell vacancy production, which is dominated for light ions impact by direct single ionization process, are also discussed. The universal scaling of measured $M$-shell x-ray production and ionization cross sections was investigated in detail. Using the present data the isotopic effect has been studied by comparing the measured $M$-shell ionization cross-section ratios for equal-velocity hydrogen $_{1}^{1}\mathrm{H}$ and $_{1}^{2}\mathrm{H}$ as well as helium $_{2}^{3}\mathrm{He}$ and $_{2}^{4}\mathrm{He}$ isotopes. In addition, the ratios of measured ionization cross sections for $_{1}^{2}\mathrm{H}$ and $_{2}^{4}\mathrm{He}$ were used to investigate the role of the binding effect. The present results are of practical importance for the application of particle-induced x-ray emission technique in trace element studies.

A test particle falling into a classical black hole crosses the event horizon and ends up in the singularity within finite eigentime. In the `more realistic' case of a `classical' evaporating black hole, an observer falling onto a black hole observes a sudden evaporation of the hole. This illustrates the fact that the discussion of the classical process commonly found in the literature may become obsolete when the black hole has a finite lifetime. The situation is basically the same for more complex cases, e.g. where a particle collides with two merging black holes. It should be pointed out that the model used in this paper is mainly of academic interest, since the description of the physics near a black hole horizon still presents a difficult problem which is not yet fully understood, but our model provides a valuable possibility for students to enter the interesting field of black hole physics and to perform numerical calculations of their own which are not very involved from the computational point of view., 6 pages, 3 figures, LATEX

Ll,L{alpha},L{beta},L{gamma},L{gamma}{sub 1+5},L{gamma}{sub 2+3},L{gamma}{sub 4+4=} {sup '} x-ray production cross sections of {sub 58}Ce, {sub 60}Nd and {sub 71}Lu induced by 4-, 6-, 8-, and 10-MeV carbon ions were measured. For Lu, L{gamma}{sub 2+3} is separated from L{gamma}{sub 2+3+6} after revision of the technique of Datz et al. so that L{gamma}{sub 1+5} was used instead of L{gamma}{sub 1}, the L{gamma}{sub 4+4{sup '}}/L{gamma}{sub 1+5} ratio was corrected for multiple ionization, and uncertainties in L{gamma}{sub 4+4{sup '}} were incorporated in the fitting process. L-subshell ionization cross sections were extracted as a weighted average from two combinations of these cross sections, {l_brace}L{alpha},L{gamma}{sub 1+5},L{gamma}{sub 2+3}{r_brace} and {l_brace}L{alpha},L{gamma}{sub 1+5},L{gamma}{r_brace}. It is shown that, to within a few percent, the first of these two combinations results in the identical cross sections as this weighted average. Within 10%, permutations of different sets of single-hole atomic parameters yielded the same ionization cross sections. These cross sections are typically within 15% and at most 35% of the cross sections obtained with atomic parameters that were altered in two different ways for multiple ionization. Extracted subshell and total L-shell ionization cross sections as well as Ce and Nd data of Braziewicz et al. are compared with the ECPSSR theory of Brandtmore » and Lapicki that accounts for the energy-loss (E), Coulomb-deflection (C), perturbed-stationary-state (PSS) and relativistic (R) effects. These measurements are also compared with the ECPSSR theory after its corrections--in a separated and united atom (USA) treatment, and for the intrashell (IS) transitions with the factors of Sarkadi and Mukoyama normalized to match L-shell cross section with the sum of L-subshell cross sections--as well as with the similarly improved semiclassical approximation of Trautmann. For Ce and Nd, the agreement of the extracted ionization cross sections with these theories is poor for L{sub 1} and good for L{sub 2}, L{sub 3}, and total L shell ionization. For the L{sub 2} subshell, this agreement is better for Ce and Nd than for Lu. The ECPSSR theory corrected for the USA and IS effects is surprisingly good for the L{sub 1}-subshell ionization of Lu, while at 4 MeV a similarly corrected semiclassical approximation is in excellent agreement with L{sub 2} and L{sub 3} data but overestimates the L{sub 1} measurement by almost a factor of 2.« less

We study the transverse momentum distribution of vector mesons produced in ultraperipheral relativistic heavy ion collisions (UPCs). In UPCs there is no strong interaction between the nuclei and the vector mesons are produced in photon-nucleus collisions where the (quasireal) photon is emitted from the other nucleus. Exchanging the role of both ions leads to interference effects. A detailed study of the transverse momentum distribution which is determined by the transverse momentum of the emitted photon, the production process on the target and the interference effect is done. We study the total unrestricted cross section and those, where an additional electromagnetic excitation of one or both of the ions takes place in addition to the vector meson production, in the latter case small impact parameters are emphasized., 12 pages, REVTeX manuscript

Continuum states of the Dirac equation are calculated numerically for the electrostatic field generated by the charge distribution of an atomic nucleus. The behavior of the wave functions of an incoming electron with a given asymptotic momentum in the nuclear region is discussed in detail and the results are compared to different approximations used in the data analysis for quasielastic electron scattering off medium and highly charged nuclei. It is found that most of the approximations provide an accurate description of the electron wave functions in the range of electron energies above 100 MeV typically used in experiments for quasielastic electron scattering off nuclei only near the center of the nucleus. It is therefore necessary that the properties of exact wave functions are investigated in detail in order to obtain reliable results in the data analysis of quasielastic (e,e'p) knockout reactions or inclusive quasielastic (e,e') scattering. Detailed arguments are given that the effective momentum approximation with a fitted potential parameter is a viable method for a simplified treatment of Coulomb corrections for certain kinematical regions used in experiments. Numerical calculations performed within the framework of the single particle shell model for nucleons lead to the conclusion that our results are incompatible with calculations performed about a decade ago, where exact electron wave functions were used in order to calculate Coulomb corrections in distorted wave Born approximation. A discussion of the exact solutions of the Dirac equation for free electrons in a Coulomb field generated by a point-like charge and some details relevant for the numerical calculations are given in the appendix., Comment: 21 pages, 5 figures, LATEX, one new section and some references added

L-subshell ionization cross sections for Au induced by 28Si and 32S ions in the energy range 10–15 MeV have been investigated. The experimental ionization cross section for the L2-subshell shows an unexpected suppression for the 32S ion as compared to the 28Si ion result. Accordingly the projectile dependence of the σ L 1 σ L 2 and σ L 3 σ L 2 ratios for the two ions shows a reversal of the trend seen in the case of other light ions (Z ≤ 14). The measured ionization cross sections and their ratios deviate considerably from the theoretical predictions.

The STAR collaboration at RHIC is measuring the production of electron-positron pairs at small impact parameters, larger than but already close to the range, where the ions interact strongly with each other. We calculate the total cross section, as well as, differential distributions of the pair production process with the electromagnetic excitation of both ions in a semiclassical approach and within a lowest order QED calculation. We compare the distribution of electron and positron with the one coming from the cross section calculation without restriction on impact parameter. Finally we give an outlook of possible results at the LHC., 15 pages, 8 figures

We discuss the derivation of a ``cluster sum rule'' from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions and approximations. Some applications of the sum rule for halo nuclei, as well as, nuclei with a pronounced cluster structure are discussed., 14 pages, to be published in Nucl. Phys. A