We study relativistic collisions between helium-like uranium ions initially in the ground state and atoms in which, in a single collision event, one of the electrons of the ion is emitted and the other is transferred into an excited state of the residual hydrogen-like ion. We consider this two-electron process at not very high impact energies, where the action of the atom on the electrons of the ion can be well approximated as occurring solely due to the interaction with the nucleus of the atom and, hence, the process can be regarded as a four-body problem. Using the independent electron model we show that a very substantial improvement in the calculated cross sections is obtained if, instead of the first order approximation, the relativistic symmetric eikonal and continuum-distorted-wave-eikonal-initial-state models are employed to describe the single-electron probabilities for the excitation and loss, respectively.
We consider single ionization of helium by fast highly charged ions. The ionization is treated as a three-body problem which involves the 'active' target electron, the target core (consisting of the target nucleus and the 'passive' target electron) and the projectile-ion. We show that, unless the transverse momentum transfer in the collision is large, the deviation of the interaction between the projectile and the target core from the purely coulomb law has a weak effect on the ionization. In particular, the account of this deviation does not enable one to get an agreement with experimental da…
The K x-ray spectra of different targets (Cu, Zn, and Ge) induced by 3 to 5 MeV/u Si projectile ions have been measured to determine the K-shell ionization cross-section. A significant difference is observed between the measurements and theoretical estimates, with the latter being about 50% below the experimental results. This underestimation} is attributed to the charge-exchange from target K-shell to projectile K- and L-shells. Such observation can only be possible if the projectile ions attain up to H- and He-like charge states. Corresponding projectile charge state fractions have been eval…
We report the energy and angular distribution of ejected electrons from CH$_4$ and H$_{2}$O molecules impacted by 1 MeV H$^+$, He$^+$ and 650 keV N$^+$ ions. Spectra were measured at different observation angles, from 2 eV to 2000 eV. The obtained absolute double-differential-electron-emission cross sections (DDCS) were compared with the results of CTMC and CDW-EIS calculations. For the bare H+ projectile both theories show remarkable agreement with the experiment at all observed angles and energies. The CTMC results are in similarly good agreement with the DDCS spectra obtained for impact by …
We study the fragmentation of He$_2$ dimers into He$^+$ ions by relativistic highly-charged projectiles. It is demonstrated that the interaction between an ultrafast projectile with an extremely extended object -- the helium dimer -- possesses interesting features which are absent in collisions with "normal" molecules. It is also shown that such projectiles, due to their enormous interaction range, can accurately probe the ground state of the dimer and even be used for a precise determination of its binding energy.
The Cold-target recoil-ion momentum spectroscopy (COLTRIMS) has been employed to study the single-electron capture processes in collisions of N3+ ions with He atoms at an impact energy of 30 keV. The relative differential cross sections for the capture to different orbitals of N3+ ions are obtained and are compared with other experiments at low energy. The predictions of the molecular Columbic barrier model have been made. From the longitudinal momentum spectrum of recoil ions, the different electronic configuration was identified and the metastable projectile ions were distinguished. The sing…
We study theoretically the fragmentation of the helium dimer, $^4$He$_2$, into singly charged ions in collisions with relativistic highly-charged projectiles. We discuss the main mechanisms driving this process with the focus on the fragmentation caused by direct ionization of both atomic sites of the dimer in a single collision with the projectile. This direct mechanism dominates the He$_2$ $\to $ He$^+$ + He$^+$ breakup events with the kinetic energies of the emerging ionic fragments below $4$--$5$ eV. We explore the energy and angular distributions of the He$^+$ ions produced in collisions …
In this work we study the single ionization of hydrogen and helium by the impact of a punctual Coulomb projectile. To interpretate the cross section we introduce a series of Padé approximant. The nodes of the denominator of the Padé approximant give rise to poles in the charge complex plane. These poles move with the projectile velocity following a certain pattern. We find the positions of the poles of the Continuum Distorted Wave theory and an ensamble of experimental results. It was found that the ionization cross section may have oscillations in terms of the incident charge for a given impa…
A description of the DEPOSIT computer code is presented. The code is intended to calculate total and m-fold electron-loss cross sections (m is the number of ionized electrons) and the energy T(b) deposited to the projectile (positive or negative ion) during a collision with a neutral atom at low and intermediate collision energies as a function of the impact parameter b. The deposited energy is calculated as a 3D-integral over the projectile coordinate space in the classical energy-deposition model. Examples of the calculated deposited energies, ionization probabilities and electron-loss cross…
Two-electron one-photon transitions have been successfully observed for the Ne projectile and Al target at low energy regime. Experimental energy values of two-electron one-photon transitions are compared with previously reported theoretical and experimental values. Ionization cross-section of two-electron one-photon transition is reported.
Ionization of highly charged relativistic ions by neutral atoms and ions is considered. Numerical results of recently developed computer codes based on the relativistic Born and the equivalent-photon approximations are presented. The ionization of the outer shells dominate. For the outer projectile electron shells, which give the main contribution to the process, the non-relativistic Schrödinger wave functions can be used. The formulae for the non-relativistic reduction of the Dirac matrix-elements are obtained for ionization of electrons with arbitrary quantum numbers $n$ and $\ell$.
At impact energies $ \stackrel{>}{\sim}1$ GeV/u the projectile-electron excitation and loss occurring in collisions between highly charged ions and neutral atoms is already strongly influenced by the presence of atomic electrons. In order to treat these processes in collisions with heavy atoms we generalize the symmetric eikonal model, used earlier for considerations of electron transitions in ion-atom collisions within the scope of a three-body Coulomb problem. We show that at asymptotically high collision energies this model leads to an exact transition amplitude and is very well suited to d…
We study the process of single ionization of Li in collisions with H$^+$ and O$^{8+}$ projectile ions at 6 MeV and 1.5-MeV/amu impact energies, respectively. Using the frameworks of the independent-electron model and the impact parameter picture, fully (FDCS) and doubly (DDCS) differential cross sections are evaluated in the continuum distorted-wave with eikonal initial-state approximation. Comparisons are made with the recent measurements of LaForge \textit{et al} [J. Phys. B \textbf{46} 031001 (2013)] for the DDCS and Hubele \textit{et al} [Phys. Rev. Lett. \textbf{110} 133201 (2013)] for th…
We present calculations of the total and m-fold electron-loss cross sections using the DEPOSIT code for highly charged U(q+) ions (q=10,31,33) colliding with Ne and Ar targets at projectile energies E=1.4 and 3.5 MeV/u. Typical examples of the deposited energy T(b) and m-fold ionization probabilities Pm(b) used for the cross-section calculations as a function of the impact parameter b are given. Calculated m-fold electron-loss cross sections are in a good agreement with available experimental data. Although the projectile charge is rather high, a contribution of multiple-electron loss cross se…
For the first time, we report a theoretical methodology to predict charge state distribution of projectile ions inside a solid-target. The method utilizes either a simple Fermi gas model or an ab initio theoretical method and a certain parameterization of width for the Lorentzian charge state distributions. Results obtained from the two approaches are comparable, but the former has a certain edge over the latter. The projectile charge state distribution inside a solid-target plays a significant role in estimating electron capture cross-sections and then to describe the observed K-shell ionizat…
We consider single ionization of lithium atom in collisions with $p$ and O$^{8+}$ projectiles. Doubly differential cross sections for ionization are calculated within a relativistic non-perturbative approach. Comparisons with the recent measurements and theoretical predictions are made.
We investigate experimentally and theoretically the electron emission in collisions between He atoms and Li$^{q+}$ (q=1,2) projectiles at intermediate-high incident energies. We report on measured absolute values of double differential cross-sections, as a function of the emitted electron energy and angle, at a collision energy of 440~keV/u. The different contributions from target-ionisation, projectile-ionisation, and simultaneous target-projectile ionisation are calculated with the quantum-mechanical Continuum Distorted Wave and Continuum Distorted Wave -- Eikonal Initial State models, and w…
Recent theoretical investigations of pair-production probabilities for given sets of nuclear trajectories predict the observability of spontaneous positron emission in elastic collisions of heavy ions. These calculations are extended to the investigation of ratios $P_{y}(η)/P_{y}(1)$ for partial probabilities of positron emission at small positron energies. The results suggest a possible observability of spontaneous positron emission in elastic collisions of bare heavy ions by analyzing the slope of $P_{y}(η)/P_{y}(1)$ for values of $R_{min}$ $~_{\sim}\!\!\!\!^<$ 0.75 $R_{cr}$. In addition cal…
Using the cold target recoil ion momentum spectroscopy (COLTRIMS) technique, we have measured the simultaneous projectile and target ionization in collisions of He$^+$ projectiles with a mixture of gaseous H$_2$ and D$_2$ for an incident projectile energy of 650 keV. Motivated by Cooper et al. [Phys. Rev. Lett. 100, 043204 (2008)], we look for differences in the ionization cross section of the two isotopes with the highest resolution and statistical significance. Contributions of the electron-electron and electron-nucleus interactions have been clearly separated kinematically by measuring the …
Doppler-shifted X-ray Spectroscopy of Nonradiative Electron Capture in Relativistic Collisions of Xe54+ Ions with Kr and Xe Atoms
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, St. Petersburg State University（圣彼得堡国立大学物理系）；Petersburg Nuclear Physics Institute named by B.P. Konstantinov of National Research Centre “Kurchatov Institute,”（俄罗斯国家研究中心“库尔恰托夫研究所”下属的B.P.康斯坦丁诺夫彼得堡核物理研究所）；Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University（西北师范大学物理与电子工程学院甘肃省原子分子物理与功能材料重点实验室）；Department of Medical Imaging, Hangzhou Medical College（杭州医学院医学影像系）；School of Basic Medical Sciences, Shanxi Medical University（山西医科大学基础医学院）
Production of projectile Rydberg states in fast ion-solid collisions in H-like ions exhibits a pronounce target thickness dependence in spite of these states forming at the last layers. This occurs due to important role of the surface wake field which varies with the target foil thickness. Further, according to the proposed model Rydberg states with low angular momentum are transformed into a circular Rydberg states while passing through the field. The transfer occurs by a single multiphoton process with high probability depending upon the projectile ion velocity with respect to the Fermi velo…
Absolute total cross sections for electron capture between slow, highly charged ions and alkali targets have been recently measured. It is found that these cross sections follow a scaling law with the projectile charge which is different from the one previously proposed basing on a classical over-barrier model (OBM) and verified using rare gases and molecules as targets. In this paper we develop a "semi-classical" (i.e. including some quantal features) OBM attempting to recover experimental results. The method is then applied to ion-hydrogen collisions and compared with the result of a sophist…
We re-calculate electron yields and stopping power of protons colliding with surfaces of NaCl-type insulators. In this article, the projectile is considered to move taking into account the static and polarization potentials with all the individual ions forming the surface lattice unlike our previous work (Phys. Rev. A 75, 042904 (2007)) where the projectile was considered to move in an homogeneous planar potential. Substantial differences (up to forty percent of increment) have been found especially when the projectile incident angle approaches the critical one. We compare our prediction for e…
We have performed classical trajectory Monte Carlo (CTMC) studies of electron capture and ionization in multiply charged (Q=8) ion-Rydberg atom collisions at intermediate impact velocities. Impact parallel to the minor and to the major axis, respectively, of the initial Kepler electron ellipse has been investigated. The important role of the initial electron momentum distribution found for singly charged ion impact is strongly disminished for higher projectile charge, while the initial spatial distribution remains important for all values of Q studied.
Radiative double electron capture (RDEC), the one-step process occurring in ion-atom collisions, has been investigated for bare fluorine ions colliding with carbon. RDEC is completed when two target electrons are captured to a bound state of a projectile simultaneously with the emission of a single photon. This work is a follow-up to our earlier measurement of RDEC for bare oxygen projectiles, thus providing a recipient system free of electron-related Coulomb fields in both cases and allowing for the comparison between the two collision systems as well as with available theoretical studies. Th…
Multiple ionization and charge equilibration in slow, multiply charged $\mathrm{Ar^{q+} + Ar}$ collision studied via L-MM Auger-Meitner electron spectroscopy
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Tata Institute of Fundamental Research（塔塔基础研究所）
We report on the observation of a strong perturbation of the electron gas induced by 20 MeV/u U$^{91+}$ ions and 13 MeV/u Pb$^{81+}$ ions channeled in silicon crystals. This collective response (wake effect) in-duces a shift of the continuum energy level by more than 100 eV, which is observed by means of Radiative Electron Capture into the K and L-shells of the projectiles. We also observe an increase of the REC probability by 20-50% relative to the probability in a non-perturbed electron gas. The energy shift is in agreement with calculations using the linear response theory, whereas the loca…
Electrons colliding with spatially fixed ions in strong laser fields are investigated by solving the time-dependent Schrödinger equation. Considering first simple one-dimensional model systems, the mechanisms and energy spectra of fast electrons are analyzed, starting from collisions on a single ion. By using these electrons as projectiles for a second and third collision, the maximum possible energy obtained can be significantly increased. We then generalize the analysis to 2D systems where additional angular degrees of freedom lead to a drastic loss of efficiency. This problem can be overcom…
A recently proposed classical-trajectory dynamical screening model for the description of multiple ionization and capture during ion-water molecule collisions is extended to incorporate dynamical screening on both the multi-center target potential and the projectile ion. Comparison with available experimental data for He$^{2+}$ + H$_2$O collisions at intermediate energies (10-150 keV/u) and Li$^{3+}$ + H$_2$O at higher energies (100-850 keV/u) demonstrates the importance of both screening mechanisms. The question of how to deal with the repartitioning of the capture flux into allowed capture c…
The direct photodissociation of trapped $^{85}$Rb$_2^+$ (rubidium) molecular ions by the cooling light for the $^{85}$Rb magneto-optical trap (MOT) is studied, both experimentally and theoretically. Vibrationally excited Rb$_{2}^{+}$ ions are created by photoionization of Rb$_{2}$ molecules formed photoassociatively in the Rb MOT and are trapped in a modified spherical Paul trap. The decay rate of the trapped Rb$_{2}^{+}$ ion signal in the presence of the MOT cooling light is measured and agreement with our calculated rates for molecular ion photodissociation is observed. The photodissociation…
Electronic stopping cross sections (SCS) of nickel, silicon and nickel-silicon alloys for protons and helium (He) ions are studied in the regime of medium and low energy ion scattering, i.e., for ion energies in the range from 500 eV to 200 keV. For protons, at velocities below the Bohr velocity the deduced SCS is proportional to the ion velocity for all investigated materials. In contrast, for He ions non-linear velocity scaling is observed in all investigated materials. Static calculations using density functional theory (DFT) available from literature accurately predict the SCS of Ni and Ni…
We provide the experimental evidence that the single electron capture process in slow collisions between O$^{3+}$ ions and neon dimer targets leads to an unexpected production of low-energy electrons. This production results from the interatomic Coulombic decay process, subsequent to inner shell single electron capture from one site of the neon dimer. Although pure one-electron capture from inner shell is expected to be negligible in the low collision energy regime investigated here, the electron production due to this process overtakes by one order of magnitude the emission of Auger electrons…
A novel technique to identify small fluxes of mixed highly charged ion beams extracted from an Electron Beam Ion Trap (EBIT) is presented and practically demonstrated. The method exploits projectile charge state dependent potential emission of electrons as induced by ion impact on a metal surface to separate ions with identical or very similar mass-to-charge ratio.
Charge state distributions of $^{56}$Fe and $^{58}$Ni projectile ions passing through thin carbon foils have been studied in the energy range of 1.44 - 2.69 MeV/u using a novel method from the x-ray spectroscopy technique. Interestingly the charge state distribution in the bulk show Lorentzian behavior instead of usual Gaussian distribution. Further, different parameters of charge state distribution like mean charge state, distribution width and asymmetric parameter are determined and compared with the empirical calculations and ETACHA predictions. It is found that the x-ray measurement techni…
We present a theory for excitation of heavy hydrogen-like projectile-ions by light target-atoms in collisions where the momentum transfers to the atom are very large on the atomic scale. It is shown that in this process the electrons and the nucleus of the atom behave as (quasi-) free particles with respect to each other and that their motion is governed by the field of the nucleus of the ion. The effect of this field on the atomic particles can be crucial for the contribution to the excitation of the ion caused by the electrons of the atom. Due to comparatively very large nuclear mass, howeve…
We consider relativistic collisions of heavy hydrogen-like ions with hydrogen and helium atoms in which the ion-atom interaction causes both colliding particles to undergo transitions between their internal states. Using an approach enabling one, for the first time, to give a detailed description of this important case of the relativistic quantum few-body problem we concentrate on the study of the longitudinal momentum spectrum of the atomic recoil ions. We discuss the role of relativistic and higher order effects, predict a surprisingly strong influence of the projectile's electron on the mom…
A model for the description of proton collisions from molecules composed of atoms such as hydrogen, carbon, nitrogen, oxygen and phosphorus (H, C, N, O, P) was recently extended to treat collisions with multiply charged ions with a focus on net ionization. Here we complement the work by focusing on net capture. The ion-atom collisions are computed using the two-center basis generator method. The atomic net capture cross sections are then used to assemble two models for ion-molecule collisions: an independent atom model (IAM) based on the Bragg additivity rule (labeled IAM-AR), and also the so-…
A classical description of electron emission differential ionization cross sections for highly-charged high-velocity ions ($\sim$ 10 a.u.) impinging on water molecules is presented. We investigate the validity of the classical statistical mechanics description of ionization ($\hbar=0$ limit of quantum mechanics) in different ranges of electron emission energy and solid angle, where mechanisms such as soft and binary collisions are expected to contribute. The classical-trajectory Monte Carlo method is employed to calculate doubly and singly differential cross sections for C$^{6+}$, O$^{8+}$ and…
Molecular fragmentation leading to the formation of negatively and positively charged hydrogen ions in 7-keV OH$^+$ + Ar collisions is investigated experimentally. The most striking finding is that negative and positive hydrogen ions are emitted with very similar angular dependences. Also, the kinetic energy distribution of the H$^+$ fragment shows strong similarities with that of the ejected H$^-$ ion. The kinematics of the emitted H core is found to be essentially driven by its scattering on the atomic target. However, in addition to this binary-encounter process, dissociative electronic exc…
The delta function gauge of the electromagnetic potential allows semiclassical formulas to be obtained for the probability of exciting a single electron out of the ground state in an ultrarelativistic heavy ion reaction. Exact formulas have been obtained in the limits of zero impact parameter and large, perturbative, impact parameter. The perturbative impact parameter result can be exploited to obtain a semi-empirical cross section formula of the form, sigma = A ln(gamma) + B, for single electron ionization. A and B can be evaluated for any combination of target and projectile, and the resulti…
We study electron loss from a hydrogen-like highly charged ion by the impact of equivelocity electrons and protons and also in collisions with hydrogen and helium. The collision velocity $v$ varies between $v_{min}$ and $v_{max}$, where $v_{min}$ and $v_{max}$ correspond to the energy threshold $\varepsilon_{th}$ for electron loss in collisions with a free electron and to $\approx 5 \, \varepsilon_{th}$, respectively. Our results show that in this range of $v$: i) compared to equivelocity electrons protons are more effective in inducing electron loss (due to a substantially larger volume of th…
Ionization of helium-like ions with simultaneous excitation of the ns-states due to photon scattering is considered. The differential and total cross sections of the process are calculated to leading order of perturbation theory with respect to the interelectron interaction. The formulas obtained are applicable in the nonrelativistic energy range far beyond the ionization threshold.
Simultaneous Determination of Multiple Nuclear Parameters of $^{229}$Th Using Highly Charged Ions
State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院武汉物理与数学研究所磁共振与原子分子物理国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, University of New Brunswick（新不伦瑞克大学物理系）
The two-center Dirac equation for an electron in the external electromagnetic field of two colliding heavy ions in the limit in which the ions are moving at the speed of light is exactly solved and nonperturbative amplitudes for free electron-positron pair production are obtained. We find the condition for the applicability of this solution for large but finite collision energy, and use it to explain recent experimental results. The observed scaling of positron yields as the square of the projectile and target charges is a result of an exact cancellation of a nonperturbative charge dependence …
The yield of electrons generated by gold nanoparticles due to irradiation by fast charged projectiles is estimated. The results of calculations are compared to those obtained for pure water medium. It is demonstrated that a significant increase in the number of emitted electrons arises from collective electron excitations in the nanoparticle. The dominating enhancement mechanisms are related to the formation of (i) plasmons excited in a whole nanoparticle, and (ii) atomic giant resonances due to excitation of d electrons in individual atoms. Decay of the collective electron excitations in a na…
Experimental and theoretical state-selective X-ray spectra resulting from single-electron capture in charge exchange (CX) collisions of Ne^10+ with He, Ne, and Ar are presented for a collision velocity of 933 km s^-1 (4.54 keV nucleon^-1), comparable to the highest velocity components of the fast solar wind. The experimental spectra were obtained by detecting scattered projectiles, target recoil ions, and X-rays in coincidence; with simultaneous determination of the recoil ion momenta. Use and interpretation of these spectra are free from the complications of non-coincident total X-ray measure…
A recently developed model to describe proton collisions from molecules involving basic atoms such as hydrogen, carbon, nitrogen, oxygen and phosphorus (H, C, N, O, P) is extended to treat collisions with multiply charged ions. The ion-atom collisions are computed using the two-center basis generator method (TC-BGM), which has a proven track record of yielding accurate total cross sections for electron capture and ionization. The atomic net ionization cross sections are then used to assemble two models for ion-molecule collisions: an independent atom model (IAM) that follows the Bragg additivi…
We have measured the stopping powers and straggling of fast, highly ionized atoms passing through thin bilayer targets made up of metals and insulators. We were surprised to find that the energy losses as well as the straggling depend on the ordering of the target and have small but significantly different values on bilayer reversal. We ascribe this newly found difference in energy loss to the surface energy loss field effect due to the differing surface wake fields as the beam exits the target in the two cases. This finding is validated with experiments using several different projectiles, ve…
We have performed laser cooling of Mg ions confined in a Penning trap. The externally produced ions were captured in flight, stored and laser cooled. Laser-induced fluorescence was observed perpendicular to the cooling laser axis. Optical detection down to the single ion level together with electronic detection of the ion oscillations inside the Penning trap have been used to acquire information on the ion storage time, ion number and ion temperature. Evidence for formation of ion crystals has been observed. These investigations are an important prerequisite for sympathetic cooling of simultan…
In order to use a collection of trapped ions for experiments where a well defined preparation of vibrational states is necessary, all vibrational modes have to be cooled to ensure precise and repeatable manipulation of the ions' quantum states. A method for simultaneous sideband cooling of all axial vibrational modes is proposed. By application of a magnetic field gradient the absorption spectrum of each ion is modified such that sideband resonances of different vibrational modes coincide. The ion string is then irradiated with monochromatic electromagnetic radiation, in the optical or microwa…
