Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.     

Electron-electron interaction in slow charge exchange collisions

The influence of excited projectile electrons on the charge exchange mechanism is studied in slow collisions of multiply charged ions with atoms. Translational energy spectra for single electron capture are measured for projectile ions being prepared in the ground state and in an excited metastable state. The differences are discussed in terms of the electron-electron interaction, which turns out to be more important in collision systems with projectiles in low charge states.     

Halfway house variational continuum distorted wave theory: high energy cross sections in the distorted wave perturbation approximation

The total cross section for charge transfer at high but non-relativistic energy is investigated within a new time-independent wave version of the halfway-house phase integral variational continuum distorted wave formalism, using simple first order perturbation theory. Following Crothers, Dubé and Brown this theory satisfies all known short and long range Coulomb boundary conditions which is essential if intermediate elastic divergences are to be avoided. The discussion is specialised to the particular case ofls →ls capture. Numerical results for this amplitude are obtained by a double numerical integration. Wave results derived for the capture process $$P^{Z_P^ + } + (T^{Z_T^ + } + e^ - ) \to (P^{Z_P^ + } + e^ - ) + T^{Z_T^ + } $$ in the caseZ _T = 1 =Z _P are compared with various theoretical impact parameter models and experimental data. Representative distributions of the total cross sections are presented as a function of the impact energy.     

Second-order theories for electron loss in fast collisions with He atoms

The momentum distribution of projectile electrons ejected in collisions with light targets is calculated within the second-order Born approximation for direct ionisation and within the electron impact approximation and the impulse approximation for electron capture to the target continuum. From comparison with available experimental data it is found that for forward emission angles the electron is well described by a projectile eigenstate, while at backward angles a target final state is more appropriate. At all angles the inclusion of simultaneous target excitation is very important.     

Angular distribution of scattered projectiles following double electron capture processes at low-energy C4+ and helium collisions

A four-body classical trajectory Monte Carlo method is applied in the study of double electron capture in low-energy ${\mathrm{C}}^{4+}$ and He atom collisions. The interaction between the two target electrons is neglected throughout the collisions. The angular differential cross-sections of the scattered projectiles, following double electron capture, are calculated and compared with experimental data.     

Total and angular differential cross sections of electrons emitted in collision between antiprotons and helium atoms

We present total and angular differential single-ionization cross sections for antiproton–helium collisions in the energy range of 1–1000 keV within the framework of time-dependent coupled-channel-, a continuum distorted wave eikonal initial state and classical trajectory Monte Carlo methods. The results are compared with other theoretical results and experimental data.     

Coherence parameters of atomic excited states: comparison of results from the CTMC and the quantal calculations

The coherence parameters of excited states formed in collisions of atoms with electrons, positrons, protons and antiprotons are calculated using the Classical Trajectory Monte Carlo (CTMC) method and the results are compared to those obtained from the quantal distorted wave and close-coupling calculations. The orientation parameter and the components of the electric dipole moment of the electronic charge cloud after the collision are examined for excitation and for electron capture toH(n = 2) states. It is found that the CTMC results are in qualitative agreement with the quantal distorted wave and close-coupling results for some of the coherent parameters only.     

Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: theory, implementation, and examples

Implementation of Dyson orbitals for coupled-cluster and equation-of-motion coupled-cluster wave functions with single and double substitutions is described and demonstrated by examples. Both ionizations from the ground and electronically excited states are considered. Dyson orbitals are necessary for calculating electronic factors of angular distributions of photoelectrons, Compton profiles, electron momentum spectra, etc, and can be interpreted as states of the leaving electron. Formally, Dyson orbitals represent the overlap between an initial N-electron wave function and the N-1 electron wave function of the corresponding ionized system. For the ground state ionization, Dyson orbitals are often similar to the corresponding Hartree-Fock molecular orbitals (MOs); however, for ionization from electronically excited states Dyson orbitals include contributions from several MOs and their shapes are more complex. The theory is applied to calculating the Dyson orbitals for ionization of formaldehyde from the ground and electronically excited states. Partial-wave analysis is employed to compute the probabilities to find the ejected electron in different angular momentum states using the freestanding and Coulomb wave representations of the ionized electron. Rydberg states are shown to yield higher angular momentum electrons, as compared to valence states of the same symmetry. Likewise, faster photoelectrons are most likely to have higher angular momentum.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Theory of electron transfer in systems with intermediate link

A theory is proposed for electron transfer through an intermediate link, the theory being based on solution of the time-dependent wave equation of the system with the exact Hamiltonian by assigning a wave function in form of a linear combination of wave functions of the initial state (electron on the donor), intermediate state (electron on the intermediate link), and final state (electron on the acceptor). The squares of the moduli of the time-dependent coefficients in these wave functions represent the probabilities of finding electrons in the indicated states. The coefficients have been determined by means of Laplace transforms, and an expression has been obtained for the rate of electron transfer through the intermediate link.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 3, pp. 288–293, May–June, 1985.     

Atomic and molecular impurities in4He clusters

Recoil-ion charge distributions produced in single collisions of 8 MeV/u Kr¹³⁺ and Kr³²⁺ projectiles with Xe atoms have been measured using time-of-flight spectroscopy. The post-collision charge states of the projectile ions were determined by magnetic dispersion onto a position sensitive microchannel plate detector. The recoil-ion distributions for ionization accompanied by electron loss from Kr¹³⁺ projectiles were bell-shaped with averages that ranged from 7.4 for 1-electron loss to 13.9 for 5-electron loss. The recoil-ion distributions for ionization accompanied by electron capture to Kr³²⁺ projectiles were also bell-shaped, but had much higher average charges that ranged from 20.4 for 1-electron capture to 28.5 for 4-electron capture. The large difference in the average charges produced in the two types of collisions is mainly attributable to charge magnification by Auger decay. A simple model quantitatively explains the variation of the capture-ionization charge distribution width and average charge as a function of the number of captured electrons.     

Experimental and theoretical (e,2e) ionization cross sections for a hydrogen target at 75.3 eV incident energy in a coplanar asymmetric geometry

Very recently it was shown that the molecular three-body distorted wave (M3DW) approach gives good agreement with the shape of the experimental data for electron-impact ionization of H(2) in a coplanar symmetric geometry, providing the incident electrons have an energy of 35 eV or greater. One of the weaknesses of these studies was that only the shape of the cross section could be compared to experiment, since there was no absolute or relative normalization of the data. Here we report a joint experimental/theoretical study of electron-impact ionization of H(2) in a coplanar asymmetric geometry where the energy of the incident electron was fixed, and different pairs of final state electron energies were used. In this case, the experimental data can be normalized such that only one renormalization factor is required. It is shown that the M3DW is pretty good in agreement with experiment. However, a better treatment of polarization and exchange between the continuum and bound state electrons is required before quantitative agreement between experiment and theory is achieved.     

Charge exchange in collisions of beryllium with its ion

Close-coupling calculations of the resonance and near resonance charge exchange in ion-atom collisions of Be at low and intermediate energies are presented. Accurate ab initio calculations are carried out of the Born-Oppenheimer potentials and the non-adiabatic couplings that are due to the finite nuclear masses and drive the near resonance charge exchange. We show that the near resonance charge exchange cross section follows Wigner's threshold law of inelastic processes for energies below 10(-8) eV and that the zero temperature rate constant for it is 4.5 × 10(-10) cm(3) s(-1). At collision energies much larger than the isotope shift of the ionization potentials of the atoms, we show that the near resonance charge exchange process is equivalent to the resonance charge exchange with cross sections having a logarithmic dependence. We also investigate the perturbation to the charge exchange process due to the non-adiabatic interaction to an electronic excited state. We show that the influence is negligible at low temperatures and still small at intermediate energies despite the presence of resonances.     

Quantum dynamics of Ne-Br2 vibrational predissociation: the role of continuum resonances as doorway states

Wave-packet simulations of the Ne-Br2(B,upsilon') vibrational predissociation dynamics in the range upsilon' = 16-29 are reported. The aim is to interpret recent time-dependent pump-probe experiments [Cabrera et al., J. Chem. Phys. 123, 054311 (2005)]. Good agreement is found between the calculated and the experimental lifetimes corresponding to decay of the Ne-Br2(B,upsilon') initial state and to appearance of Br2(B,upsilon相似文献   

Ion induced ridge electrons and their diffraction in solid foil targets

We present detailed double differential distributions of electrons emitted downstream when 100 and 170 keV protons interact with thin carbon, gold and aluminuum foils and compare them to those obtained with protons and neutral hydrogen projectiles interacting with helium gas. The distributions obtained with the gas target show, besides the well known convoy electron peak produced by capture or loss of electrons into the continuum of the emerging ion, a narrow ridge that is aligned with the beam direction. This ridge, which is attributed to electrons moving in the two Coulomb center potential saddle determined by the target and projectile ions, also appears in the ion-solid electron distributions. A typical solid state effect consists in the appearance of two strong lateral humps which are explained as due to diffraction of the ridge electrons in the three dimensional lattice of the polycrystalline foil material. Contrarily the diffraction of convoy electrons is impeded by their strong correlation to the moving ions. In the case of the Aluminuun target the observed diffraction is typical for Al₂O₃. This indicates that the observed electrons originate from a thin polycrystalline oxyde layer close to the downstream surface of emission.     

Coulomb explosion of nitrogen and oxygen molecules through non-Coulombic states

We have systematically studied Coulomb explosion of nitrogen and oxygen molecules in intense 8 and 24 fs laser pulses. In the experiment, we explicitly separated all explosion pathways through coincident measurements. The high resolution kinetic energy releases (KERs) and the exotic angular distributions of atomic ions provide direct evidence that Coulomb explosion occurs through non-Coulombic states. In the theory, we calculated dissociation potential energy curves (PECs) of nitrogen and oxygen molecules and their multicharged molecular ions using multiconfiguration second-order perturbation theory. The results indicate that Coulomb potentials are close to the accurate PECs of multicharged molecular ions only when the internuclear distance is larger than 3 ?. In comparison with the experimental observations and the theoretical calculations, we determined the internuclear distance when Coulombic explosion occurs. It is near the equilibrium distance of the neutral molecules in the case of 8 fs laser pulses and expands gradually with the increase of the charge state of the molecular ions in the case of 24 fs laser pulses.     

Intermediate state representation approach to physical properties of electronically excited molecules

Propagator methods provide a direct approach to energies and transition moments for (generalized) electronic excitations from the ground state, but they do not usually allow one to determine excited state wave functions and properties. Using a specific intermediate state representation (ISR) concept, we here show how this restriction can be overcome in the case of the algebraic-diagrammatic construction (ADC) propagator approach. In the ISR reformulation of the theory the basic ADC secular matrix is written as a representation of the Hamiltonian (or the shifted Hamiltonian) in terms of explicitly constructable states, referred to as intermediate (or ADC) states. Similar intermediate state representations can be derived for operators other than the Hamiltonian. Together with the ADC eigenvectors, the intermediate states give rise to an explicit formulation of the excited wave functions and allow one to calculate physical properties of excited states as well as transition moments for transitions between different excited states. As for the ground-state excitation energies and transition moments, the ADC excited state properties are size consistent so that the theory is suitable for applications to large systems. The established hierarchy of higher-order [ADC(n)] approximations, corresponding to systematic truncations of the IS configuration space and the perturbation-theoretical expansions of the ISR matrix elements, can readily be extended to the excited state properties. Explicit ISR matrix elements for arbitrary one-particle operators have been derived and coded at the second-order [ADC(2)] level of theory. As a first computational test of the method we have carried out ADC(2) calculations for singlet and triplet excited state dipole moments in H(2)O and HF, where comparison to full CI results can be made. The potential of the ADC(2) method is further demonstrated in an exploratory study of the excitation energies and dipole moments of the low-lying excited states of paranitroaniline. We find that four triplet states, T1-T4, and two singlet states, S1 and S2, lie (vertically) below the prominent charge transfer (CT) excitation, S3. The dipole moment of the S3 state (17.0D) is distinctly larger than that of the corresponding T3 triplet state (11.7D).