Electron capture by fast protons from helium, nitrogen, and oxygen: The corrected first Born approximation.

The authors calculate the differential cross sections for charge exchange at high energies by means of the continuum-distorted-wave (CDW) approximation. The calculations show the importance of contributions from second-order terms in the electron-nucleus interaction for both the magnitude of the cross section and its variation with angle. The internuclear repulsion is included exactly within a first-order expansion in the ratio of the electron to proton mass. Comparisons are made with recent experimental data on H+-He and H+-Ar collisions.

The DUET Collaboration reports on the measurements of the absorption ($\sigma_{\mathrm{ABS}}$) and charge exchange ($\sigma_{\mathrm{CX}}$) cross sections of positively charged pions on carbon nuclei for the momentum range 201.6 MeV$/c$ to 295.1 MeV$/c$. The uncertainties on the absorption and charge exchange cross sections are $\sim$9.5\% and $\sim$18\%, respectively. The results are in good agreement with previous experiments. A covariance matrix correlating the 5 $\sigma_{\mathrm{ABS}}$ and 5 $\sigma_{\mathrm{CX}}$ measured data points is also reported

An overview of experimental data and theoretical computational methods is given for effective cross sections of charge exchange (electron capture) and electron loss (projectile ionization) processes involving heavy many-electron ions (like , , , ) colliding with neutral atoms (H, He, N, Ne, Ar, Kr, Xe) in the energy range, i.e., from low up to relativistic energies. These charge-changing processes can occur with a high probability, reaching cross-section values and, therefore, they play a key role in the kinetics of laboratory and astrophysical plasmas and influence the lifetimes of ion beams in accelerator facilities. Multielectron capture and loss processes are considered, as well, since their importance in the case of heavy atomic projectiles strongly increases, and a contribution to the total cross sections reaches more than 50%. An important aspect of the overview is a consideration of the influence of the inner-shell electrons of two colliding systems and a role of isotope effects in electron capture by very slow ions () from hydrogen isotopes H, D, and T. A short description of the corresponding computer codes is given for the calculation of cross sections of electron capture and electron loss processes for complex atoms and ions over a wide collision energy range.

Elastic scattering phenomena arising in electron-helium scattering are dominant processes. The determination of accurate elastic differential cross sections for electron-helium scattering has a considerable importance. An accurate calculation of the plane-wave first Born exchange amplitude of electrons elastic scattering by helium atoms is reported. The direct and exchange amplitudes are calculated analytically from the Hartree-Fock orbital wave functions by using a variational method. The forms of these wave functions are very suitable for analytical calculations and powerful to generalize to more complex atomic systems. The interaction potential is modelled by the static Coulomb interaction between the incident electron and the atomic system. The differential cross sections are calculated at intermediate energies taking into account the exchange effects. We have established in the high energies region, by neglecting the exchange effects, the analytical expressions of the total and momentum transport cross sections suitable for the calculation of the plasma transport properties. A very compact form of the Born amplitude has been proposed as a finite series of Gaussian functions, which represents a major tool in the calculations of differential cross sections of two-electron atomic systems. Numerical results are used to analyze the contribution of the exchange amplitude to the differential cross sections at intermediate and high energies. The differential cross sections are calculated for the energy range 30-400 eV. We find good agreement in high energy domain scattering with experimental results and other sophisticated calculations without using any adjustable parameter.

The energy dependence of the total cross section for symmetric charge exchange in helium is measured in the range from 400-2000 eV. Beam-attenuation techniques are used, and all measurements are made on the forward-scattered ions and the high-energy neutrals resulting from the charge exchange. Cross-section values are given at 100-eV intervals, and the results show a cross section decreasing as the energy increases, with a value at 1000 eV of 1.04 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$. The absolute cross sections are accurate to \ifmmode\pm\else\textpm\fi{} 12%. Relative cross-section values accurate to \ifmmode\pm\else\textpm\fi{} 6% are reported.

A three-body general-type rearrangement collision is considered where the initial and final bound states are described by hydrogenlike wave functions. The solution obtained is for the first Born approximation where the full interaction potential is taken into account. When the initial state is the ground state, it is shown that for n/$mu$Z very-much-greater-than 1, where n,$mu$, and Z are, respectively, the principal quantum number, the reduced mass, and the nuclear charge of the formed atom, the capture cross section at all incident energies and for capture into the s, p, and d angular momentum states behaves as C/n$sup 3$ + O (1/n$sup 5$), where C depends on masses and charges of the particles, the final angular momentum, and the incident energy. An analytic expression for C is given. It is shown that for the low-lying levels the 1/n$sup 3$ scaling law at all incident energies is only approximately satisfied. The only exception is for capture into the s states according to the Oppenheimer- Brinkman-Kramers approximation. The case for the symmetric collisions is considered and it is shown that for high n and high incident energy E, the cross section behaves as 1/E$sup 3$. Zeros and minima in the differential crossmore » sections are given in the limit of high n for electron capture by protons from atomic hydrogen, and for positronium formation by proton--atomic-hydrogen collisions.« less

The physics of multicharged ions has considerably developed during the last years1. Aside from purely academic and fundamental interest, the initial motivation arose from fusion research. Indeed from simple theoretical arguments it could be predicted that cross sections for charge exchange between highly charged impurities present in tokomak devices, and hydrogen atom would be very large (10-15–10-14 cm2). Knowledge of the plasma properties would therefore require measurement of the corresponding cross sections as well as a better understanding of the collision process. A large number of experiments were therefore undertaken to determine the total (all processes included) electron capture cross section for a variety of multicharged ions. In contrast, very little work was devoted to the identification of the states which are effectively populated by the collision process. A similar effort was undertaken in theory, for the collision energy range of interest for nuclear fusion (say few keV/Nucleon). At these energies the electron velocity v is much larger than the collision velocity V so that the electron motion adapts itself adiabatically (or quasi-adiabatically) to the nuclear motion as in a molecule.

It is well known that in relativistic quantum theory there is not exact analytical formula for cross section of a charged particle elastic scattering on arbitrary electrostatic potential \(\varphi (\mathbf {r})\). Even in case of Coulomb field for which the exact solution of Dirac equation is known, relativistic “Coulomb wave functions”, nevertheless, because of its complex character it is impossible to obtain exact analytical expression for scattering cross section via these wave functions. The elastic scattering in relativistic domain is mainly described in approximations when the scattering potential can be considered as a perturbation (in opposite limits). These are the well-known Born and eikonal approximations corresponding to quantum perturbation theory by particle wave function (when the condition \(\left| U\right| \ll \hbar \mathrm {v}/a\) is satisfied; U is the potential energy, a is the space size of the range of effective scattering, \(\mathrm {v}\) is the particle initial velocity), and high-momentum approximation (if potential energy in the scattering field is much less than the particle initial energy: \(\left| U\right| \ll p\mathrm {v}\)), respectively. In case of Coulomb field there is also an approximation of large impact parameters (large momenta)—Farry-Sommerfeld-Maue (FSM) approximation , which describes well enough the scattering at the small angles. It is also known that the wave function in the eikonal approximation describes the particle state only in a limited space range of the scattering process (\(z\ll pa^{2}/\hbar \); z is the coordinate along the direction of particle initial momentum), i.e., the eikonal solution is not valid at large distances. The wave function of the Born approximation , in contrast to the eikonal one, describes the particle state at arbitrary point in the scattering range, particularly at asymptotically large distances. Nevertheless, the common region where both approximations under consideration are valid is very restricted. On the other hand, within the (small) potential range where both approximations are applicable, these wave functions describe the scattering by different accuracies. Practically, these wave functions describe the scattering at the opposite conditions: the eikonal wave function describes the particle state when the opposite condition of the Born approximation holds (e.g., for Coulomb field with a charge \(Z_{a}e\)—at the condition: \(Z_{a}e^{2}/\hbar \mathrm {v}\gtrsim 1\)). In these circumstances a natural question arises—is it possible to find out such an approximate solution of Dirac equation beyond the scope both perturbation theory and eikonal approximation—corresponding to more general wave function being applicable in both quantum and quasiclassical limits for relativistic potential scattering (including in particular the Born and eikonal approximations in corresponding limits—under its conditions of applicability)? Here we will try to derive such an approximate solution of the Dirac equation which satisfies the formulated requests. We will call it generalized eikonal approximation (GEA) for a spinor particle scattering on the arbitrary short-range or long-range electrostatic potential. Then we will clear up the relationship of this approximation to the known ones for electron elastic scattering on the short-range (Born and eikonal approximations) and long-range Coulomb potentials (Born, eikonal, and Farry-Sommerfeld-Maue approximations ). This GEA approximation is developed for electron inelastic scattering process too—to describe the relativistic stimulated bremsstrahlung in the field of strong and superstrong laser radiation with electrostatic potential fields of arbitrary form and finite or infinite effective radiuses (atoms, ions, etc.). The significance of GEA type wave function for description of such laser-assisted electron–atom–ion scattering processes, apart from the known restrictions of mentioned above approximations, is also conditioned with the fact that the wave functions in known approximations describe the particle state factorized by elastic scattering and induced radiation-absorption processes. In the result, we lose the phase relations at the description of electron quantum dynamics interacting with the both fields simultaneously, which have important role for induced process, in particular, for coherent part of interaction. Therefore, for description of strong and superstrong laser–matter (plasma) interaction processes, we need the electron wave function that takes into account the simultaneous influence of both scattering and radiation fields including dynamic phase relations. This induced GEA wave function may be applied specifically for the description of the above-threshold ionization (ATI) process of atoms/ions by superstrong laser fields in relativistic theory taking into account the photoelectron rescattering effect on the atomic remainder because of the action of long-range Coulomb field of atomic ion on the photoelectron final state (this process is considered in the next chapter of this book).

For pt.I see ibid., vol.24, no.18, p.4049-60 (1991). The authors report a treatment of slow C3++H collisions for impact energies E=0.04-9 keV amu-1, using an expansion in terms of 22 molecular states modified with a common translation factor. Calculated partial and total cross sections for charge exchange are in good agreement with measured ones. Cross sections and values for the alignment parameter for C3+ excitation are predicted. A detailed study of the collision dynamics is presented.

The absolute single-photoionization cross sections of singly charged nitrogen and oxygen ions have been measured from 29-80 eV and 30-150 eV, respectively, by merging a synchrotron-radiation beam from an undulator with a 2 keV ion beam. In the case of O+, separate data sets were obtained for the 4S ground state and the 2D/2P metastable states by attenuating the target-ion beam with N2 gas, exploiting the fact that cross sections for charge exchange between O+ ions, in the 4S or in the 2D/2P states, and N2 are different. The spectral structures were very different for the ground and the metastable states, whereas the cross sections for photoionization into the continua were nearly identical. The agreement between the experimental data and data calculated using the model function by Verner et al. or obtained from R-matrix calculations performed within the Opacity and the Iron projects is rather good. Finally, double photoionization (direct) was observed for O+ ions, with an approximately linear onset at 90 eV and a maximum cross section of 0.04 Mb.

A formalism is presented for the calculation of spin transfer cross section for intermediate energy charge exchange ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ [and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})]$ reactions to the continuum. The nuclear structure part of the formalism is based on the continuum Tamm-Dancoff method and the nuclear reaction part is treated within the distorted wave impulse approximation. In the nuclear structure part, we thus include particle-hole correlations and continuum effects on the excited particle. The knockon-exchange effect and the damping of the particle through an imaginary potential added to the single particle real potential are also taken into account. Results of numerical calculations are presented for the inclusive cross sections $\ensuremath{\sigma}(0\ifmmode^\circ\else\textdegree\fi{})$ and the spin transfer coefficients ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for forward scattering, for the intermediate energy ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})$ reactions on ${}^{12}\mathrm{C}$ and ${}^{90}\mathrm{Zr}$ targets leading to Gamow-Teller resonances in the continuum. It is shown that ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for this case takes a value of $\ensuremath{-}1/3,$ regardless of the details of nuclear structure and reaction mechanisms, if the reaction is assumed to proceed as an orbital angular momentum transfer ${l}_{t}=0$ process, and that deviations from $\ensuremath{-}1/3$ come from admixture of ${l}_{t}=2$ components. A simple closed form of the expression is derived which can be used to understand a subtle dependence of the ${D}_{\mathrm{nn}}$ values on nuclear structure and effective interaction.

The total cross section for charge exchange or breakup when ${\mathrm{D}}_{2}^{+}$ is incident on Cs has been measured in the energy range 3.0-23 keV. The cross section has a value of (1362 \ifmmode\pm\else\textpm\fi{} 80) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 3 keV and falls rapidly with increasing energy, reaching a value of (594 \ifmmode\pm\else\textpm\fi{} 40) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 23 keV. The equilibrium fraction of ${\mathrm{D}}^{\ensuremath{-}}$ obtained when ${\mathrm{D}}_{2}^{+}$ is incident on Cs has also been measured. The equilibrium fraction of ${\mathrm{D}}^{\ensuremath{-}}$ is (10.5 \ifmmode\pm\else\textpm\fi{} 2.0)% at 3 keV, (7.3 \ifmmode\pm\else\textpm\fi{} 1.6)% at 5 keV, (3.4 \ifmmode\pm\else\textpm\fi{} 0.7)% at 11.5 keV, (2.0 \ifmmode\pm\else\textpm\fi{} 0.4)% at 17.3 keV, and (1.5 \ifmmode\pm\else\textpm\fi{} 0.3)% at 23 keV. The equilibrium fraction of ${\mathrm{D}}^{\ensuremath{-}}$ obtained when ${\mathrm{D}}_{2}^{+}$ is incident on Cs at an energy $E$ is shown experimentally to be the same as the equilibrium fraction of ${\mathrm{D}}^{\ensuremath{-}}$ obtained when ${\mathrm{D}}^{+}$ is incident on Cs at an energy $\frac{1}{2}E$. The angular distribution of the reaction products when ${\mathrm{D}}_{2}^{+}$ ions are incident on Cs includes appreciable scattering into angles which are larger than 1\ifmmode^\circ\else\textdegree\fi{}. An explanation of these large scattering angles is offered.

In a static electric field a one‐dimensional model of the motion of ions, controlled solely by charge exchange (electron capture from gas moleculs) is considered. Solutions of the kinetic equastions for ions and fast neutrals are derived in several special cases. If the charge exchange cross section is constant, the kinetic equation is easily solvable in a closed form; if the cross section is a function of ion energy, however, the problem is reducible to a simple integral equation for the energy distribution function.

Summary form only given. A number of critical ionization velocity (CIV) experiments have been performed in space. CIV has been observed in laboratory experiments, but experiments in space have been inconclusive. Most space experiments have used barium which ionizes easily, and with emission lines from both neutrals and ions in the visible optical observations can be made from the ground. High initial ionization in some barium release experiments has been claimed due to CIV. However, a number of reactions between barium and the ambient plasma have been suggested as more likely processes. Currently the most popular process in this debate is charge exchange with O/sup +/. This process has a large cross section, but the question is whether it is large enough. The cross section for charge exchange with calcium should be even larger, but in a double release of barium and calcium (part of the NASA Combined Release and Radiation Effects Satellite release experiments) most ionization was observed from the barium release. Moreover, if charge exchange is the dominant process, the amount of ionization should relate to the oxygen ion density, and that does not appear to be the case.

theoretical rate equations in order to determine the average charge exchange rates. These rates were compared to charge exchange rates of an ion with a known charge exchange cross section (Ar{sup 11+}) measured in a similar manner in order to determine the average charge exchange cross sections for the highly charged ions. The energy of interaction between the highly charged ions and hydrogen was estimated to be 4 eV in the center of mass frame. The mean charge exchange cross sections were 9 {times} 10{sup {minus}14} cm{sup 2} for Xe{sup 43+} to Xe{sup 46+} and 2 {times} 10{sup {minus}13} cm{sup 2} for Th{sup 73+} to Th{sup 79+}. Double capture was approximately 20--25% of the total for both xenon and thorium. A fit indicated that the cross sections were approximately proportional to q. This is consistent with a linear dependence of cross section on q within the measurement uncertainties.