Differential cross sections for charge exchange at high energies

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

The first Born approximation corrected for the boundary conditions is used to compute total cross sections for charge exchange in ${\mathrm{H}}^{+}$-He, ${\mathrm{H}}^{+}$-N, and ${\mathrm{H}}^{+}$-O collisions at intermediate and high energies. An independent-particle method is employed with a one-electron orbital for the target. Two sets of computation are presented in which the initial state of the active electron is described by the Roothaan-Hartree-Fock and hydrogenlike wave functions. These two approaches yield noticeably different results for the cross sections. Excellent agreement with existing experimental data is obtained at energies ranging from 50 keV to 50 MeV by using the Roothaan-Hartree-Fock wave function as a linear combination of normalized Slater-type orbitals.

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.

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.

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.

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 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.

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.

Highly charged xenon (35+ to 46+) and thorium (72+ to 79+) ions were produced in an Electron Beam Ion Trap (EBIT). The ions were extracted from EBIT in a short pulse. Ions of one charge state were selected using an electromagnet. The ions were recaptured at low energy in a cryogenic Penning trap (RETRAP). As the ions captured electrons from molecular hydrogen, populations of the various charge states were obtained by measuring the image currents induced by the ions on the electrodes of the trap. Data on the number of ions in each charge state vs. time were compared to 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.

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.

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.

X-ray emission from a comet was observed for the first time in 1996. One of the mechanisms believed to be contributing to this surprisingly strong emission is the interaction of highly charged solar wind ions with cometary gases. Reported herein are total absolute charge-exchange and normalized line-emission (X-ray) cross sections for collisions of high-charge state (+3 to +10) C, N, O, and Ne ions with the cometary species H2O and CO2. It is found that in several cases the double charge-exchange cross sections can be large, and in the case of C3+ they are equal to those for single charge exchange. Present results are compared to cross section values used in recent comet models. The importance of applying accurate cross sections, including double charge exchange, to obtain absolute line-emission intensities is emphasized.

The forward-angle differential cross sections of pion single charge exchange on $^{7}\mathrm{Li}$ and $^{13}\mathrm{C}$ were measured at 70, 100, 150, 165, and 180 MeV. The cross sections rise steeply up to 150 MeV and remain almost constant between 150 and 180 MeV. Comparisons with theoretical calculations and with the free charge-exchange cross sections are presented. There is poor agreement with the data. Only phenomenological calculations can fit the resonance region. The isobaric analog excitation functions rise more steeply than the continuum single-charge-exchange cross sections.

The proportion of N4+ photofragmenting to yield N2+ in X 2Σg+v≳0 states has been measured by observing the yield of the fragments’ charge transfer reaction with Ar. Such a determination is possible because N2+ in the v=0 level has a cross section for charge exchange with Ar that is 2 orders of magnitude smaller than in higher vibrational levels. The fraction of N2+(v≳0) fragments increases from 0.30 at 620 nm to 0.37 at 266 nm. Calculations, which treat the N2+ and N2 fragments as quantum harmonic oscillators and the dissociation coordinate classically, predict an N2+ fragment vibrational content that is of the same order as that observed. The substantial population of vibrationally quiescent N2+ fragments, along with previous kinetic energy release studies of N4+ photodissociation, that show a limited fraction of the available energy appears as translational motion [M. F. Jarrold, A. J. Illies, and M. T. Bowers, J. Chem. Phys. 81, 214 (1984)], suggest that the fate of much of the photon’s energy is either in product rotational motion or in the neutral N2 vibration. Mechanisms for the dissociation are discussed.

The interpenetration of laser produced plasmas can be detected by the occurrence of charge exchange reactions. Such reactions only occur if highly charged ions collide with ions of a significantly lower charge in suitable energy levels. This leads to selective population of a specific level of the highly charged ion resulting in an enhancement of particular lines in the region of the interaction. In case of interpenetrating carbon plasmas these reactions lead to enhanced line emission at 18.2 nm (H α line of C Vl).We present spatially and temporally resolved investigations of the interaction region of colliding plasmas;we show results of calculations of the cross sections for charge exchange obtained with a semi-classical model and compare measured spectra with calculated ones obtained from a collisional radiative model.