Resonant Charge Transfer Cross Section Research Articles

The Rb + –Rb collision rate in the energy range of 103–104 K

We study both theoretically and experimentally the energy dependence of the low-energy Rb+–Rb total collision rate k ia in the energy range from 103 to 104 K. We calculate the integral elastic cross-section and the resonant charge-transfer cross-section by the quantum mechanical molecular orbital close-coupling method, and then obtain k ia for temperatures by averaging the cross-sections over a Maxwell–Boltzmann velocity distribution. The experiments are conducted in an ion–neutral hybrid trap, where the Rb+ ions are created by photo-ionization of the cold atoms in a magneto-optic trap (MOT) and accumulated in the linear Paul ion trap. The total ion–atom collision rate k ia is measured by monitoring the fluorescence reduction of the steady-state MOT atoms by sequentially introducing photo-ionization and ion–atom collisions. The ion–atom collision energy E col ≈ T i is modified by changing T i due to T i being more than six orders of magnitude larger than the T a of cold atoms. The temperature of ions T i is obtained by comparing the time-of-flight mass spectrometry of Rb+ from experimental results to that obtained by SIMION simulation. The equilibrium steady T i is modified by changing the initial root-mean-squared position of the ion cloud, and the k ia are measured with E col from 8000 to 16 000 K. Both the theoretical and experimental results show that k ia increases with E col. More specifically, the measured k ia increases rapidly with the enlargement of E col near 10 000 K. The theoretical calculation results show that k ia increases slowly with E col. The specific difference may be due to the influence of the ratio of excited states f e on the trend of k ia at different E col.

Quantum tunneling resonant electron transfer process in Lorentzian plasmas

The quantum tunneling resonant electron transfer process between a positive ion and a neutral atom collision is investigated in nonthermal generalized Lorentzian plasmas. The result shows that the nonthermal effect enhances the resonant electron transfer cross section in Lorentzian plasmas. It is found that the nonthermal effect on the classical resonant electron transfer cross section is more significant than that on the quantum tunneling resonant charge transfer cross section. It is shown that the nonthermal effect on the resonant electron transfer cross section decreases with an increase of the Debye length. In addition, the nonthermal effect on the quantum tunneling resonant electron transfer cross section decreases with increasing collision energy. The variation of nonthermal and plasma shielding effects on the quantum tunneling resonant electron transfer process is also discussed.

Charge exchange of a polar molecule at its cation

The Landau-Herring method is used to derive an analytic expression for the one-electron exchange interaction of a polar molecule with its positively charged ion, induced by a σ-electron. Analogously to the classical Van der Pole method, the exchange interaction potential is averaged over the rotational states of colliding particles. The resonant charge-transfer cross section is calculated, and the effect of the dipole moments of the core on the cross section is analyzed. It is shown that allowance for the dependence of the exchange potential on the orientation of the dipole moments relative to the molecular axis may change the dependence of the cross section on the velocity of colliding particles, which is typical of the resonant charge exchange, from the resonance to the quasi-resonance dependence.

Resonant charge transfer between H+ and H from 1 to 5000 eV

We employ the electron–nuclear dynamics (END) formalism to investigate the resonant charge transfer and scattering processes in the collision of protons on atomic hydrogen as an introduction to investigations of resonant charge transfer in larger atomic and molecular systems. The END method consists of an ab initio, non-adiabatic treatment of the electronic and nuclear degrees of freedom. The results span an energy range from 1 eV to 5 keV. We present electron transfer probabilities, absolute charge transfer differential and integral cross sections, and state-to-state differential cross sections for principal energy levels n = 1 and 2. The present results compare favourably with experimental data and other theoretical results. For the total resonant charge transfer cross section, we confirm the relation σ1/2trans ∼ ln E. The role of non-adiabatic couplings in transfer into the n = 2 level is confirmed, and the effect of basis set size on the dynamics of the transfer is probed.

CROSS SECTIONS FOR RESONANT CHARGE TRANSFER BETWEEN ATOMS AND THEIR POSITIVE IONS

A comparatively simple interpretation of the method of Firsov [Sov. Phys. JETP21,1001 (1951)] is used to calculate symmetric resonant charge transfer cross sections for the first 20 (nontransition) elements H through Ca in the range of low and intermediate collision velocities (≤1.0 × 108cm/s). The results obtained show good agreement with corresponding experimental data and with the theoretical results of Sakabe and Izawa [AtomicData andNuclearDataTables49,257 (1991)]. Discrepancies between the two sets of theoretical data are discussed.

Charge Transfer Cross Section for Gadolinium.

Symmetric resonance charge transfer cross sections between singly ionized gadolinium ion and the parent atom were measured in the impact energy range of 100~1000 eV. The cross sections were determined from the ratio between the number of ions produced by charge transfer and those in primary ion beam. The primary ion beam of gadolinium was produced by a laser ion source in which gadolinium atoms were ionized by resonance photoionization. The slow ions produced by charge transfer and fast primary ions were detected with Faraday cups. The obtained cross section was about 1.5×10-14cm2 at impact energy of 500 eV. The dependence of the measured cross sections on the impact energy roughly agrees with theoretical prediction.

Symmetric resonant charge transfer in H++H and He2++He collisions at extremely low energies.

Symmetric resonant charge transfer (RCT) in ${\mathrm{H}}^{+}$+H and ${\mathrm{He}}^{2+}$+He collisions has been investigated in the ultralow-collision-energy range ${10}^{\mathrm{\ensuremath{-}}3}$--${10}^{\mathrm{\ensuremath{-}}7}$ eV. The RCT cross section has been computed by partial-wave expansion in the molecular-orbital expansion method within the fully quantum-mechanical formalism. The calculated RCT cross sections become constant below E\ensuremath{\simeq}${10}^{\mathrm{\ensuremath{-}}6}$ eV, corresponding to a scattering length of \ensuremath{\sim}6${a}_{0}$ and \ensuremath{\sim}2${a}_{0}$ for ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ and ${\mathrm{He}}_{2}$${\mathrm{}}^{2+}$, respectively.

Symmetric resonance multiple charge transfer of Neq+and Arq+(q⩽4)

Cross sections for resonance charge transfer processes, Aq++A to A+Aq+, have been measured for Ne1-4+ and Ar1-4+ at ion acceleration voltages of 2, 3 and 4 kV. The cross sections obtained at 2 kV are 6.9*10-16, 1.74*10-16, 4.9*10-17 and 3.4*10-18 cm2 for Ne+, Ne2+, Ne3+ and Ne4+, respectively, and 2.4*10-15, 5.5*10-16, 9.0*10-17 and 3*10-18 cm2 for Ar+, Ar2+, Ar3+ and Ar4+, respectively. This is the first measurement of resonance charge transfer cross sections for quadruply charged ions. The results obtained are discussed in terms of the total ionisation energies Sigma jqIj of the ions, where Ij is the jth ionisation potential. A concept of the 'survival factor' is introduced.

Model potential simulations and charge transfer cross-sections

Total resonant charge transfer cross-sections are calculated for the Rb++Rb→Rb+Rb+ reaction by using an atomic two-state picture within the impact parameter formalism and a model potential approach. Different model potential simulations of the alkali atom are used. In two cases the calculated total cross-sections exhibit an oscillatory structure, while in the other two cases no oscillation is present. It shows that the results are critically dependent upon the alkali atom treatment. An effort is made to correlate the behaviour and the absolute values of the cross-sections to the peculiarities of the different model potential simulations. In particular, it is suggested that the oscillatory behaviour is exhibited by the cross-sections only when the model potential and the model wave function give rise to a barrier along the line joining the two alkali cores not too high nor too large at small internuclear distances such as to allow the valence electron to undergo a process of alternate tunnelling. Furthermore, it is shown that again the model potentials and the model wave functions affect the absolute value of the cross-sections through the tail of the gerade potential.

Precise resonant charge-transfer cross sections for He-He+between 2 and 100 eV

Ground-state total charge-transfer cross sections sigma 10 for He-He+ collisions at relative impact energies between 2 and 100 eV have been measured by observing the attenuation of a He+ ion beam in helium gas. Fitting these results to the usual functional form yields the relation sigma 1012/=6.61-0.621 ln nu , where sigma 10 is in AA2 and nu is the impact velocity in km s-1. The absolute accuracy of sigma 10 is about +or-2%.

An experimental estimate of the O+-O resonant charge transfer cross section, collision frequency, and energy transfer rate

The resonant-charge-transfer cross section dominates the interaction between neutral and ionized atomic oxygen at temperatures greater than several hundred degrees Kelvin. This cross section is of direct importance to F-region studies of ion diffusion, ion thermal balance, and neutral atmospheric winds and pressure gradients, since it determines collision frequencies and energy and momentum transfer rates. However, the uncertainty in this cross section is roughly 25-40%. Incoherent-scatter measurements allow determination of the product of the atomic oxygen concentration multiplied by the cross section. If present-day atmospheric models are accepted as statistically representative of F-region atomic oxygen concentrations experimental (aeronomical) data presented indicate that the resonant-charge-transfer cross section is about 1.3 times greater than the value presently in general use, though in excellent agreement with the only other available (laboratory) experimental value. This revised cross section has obvious implications for thermospheric studies.

The gerade-ungerade splitting of N 2+ potentials: effects on the resonant charge transfer cross sections of nitrogen atoms

Ab initio N 2 +( 2,4,6Σ g,u, 2,4,6Π g,u) potential splittings have been calculated in the internuclear distance range 2–5 A. The results for the Σ potentials have been obtained in the Heitler-London formulation either retaining all relevant integrals (method 1), or by neglecting some terms (method 2), while the Π splittings have been calculated only within the more approximate method 2. The results have been used for calculating the total charge transfer sections Q tr of the process N( 4S) + (N +( 3P) = N 3P) + N( 4S). A reasonably satisfactory agreement with the corresponding Q tr values obtained from previous potentials can be pointed out, with the exception of the results based on the extrapolation of spectroscopic potential curves. A good agreement has also been found with the experimental Q tr values of Belyaev as well as with the Q tr cross sections derived by Duman and Smirnov by means of a completely different theoretical approach.

Near resonant charge transfer processes at thermal energies

A useful procedure is described for the evaluation of near resonant charge transfer cross-sections at thermal energies. The method is based on a generalization of a semi-classical approach introduced by Bates and Mapleton for the study of symmetric resonant charge transfer processes. The rate coefficient is calculated for the reaction O++H⇆H++O as a function of temperature between 10 and 104 K; the results are compared to those obtained using the ‘orbiting approximation’. A brief application of these rates to the interstellar medium is made where it is found that substantial differences emerge between cases where the gas is heated by cosmic rays or by X-Rays.

Potential curves for Na 2+ and resonance charge transfer cross sections

A model potential method, applied earlier to Li 2 +, is used to calculate the six lowest potential energy curves of Na 2 +. Charge transfer cross sections are calculated for Li + on Li and for Na + on Na and found to be in reasonable agreement with experiment.

Ion-Slip Coefficients for Partially Ionized Argon and Helium

Abstract Ion-slip coefficients in Demetriades and Argyropoulos' generalized Ohm's law are studied quan-titatively in the first approximation for partially ionized Ar and He under various non-isothermal gas conditions. The macroscopic forces due to collisions between electrons, ion, and neutral atoms are accounted by averaging the momentum transfer cross sections over the Maxwellian velocity distributions of the colliding particles. To incorporate the appropriate interpolation and extrapola-tion techniques in the low energy limit, Frost and Phelps' cross sections for electron-atom collisions and Dalgarno's value for ion-atom resonant charge-transfer cross sections were used. The weighted average momentum transfer cross sections thus obtained, which are also important in other diffusion and transport processes, are tabulated at various particle kinetic temperatures for both gases. A family of curves representing values of ion-slip coefficients calculated from these data is plotted. With the generalized Ohm's law written in its inverted form, the influence of ion-slip on the "Hall conductivity" in Kruger et al's formulation is discussed.

Resonance charge transfer in He2+-H(1s) collisions

The resonance charge-transfer cross sections for the collision process He2+ + H(1s) -> He+(2s, 2p) + H+ have been evaluated in the atomic two-state and five-state approximations of the impact-parameter method. Momentum transfer was taken into account by the procedure described by Cheshire in 1967. The total and individual cross sections obtained in the five-state approximation exceed the corresponding cross sections obtained in the two-state approximation.

Oscillations in the caesium and rubidium resonant charge transfer cross sections

The oscillations found in the caesium and rubidium charge transfer cross sections by Perel et al. can be explained using a two-state wave theory and two potentials whose difference passes through a maximum.

Effect on Symmetrical Resonance Charge Transfer Cross Sections of Change in Relative Motion during Encounter

Taking into account the effect which the force between the colliding systems has on the relative motion, a formula is derived for the cross section for symmetrical resonance charge transfer. Detailed calculations are carried out on H+ + H(1s) → H(1s) + H+ and on He2+ + He+(1s) → He+(1s) + He2+. In the case of the former, the effect under investigation is inappreciable; but in the case of the latter it is quite large, causing the cross section to pass through a maximum of 8.9πa02 at an energy of relative motion of about 100 eV. A simple method of allowing for the effect of a Coulomb repulsion is described. Evidence is adduced regarding the accuracy of Firsov's approximation.

Charge Transfer of Protons in Excited Atomic Hydrogen

Resonance charge transfer cross sections are calculated for protons in atomic hydrogen in the ground and first two excited states. The cross sections for an excited atom are nearly an order of magnitude larger than those for the ground state.