Multiple ionization in relativistic heavy-ion-atom collisions.

A method is suggested for quickly and easily estimating multiple ionization (MI) cross sections of heavy atoms colliding with highly charged ions, using the independent-particle model (IPM). One-electron ionization probabilities p(b) are calculated using the geometrical model for values at zero impact parameter b and the relativistic Born approximation for one-electron ionization cross sections. Numerical results of MI cross sections are presented for Ne and Ar atoms colliding with Ar8+, Fe20+, Au24+, Bi67+ and U90+ ions at energies 1 MeV u–10 GeV uand compared with available experimental data and CTMC (classical trajectory Monte Carlo) calculations. The present method of calculation describes experimental dependencies of MI cross sections on the number of ejected electrons m within a factor of two to three. Numerical calculations show that at intermediate ion energies E = 1 − 10 MeV u, the contribution of MI cross sections to the total, i.e. summed over all m values, is quite large ∼35% and decreases with increasing energy.

We present positron-impact multiple (single to quintuple) and total ionization cross sections of Ne, Ar, Kr, and Xe, covering an extended energy range from 50 eV to 7 keV. We improve on previous calculations of the ionization thresholds by adding the mean kinetic energy transferred to the target electrons. In this way the thresholds compare rather well with the experimental appearance energies for the different k-fold ionization cross sections. Present results include not only the novel energy threshold at low energies but also the post-collisional contribution at high energies. We performed a quite complete particle–antiparticle comparison by including our positron-impact results, new calculations for electron-impact ionization including the threshold correction, and a detailed compilation of experimental data. Present positron-impact multiple ionization cross sections are the first ones in such an extended energy region.

The method of convolutions is used to form smoothed functions from approximate wave functions which are discontinuous or have discontinuous first derivatives. As a parameter ε in the smoothed function decreases, the smoothed function approaches the approximate wave function. The expectation values for physical properties corresponding to the approximate wave function are defined to be the limit as ε approaches zero of the expectation values corresponding to the smoothed function. It is found that if the approximate wave function is discontinuous, the corresponding expectation value for the kinetic energy is infinite. Therefore, it seems unlikely that discontinuous approximate wave functions can ever be useful. However, if the approximate wave function is continuous but has a discontinuity in its first derivative, then, as a result of the discontinuity, there is a contribution δT̄12 to the expectation value of the kinetic energy. For a one-dimensional problem δT̄12=−(ℏ2/2m)ψ*(0) [ψ2′(0)−ψ1′(0)].Here ψ(0) is the value of the approximate wave function at the point zero where the discontinuity in its first derivative occurs, and ψ1′(0) and ψ2′(0) are the first derivatives of ψ taken from the left and from the right, respectively, at this point. Similarly, for an N-dimensional problem having a surface S12=0 over which the first derivatives of the approximate wave function are discontinuous, δT̄12= ∫ surfaceψ*[(∂/∂n) (ψ2−ψ1)]dS12.Here the ∂/∂n is the normal derivative with the normal pointed from region 1 towards region 2.

Probing superheavy quasimolecular collisions with incoming inner shell vacancies

We have studied the stabilities of multiply charged van der Waals dimers in slow Xe30+ + [C60]2([C60C70], [C70]2) → Xe(30-s)+ + [C60]2r+([C60C70]r+, [C70]2r+) + (r-s)e-electron-transfer collisions (v = 0.4 a.u. and r ≤ 7). The relative ionization cross sections display even-odd variations as functions of r for [C60]2r+, [C60C70]r+, and [C70]2r+. This is in clear contrast to the typical smooth decreasing behavior of the cross sections for multiple ionization of fullerene monomers, which can be explained within the framework of the classical over-the-barrier model. In addition, we report the branching ratios and the kinetic energy releases for the dominant fragmentation processes that yield intact fullerenes. The experimental results are discussed in view of a simple electrostatic model for dimer ionization and recent results from high level density functional theory calculations.

The ionization and dissociation of ammonia by impact of protons is investigated experimentally in a wide range of energies from 125 to 2700 keV. Coincidence measurements are used to separate single from multiple ionization. The role of the charge sign of the projectile was analyzed for the ionization by comparing the proton with previous electron data. The energy dependence of the single and multiple-ionization cross sections allowed us to evaluate the role of second-order mechanisms. For single ionization, the role of a two-step mechanism was inferred. The double-ionization cross section showed that postcollisional deexcitation takes over the two-step sequential ionization above 800 keV. Triple ionization is prompted mostly by postcollisional Auger decay.

Chapter 7 - Ionization — many electrons

We report on the first experiment that measures simultaneously the full momentum vector of recoil ions and projectile energy loss and scattering angle in ion-atom collisions. We studied multiple ionization in the collisions of 0.83-MeV/u O7+ with Ne. Recoil ions ( Ne(q+), q = 1-8) were detected in coincidence with single capture to O6+. The results give the first experimental evidence for the increase of the average electron energy with increasing recoil charge state q. The average ejection angle shows a dramatic decrease with q. Results are compared with n-electron classical trajectory Monte Carlo calculations.

Multiple ionization of Au by fast Sq+ ions of energy 0.4–3.8 MeV/amu

L-subshell ionization of heavy elements by S ions with energy of 0.4–3.8 MeV/amu

A previously derived statistical model of atomic collisions is discussed and applied to the problem of ionization in the collision of two slow heavy atoms. The diffusion equation (in energy of excitation) resulting from the model is solved for a simplified nontrivial model. A universal curve is obtained for the cross section for single ionization. The experimental data of Lee and Gilbody are fitted remarkably well.

Measurement of inelasticities for charge correlated multiple ionization of Ne by fast C 6+ ions

An approximate light-cone wave function for the pion effective quark-antiquark Fock sector corresponding to a small value of the renormalization group parameter is presented. The approximate wave function is motivated by the LF-holography and the quadratic confinement potential in the front form of Hamiltonian dynamics, which is in harmony with the linear confining potential in the instant form. The pion radius, decay constant and form-factor are also presented.

ECPSSR cross sections for inner-shell ionization are compared with numerical calculations that use correct and wrong expressions for exact limits of momentum transfer. For very adiabatic collisions, the employment of the wrong expression, as done in several popularly utilized computer codes, overestimates the cross sections up to two orders of magnitude. By contrast, even in such collisions the original ECPSSR approach of Brandt and Lapicki that approximates the effect of projectile energy loss by a multiplicative correction function fS and the relativistic effects by a relativistically corrected electron mass yields cross sections that are in agreement within a factor of two with respect to the calculation with hydrogenic Dirac wavefunctions and exact limits of integration with no relativistic correction. For plane-wave Born approximation calculations, the relativistic corrected expressions of the exact limits of integration are presented. The cross section calculated with such limits differs from the ECPSSR calculation using the fS-function by less than 2% in the region of lowest collision velocities covered by experiments. A straightforward modification of the existing computer codes with the correct expression for exact momentum transfer is suggested.

In this paper, we extend our previous work of COBI model to study the multiple ionization and mean charge state of noble gases collided by heavy ions at energies not far from Bragg peaks of several to hundreds keV/amu. Being in good agreement with various experimental data and taking extremely small computational time make the model helpful to study the charge state distribution and multiple ionization of gases transforming to plasmas.