Calculation of electron-impact total-ionization cross sections

A computationally efficient analytic form of the Born-approximation electron-impact ionization amplitude is derived for general neutral-atom targets. High-quality Hartree-Fock Slater orbitals are used to model the target wave function. Full orthogonalization of the continuum Coulomb wave to all occupied orbitals of the target atom is enforced. Results are presented for noble gases (Ne, Ar, Kr, and Xe), selected transition metals (Fe, Cu, and Ag), and elements from the fourth, fifth, and sixth columns of the periodic table (Si, Ge, Sn, P, As, Sb, S, Se, and Te), where theoretical comparisons are lacking. Full orthogonalization significantly improves agreement with experimental data for the noble-gas series compared to previous Born models. Overall agreement with all elements is uniformly good and variations within each series are systematic

Comment on “Status of the convergent close-coupling method within the framework of the rigorous Coulomb scattering theory”

Shablov, Bilyk, and Popov [Phys. Rev. A 65, 042719 (2002)] claimed to have analyzed the convergent close-coupling (CCC) method within the framework of the rigorous Coulomb scattering theory, but without electron exchange. They concluded that “… the amplitude obtained within the framework of this method in principle does not converge to the observable physical amplitude.” We correct a misunderstanding of the origins of the CCC equations, and show that no-exchange CCC calculations exhibit no ready convergence, off or on the energy shell while those with exchange show convergence, but only on the energy shell. Since all previously published comparisons of CCC with experiment utilized on-shell amplitudes from calculations which included exchange, we question the stated conclusion

Efficient solution of three-body quantum collision problems: Application to the Temkin-Poet model

The solution for the three-body quantum oscillation problems were developed using a variable-spacing finite-difference algorithm. This method was applied to the Temkin-Poet electron-hydrogen model collision problem. The calculation were performed for electrons colliding with hydrogen atoms in the Temkin-Poet model for the impact energies ranging from 17.6 to 150 eV

Close-coupling approach to electron-impact ionization of helium

The close-coupling theory of electron-impact ionization of helium is studied. It is found that the "raw" convergent close-coupling equal-energy-sharing amplitudes converge to half the required amplitudes. As in the e-H case, solving the close-coupling equations yields amplitudes that behave as results of a finite Fourier expansion of a step function. We argue that the close-coupling formalism readily solves the e-He ionization problem with equal-energy outgoing electrons at all practical incident energies, and demonstrate it at the most difficult kinematic case of 2 eV above threshold

Box-based and Laguerre-based convergent close-coupling calculations of electron–helium ionization

We apply a new implementation of the convergent close-coupling (CCC) method to electron–helium scattering. The target states are obtained from one-electron He+ box-based eigenstates rather than the usual Laguerre-based orbitals. The utility of the new method is demonstrated for 50 eV electron-impact ionization of helium with three different energy sharings between the two outgoing electrons. Excellent agreement is found between previous and new CCC predictions, and also with experimental data

Coherent excitation of the singlet-triplet mixed 1s4f state of helium

In this paper, we present a detailed theoretical description for the coherent electron-impact excitation, the subsequent time evolution, and the cascading decay process of the singlet-triplet mixed 1s4f state of helium. The excitation amplitude and phase of each sublevel of this state are related to measurable coincidence intensities and polarizations of the emitted photons. It is found that the intensity and polarization of the emitted photons are time modulated due to the singlet and triplet mixing in the 1s4f state

Scaling limit of virtual states of triatomic systems

For a system with three identical atoms, the dependence of the $s-$wave virtual state energy on the weakly bound dimer and trimer binding energies is calculated in a form of a universal scaling function. The scaling function is obtained from a renormalizable three-body model with a pairwise Dirac-delta interaction. It was also discussed the threshold condition for the appearance of the trimer virtual state.Comment: 9 pages, 3 figure

Differential ionization cross-section calculations for hydrogenic targets with Z≤4 using a propagating exterior complex scaling method

The differential ionization cross sections for charged hydrogenic targets with low Z at low to moderate energies were calculated using propagating exterior complex scaling (PECS) method. The PECS method with iterative coupling proved to be highly efficient, providing an estimated 100-fold reduction in total computation time compared with the PECS method using direct coupling. Scattering wave functions were calculated for the electron impact of hydrogenic targets with nuclear charge Z≤4. The results show that the angular distributions of the differential cross sections change systematically with increasing nuclear charge for energies above the peak total ionization cross section

Scattering theory of close-coupling equations

The scattering theory implied by the close-coupling equations is studied using a Lippmann-Schwinger formalism. The new results derived can be summarized as follows: An alternative form of the equations that ensures there are no spurious solutions in the scattering region can be constructed, and moreover there is an infinite number of such forms. The Neumann- (perturbation-) series expansion diverges in general for most energies for both the old and new forms. The Born limit nevertheless holds and can be recovered by appropriate rearrangement of the Neumann series. The original integral formulation may give convergent scattering amplitudes despite the lack of uniqueness of the solutions. The conditions under which this happens are examined

Close-coupling approach to ionization processes

We briefly review recent progress in the field of electron-impact ionization of light atoms concentrating on those theories which attempt to fully solve the underlying scattering problem. Comparison between competing theories and experiment shows up some unexpected discrepancies