Partial Differential Cross Sections Research Articles

Electron impact ionization cross sections for C60 fullerene

We have extended and generalized the modified Jain–Khare (JK) semiempirical formalism to the evaluation of partial differential and partial integral ionization cross sections for fullerenes. The differential cross sections corresponding to the production of singly, doubly and triply charged cations in the electron impact ionization of C60 were evaluated at incident electron energies of 100 and 200 eV. The partial integral ionization cross sections calculated in the energy range varying from ionization thresholds to 1000 eV revealed satisfactory agreement with the available experimental and theoretical data. The ionization rate coefficients corresponding to the various cations have also been evaluated using the presently calculated ionization cross sections and Maxwell–Boltzmann energy distributions.

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

On the determination of partial differential cross sections for photodetachment and photoionization processes producing polyatomic molecules with electronic states coupled by conical intersections

A formalism is derived for the computation of partial differential cross sections for electron photodetachment and photoionization processes that leave the residual or target molecule in electronic states that are strongly coupled by conical intersections. Because the electronic states of the target are nonadiabatically coupled, the standard adiabatic states approach of solving the electronic Schrödinger equation for the detached electron at fixed nuclear geometries and then vibrationally averaging must be fundamentally modified. We use a Lippmann-Schwinger equation based approach, which leads naturally to a partitioning of the transition amplitude into a Dyson orbital like part plus a scattering correction. The requisite Green's function is that developed in our previous paper for the direct determination of total integral cross sections. The method takes proper account of electron exchange, possible nonorthogonality of the orbital describing the detached electron, and nonadiabatic effects in the product molecule. The Green's function is constructed in an L(2) basis using complex scaling techniques. The accurate treatment of nonadiabatic effects in the residual molecule is accomplished using the multimode vibronic coupling model. For photodetachment, an approximate approach, which is less computationally demanding, is suggested.

Differential cross sections for electron-impact excitation of laser-excited 174Yb (…6s6p 3P1)

We have measured and calculated electron-impact excitation cross sections from the laser-excited Yb (…6s6p 3P1) level to the higher-lying Yb (…6s6p 1P1), (…6s5d 3D1, 2, 3) and (…6s7s 3S1) levels at 20 eV impact energy. Measurements were performed using a crossed-beam apparatus, with resonant laser radiation incident on the electron–atom interaction region, providing excited-state atomic targets. Calculations were performed in the relativistic convergent close-coupling (RCCC), convergent close-coupling (CCC), and relativistic distorted-wave (RDW) approximations. We present measured and calculated partial differential cross sections (), which relate to differential cross sections and electron-impact coherence parameters through the target state anisotropy introduced by the laser geometry. Using theoretical predictions of the h electron-impact coherence parameter, we present the differential cross section for the 3P1–3S1 excitation.

Electron scattering from excited-state ytterbium

We present results of our recent experimental investigation of electron scattering from the 6s6p 3P1 laser excited state of the Yb atom. Measurements of the (partial) differential cross sections for the excitations 6s6p 3P1 → 5d6s3D1,2,3 + 6s6p1P1 (unresolved) and 6s6p3P1 → 6s7s3S1 at 20 eV impact energy are presented. P3 Stokes parameters for the corresponding, time-inverse, de-excitations are also given.

Nonresonant spontaneous bremsstrahlung by a relativistic electron scattered by a nucleus in the field of pulsed light wave

This paper presents theoretical study of nonresonant spontaneous bremsstrahlung by an electron scattered by a nucleus in the field of the pulsed light wave. The electron interaction with a Coulomb potential of a nucleus is considered in the first order of perturbation theory (the Born approximation), and the interaction with an external pulsed field is taken into account accurately. The approximation is examined when pulsewidth is considerably greater than the characteristic time of wave oscillations. The obtained differential cross-section of the process has form of a sum over partial differential cross-sections. Each of them corresponds to processes with emission (absorption) of certain number of wave photons. It is shown, that for spontaneous bremsstrahlung by an electron scattered by a nucleus in the field of a pulsed light wave the distribution of a stimulated emission-absorption probability is determined by the average value of corresponding probabilities in the case monochromatic wave.

An analytic model of rotationally inelastic collisions of polar molecules in electric fields

We present an analytic model of thermal state-to-state rotationally inelastic collisions of polar molecules in electric fields. The model is based on the Fraunhofer scattering of matter waves and requires Legendre moments characterizing the "shape" of the target in the body-fixed frame as its input. The electric field orients the target in the space-fixed frame and thereby effects a striking alteration of the dynamical observables: both the phase and amplitude of the oscillations in the partial differential cross sections undergo characteristic field-dependent changes that transgress into the partial integral cross sections. As the cross sections can be evaluated for a field applied parallel or perpendicular to the relative velocity, the model also offers predictions about steric asymmetry. We exemplify the field-dependent quantum collision dynamics with the behavior of the Ne-OCS((1)Sigma) and Ar-NO((2)Pi) systems. A comparison with the close-coupling calculations available for the latter system [Chem. Phys. Lett. 313, 491 (1999)] demonstrates the model's ability to qualitatively explain the field dependence of all the scattering features observed.

Study of isotope effect in 3He(4He)-H2 collisions

Close-coupling equation is applied to the 3He(4He)-H2 system，and the rotational excitation cross sections for incidence energy of 05eV are calculated.By analyzing the differences between these partial wave cross sections and differential cross sections，the change of the partial wave cross sections and differential cross sections with increase of quantum number，as well as with the change of the mass of isotope atom are found out. Based on the calculation，the effect of isotopic substitution on atom-diatom collision is discussed.

Diffusion radius of muonic hydrogen atoms in H-D gas

The diffusion radius of the 1S muonic hydrogen atoms in gaseous H_2 targets with various deuterium admixtures has been determined for temperatures T=30 and 300 K. The Monte Carlo calculations have been performed using the partial differential crosssections for $p\mu$ and $d\mu$ atom scattering from the molecules H$_2$, HD and D$_2$. These cross sections include hyperfine transitions in the muonic atoms, the muon exchange between the nuclei $p$ and $d$, and rotational-vibrational transitions in the target molecules. The Monte Carlo results have been used for preparing the time-projection chamber for the high-precision measurement of the nuclear $\mu^{-}$ capture in the ground-state $p\mu$ atom, which is now underway at the Paul Scherrer Institute.

Coincidence electron spectroscopy of electron-impact multiple ionization of argon

Measurements of the partial double differential ionization cross sections of argon atoms have been made by performing coincidences between recoil ions and energy- and angle-selected slow electrons produced in $12--24\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ ${e}^{\ensuremath{-}}\text{\ensuremath{-}}\mathrm{Ar}$ collisions. Results show that the ${\mathrm{Ar}}^{3+}$ ions are formed mainly by a two-step-one process via electron shake-off. These measurements have enabled determination of the shake-off probability $S=0.14\ifmmode\pm\else\textpm\fi{}0.01$ for ${L}_{2,3}$ subshell, which is in good agreement with a theoretical predication. Additionally, ${\mathrm{Ar}}^{2+}$ and ${\mathrm{Ar}}^{+}$ ions are found to arise respectively from the filling of $L$-shell vacancy by an auger transition and from the direct ionization of $M$-shell of the argon atom.

Electron impact ionization cross-sections for the N 2 and O 2 molecules

The single differential cross-sections for the production of parent ions (N 2 +, O 2 +) and fragment ions (N +, O +) resulting from the direct and dissociative ionization of N 2 and O 2 by electron impact have been evaluated by a semi-empirical formulation based on optical photo-ionization cross-sections. The electron impact cross sections are presented as a function of energy loss suffered by impinging electrons with incident electron energies ranging from 100 to 500 eV. No previous data exist with which comparison can be made for partial differential cross-sections. A critical comparison of the computed total cross sections with available experimental data revealed an agreement within the experimental error bars.

Determination of partial single differential electron ionization cross sections of H2

The partial single differential cross sections (PSDCS) for the ions H2+ and H+ resulting from the direct and dissociative ionization of H2 by electron impact have been calculated employing a semi-empirical approach. The calculations are made as a function of the secondary/ejected electron energy at 500 and 1000 eV incident electron energies. The partial ionization cross sections (PICS) for direct and dissociative ionization have also been calculated with incident electron energies varying from the ionization threshold to 10 keV. The results are compared with the available experimental data.

Photoionization of helium between theN=2andN=5thresholds ofHe+:Partial differential cross sections

Photoionization excitation of helium has been performed employing the R-matrix method with a 20-term target representation for incident photon energies between the $N=2$ and $N=5$ thresholds (69--76.8 eV) of the ${\mathrm{He}}^{+}$ ion. Partial differential cross sections for photoionization leaving the ${\mathrm{He}}^{+}$ ion in the $N=2,3,4$ levels at emission angles $0\ifmmode^\circ\else\textdegree\fi{}$ and in the $N=2$ level $90\ifmmode^\circ\else\textdegree\fi{}$ are provided. Our results to ${\mathrm{He}}^{+}$ in the $N=2$ state give fairly good agreement with the available experimental data and theoretical calculations below the $N=3$ threshold. Between the $N=3$ and $N=5$ thresholds of the ${\mathrm{He}}^{+}$ ion, our results for ${\mathrm{He}}^{+}$ in the $N=2,3,4$ states still agree with experiment qualitatively.

The modified Faddeev equation and multichannel positron-hydrogen scattering calculation

A bipolar spherical harmonics expansion of the modified Faddeev equation is used to calculate the K-matrices of the e++H scattering for up to five open channels and for total angular momentum L4. Partial cross sections and differential cross sections including hydrogen production channels are reported. Comparison with previous calculations are made whenever feasible. Good agreement is observed.

Partial differential cross sections for the ionization of the SO2 molecule by electron impact

The partial singly differential cross sections (PSDCS) for the ions SO2+, SO+, (S+,O2+), and O+ resulting from the direct and dissociative ionization of the SO2 molecule by the impact of 100 eV electrons, have been calculated employing a semi-empirical approach. Calculations have been made as a function of energy loss (the sum of the secondary electron energy and the ionization threshold) suffered by the incident electrons. The integral of PSDCS in terms of partial ionization cross sections have also been calculated. No previous experimental data exists with which to make comparisons for PSDCS. A critical comparison of the calculated partial and total ionization cross sections with the experimental data revealed an agreement within the experimental error bars. © 1998 John Wiley & Sons, Ltd.

Inelastic electron scattering by laser-excited atoms

We present experimental and theoretical results of an investigation into low-energy electron scattering from atoms coherently prepared in the state by laser excitation. We measured the differential cross section from the coherently prepared state (referred to as partial differential cross section) for excitations of the , , , and levels at and 36.7 eV incident electron energies and compared them with theoretical results obtained from unitarized distorted wave approximation calculations. In some cases (e.g. the excitation of and levels) there is reasonable or good agreement between theory and experiment, in other cases (e.g. the excitation of the and , levels) there are order of magnitude (or more) differences.

Positron scattering from polar molecules: Rotovibrationally inelastic collisions with CO targets

Quantum calculations have been carried out on the vibrational and rotational excitation processes for CO molecules in collision with positron projectiles below the threshold of Ps formation (E{sub coll}{le}7eV). The coupled equations have been solved for the vibrationally inelastic process in the body-fixed frame of reference, and Born-type corrections for the divergent behavior of the angular distributions due to the permanent molecular dipole have been applied. Detailed comparisons are made between the partial (rotational and/or vibrational) integral and differential cross sections and earlier available calculations and measurements. {copyright} {ital 1997} {ital The American Physical Society}

Partial differential cross sections for inelastic He++Ne collisions at low energy

We report differential cross section measurements with high angular resolution for different channels of the inelastic processes He++Ne→He++Ne* and He++Ne→He*+Ne+, for collision energies between 100 and 200 eV. For the Ne states (2p53s)1,3P1, which decay optically, we determined the fraction with the alignment at right angles to the scattering plane. The results are used to discuss the mechanism of the processes and the influence of the spin-orbit interaction upon the collision.

Magnetic sublevel partial differential cross sections for electron impact excitation of the Ba(...6s6p 61P1) level

Magnetic sublevel partial differential cross sections for excitation of the Ba(...6s6p 61P1) level are presented based upon the differential cross section measurements of Jensen et al. (1978), and Wang et al. (1994), in combination with new electron impact coherence parameter measurements and electron impact coherence parameter measurements previously reported by Zetner and Li (1993, 1994). These partial differential cross sections, determined for electron impact energies of E0=10, 20, 37, 50 and 80 eV, are compared with available theory.

Photoionization of He above the N=2 threshold. II. Angular distribution of photoelectrons and asymmetry parameter.

We report theoretical calculations for the ${\mathrm{\ensuremath{\beta}}}_{2\mathit{p}}$-asymmetry parameter in the photoionization of He(1${\mathit{s}}^{2}$) above the N=2 ionization threshold. We use an extension of a method recently proposed [I. S\'anchez and F. Mart\'{\i}n, Phys. Rev. A 44, 7318 (1991)] that makes use of a Feshbach partitioning of the final-state wave function and an ${\mathit{L}}^{2}$ representation of the coupled continuum states. Partial differential cross sections at emission angles 0\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} are also provided. Our results are in good agreement with the experimental data, thus showing the accuracy of the present method to study electron angular-distribution properties.