First-order Distorted-wave Born Approximation Research Articles

Second-order Born calculation of coplanar symmetric (e, 2e) process on Mg

The second-order distorted wave Born approximation (DWBA) method is employed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e, 2e) collisions for magnesium at excess energies of 6 eV–20 eV. Comparing with the standard first-order DWBA calculations, the inclusion of the second-order Born term in the scattering amplitude improves the degree of agreement with experiments, especially for backward scattering region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e, 2e) problems of two-valence-electron target in low energy range.

First-order distorted wave Born approximation for single ionization of Ar by electron impact in a coplanar doubly symmetric geometry

The first-order distorted wave Born approximation (DWBA) has been performed for single ionization of Ar(3p) by electron impact in coplanar doubly symmetric geometry from near threshold to intermediate energies. Theoretical triple differential cross sections (TDCS) are compared with the latest experimental data. It is found that when the incident electron energies are 40 eV higher than the ionization threshold, for argon, the binary and recoil collision mechanism will dominat as the energies increase, but not in the near threshold energy regime, where the distortion effects are of great significance. In order to completely describe the electron impact ionization of argon, it is imperative that more scattering mechanisms should be considered in the theoretical models.

Study of (e, 2e) process on potassium at 6 eV–60 eV above threshold in a second-order Born approximation

The standard distorted wave Born approximation (DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e, 2e) collisions for the alkali target potassium at excess energies of 6 eV–60 eV. Compared with the previous first-order DWBA calculations, the present theoretical model improves the degree of agreement with experiments, especially for the backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric (e, 2e) problems in low and intermediate energy ranges.

Second-order Born effect in coplanar doubly symmetric [formula omitted] collisions for sodium

The second-order distorted wave Born approximation (DWBA) method is employed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e,2e) collisions for alkali target sodium at excess energies of 6–60 eV. Comparing with the first-order DWBA calculations, the inclusion of second-order Born term in the scattering amplitude improves the degree of agreement with experiments, especially for backward scattering region of TDCS. This indicates the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e,2e) problems in low and intermediate energy range.

Integral cross section for electron-impact excitation of the 3p53d states of argon

Theoretical close-coupling R-matrix and two different first-order distorted-wave Born approximation (DWBA) calculations are presented for excitation of argon from its ground state to the twelve states in the (3p53d) manifold. The results are found to be very sensitive to the choice of atomic wavefunctions. The low-energy R-matrix results in general and, in several cases, the unitarized DWBA as well as the high-energy DWBA results are in fair agreement with the experimental data of Chilton and Lin (1999 Phys. Rev. A 60 3712).

Role of the postcollision interaction in electron-impact ionization of argon and krypton

There has been impressive progress in the theoretical treatment of electron collisions with atoms in the last decade. As a result, the fundamental collision problems of electron-hydrogen or electron-helium scattering are now understood fairly well. For heavier atoms, an accurate treatment of atomic ionization remains more elusive than atomic excitation due to the final-state three-body Coulomb problem. For higher impact energies, the first-order distorted-wave Born approximation is typically in reasonable agreement with fully differential cross sections (FDCS) for ionization. However, FDCS measurements are starting to be reported for lower incident electron energies and here agreement between experiment and theory is not good. In this paper we examine the importance of exchange distortion and the final-state electron-electron interaction on these collision processes.

Transfer of Angular Momentum in Electron Collisions with Alkali Atoms

Measurements of the transfer of angular momentum to rubidium and sodium atoms in collisions with electrons are reported. For excitation of the rubidium 52S1/2–52 P3/2 transition, it is found that existing first order distorted wave Born approximation calculations show poor agreement with the data and that a model which includes the relativistic interaction between the electrons and the atoms in the potential is needed. For the de-excitation of the sodium 42S1/2 –32 P3/2 transition, a long standing proposal relating to the sign of the transferred angular momentum is not supported except at small scattering angles. A convergent close coupling calculation displays excellent agreement with the measured data.

Bound-free electron-positron pair creation in relativistic heavy-ion collisions as a charge-transfer process.

Using a first-order distorted-wave Born approximation we examine the creation of bound-free electron-positron pairs in relativistic heavy-ion collisions. We consider this process as the transfer of a negative-energy electron in the Coulomb field of one of the colliding ions to a bound state of the other. We calculate differential and integral cross sections for various collision systems by employing exact relativistic single-electron wave functions in momentum space. Our results confirm the experimentally reported increase of cross sections with increasing collision energy and their unexpected strong dependence on the charge number of the ion which captures the electron. The calculated dependence on the charge number of the other colliding partner is, however, weaker than experimentally reported. A major conclusion of this investigation is that at least at moderate relativistic collision energies distortions of electronic states due to both Coulomb centers are important for this process. \textcopyright{} 1996 The American Physical Society.

An improved classical approach quantum encounter treatment of collision-induced vibrational energy transfer. Application to He + CO (ni = 1, 2)

Abstract The vibrational energy transfer in a three-dimensional molecular collision is assumed, in the recently published Classical Approach Quantum Encounter (CAQE) theory [J. Chem. Phys. 99 (1993) 2567], to occur in a brief and sharply defined encounter which can be formulated in terms of an effectively one-dimensional atom-diatomic collision, with the parameters for the encounter reflecting the local features of the potential in the neighborhood of the collision,geometry. Here we describe improvements to the original CAQE theory. A mathematical recasting renders the theory more conducive to use with accurate quantum encounter methods. The first-order distorted wave Born approximation that was used in the original CAQE theory is here replaced by a numerically exact one-dimensional encounter method. We illustrate the need for the new method using collinear calculations for Ar + HCl and He + CO, and then apply it using a log-derivative method in a three-dimensional calculation of single and multiple quantum vibrational cross sections for He + CO. The results are judged by comparison to the results of coupled states and semiclassical calculations, with good agreement being obtained for all conditions over a wide range of energies.

Differential cross sections for elastic and inelastic positron scattering from alkali atoms

We have investigated positron scattering from the alkali atoms lithium, sodium, potassium and rubidium, focusing on the calculation of differential cross sections for elastic scattering and impact excitation. The results obtained with the two-state and five-state close-coupling method as well as the first-order distorted wave Born approximation are compared with each other and with some selected results for electron scattering. Numerical problems due to lack of, or numerically inaccurate, calculation of partial waves with large angular momenta are solved through semi-empirical fitting/extrapolation procedures.

Nearly elastic scattering and the trajectory approximation.

We consider the scattering of an incident particle by bosons. We assume the coupling is linear in the boson coordinates, but can be quite general in the incident particle coordinate. We show that when the final distribution is close to elastic, the independent-boson model applies to this problem. It yields a loss distribution which is simply the exponentiation of the first-order distorted-wave Born approximation (DWBA). Furthermore, we demonstrate that in this regime, for short wavelengths of the scattered particle, this exponentiated Born approximation reduces to the trajectory approximation (TA). Thus it includes both the DWBA and the TA as special cases. We also give a simple recipe for estimating the error this approximation makes. We illustrate these results on a simple one-dimensional model involving a single oscillator, and discuss their relation to previous studies of overlapping regimes. This approximation and accompanying error estimate should prove very useful in analyzing multiphonon effects in atom-surface scattering.

Scattering of helium atoms by surfaces at low energies and temperatures

It is well known that the existing calculations for helium scattering by solid surfaces, made on the first-order distorted-wave Born approximation, within the one-phonon approximation, disagree qualitatively with experiment at low energies and temperatures. Generally, the calculations give sticking probabilities which are too low and which have the wrong trend with incident energy; further, the calculations are incorrect in the limit of zero incident energy. We investigate whether those calculations may be modified in order to correct them and to help them agree better with experiment. The modifications we make are, essentially, the introduction of reflection coefficients and the consideration of surface excitations (modes) different from those considered before.

Classical-trajectory Monte Carlo calculation for collision processes of e++(e-p) and micro++( micro-p).

Classical-trajectory Monte Carlo (CTMC) method is applied to the pickup process, A+(BC)\ensuremath{\rightarrow}(AB)+C, of a bound light particle in a heavy particle by an incident light particle as well as the breakup process A+(BC)\ensuremath{\rightarrow}A+B+C. Calculation has been made for the cross sections of the processes in the case of A=${e}^{+}$,${\ensuremath{\mu}}^{+}$, B=${e}^{\mathrm{\ensuremath{-}}}$,${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$, and C=p. The cross sections for positronium formation agree with those of recent quantum-mechanical calculations except for low impact velocities. The cross sections for (${\ensuremath{\mu}}^{+}$${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$) formation are smaller in magnitude than those of the quantum-mechanical calculations using the first-order Born approximation and the first-order distorted-wave Born approximation.

First-order Born and first-order distorted-wave Born cross sections for micro++( micro-p)-->( micro+ micro-)+p.

As one of the possible ways to produce a (${\ensuremath{\mu}}^{+}$${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$) atom, we have theoretically investigated the cross section of the process ${\ensuremath{\mu}}^{+}$+(${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$p)\ensuremath{\rightarrow}(${\ensuremath{\mu}}^{+}$${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$)+p. The general behaviors of the cross sections obtained by the first-order Born approximation (FBA) and the first-order distorted-wave Born approximation (DWBA) are discussed. From the comparison of the present results with those of classical-trajectory Monte Carlo (CTMC) calculation and from the reliability of the present method which was discussed in the case of ${e}^{+}$+H\ensuremath{\rightarrow}(${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$)+p, we can conclude that the maximum cross section is of the order of ${10}^{\mathrm{\ensuremath{-}}20}$ ${\mathrm{cm}}^{2}$ at about 2.8 keV impact energy, which is of the order of the geometrical cross section. The cross sections by FBA are of the same order with those by DWBA, agreeing to within 10--20 %. The DWBA cross section is larger than that by CTMC by 30--50 % in the velocity range of 5--10 keV. Scaling relationships between the cross section and impact velocity are discussed in the cases of ${\ensuremath{\mu}}^{+}$+(${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$p) and ${e}^{+}$+H.

Angle-resolved thermal and flash desorption: Analytical expressions for the flux, average energy, and speed ratio

An analytical expression for the energy and polar-angle distribution function of atoms desorbing from a solid surface is obtained from the first-order distorted-wave Born approximation, within the one-phonon approximation, by simplifying a certain integration over initial states to its “almost flat band” expression. Analytical expressions for the flux, the average energy, and the speed ratio are obtained by further assuming (a) that the matrix element between initial and final atom wave functions is represented by that corresponding to an oscillating repulsive wall, and (b) that the Debye energy of the solid is large in comparison with typical desorbing energies. We examine the results for both steady state (thermal) desorption and flash desorption. Because of the approximations and assumptions made, the results are expected to apply to desorption of weakly-bound atoms, of low atomic mass, at low temperatures.

Elastic and inelastic scattering of polarized protons from the isotopes 104, 106, 108, 110Pd

Vector analyzing powers A( θ) and differential cross sections σ(θ) have been measured for (p, p) scattering from the four Pd isotopes 140, 106, 108, 110Pd and for (p, p') scattering exciting the first 2 + (2 1 +) and the first 3 − (3 1 −) states of each of the Pd isotopes by using a 22.0 MeV polarized proton beam. Angular distributions of A( θ) and σ(θ) have been measured from 20° to 150° in 5° or 2.5° steps using a magnetic spectrograph. The analysis was made with the optical potential model, with the first-order distorted-wave Born approximation (DWBA) and with coupled channel (CC) calculations. A macroscopic description of the collective quadrupole (octupole) surface vibration of medium-heavy mass nuclei explains very well both the analyzing powers and cross sections for the inelastic scattering of protons exciting the 2 1 + (3 1 −) states of the four Pd isotopes. The quadrupole spin-orbit deformation plays an essential role in reproducing the observed 2 1 + analyzing powers, while the octupole spin-orbit deformation yields little effect on the 3 1 − analyzing powers. The effect of the channel coupling between the 0 g + and the 2 1 + (the 0 g + and the 3 1 −) states is not so large that the experimental data for the 2 1 + (3 1 −) states of the four Pd isotopes can be interpreted essentially with the first-order DWBA calculations. The extracted deformation parameters β 2 (β 3) increase (decrease) systematically with increasing of the mass number from 104Pd to 110Pd.

One-step and two-step contributions to two-nucleon transfer reactions

Qualitative arguments are given to show that although first-order distorted-wave Born approximation calculations are adequate for the treatment of single-nucleon transfer reactions, there is little reason to trust them for two-nucleon or multinucleon transfer reactions. A first-plus-second Born approximation calculation is presented for the $^{208}\mathrm{Pb}$($^{16}\mathrm{O}$, $^{18}\mathrm{O}$)$^{206}\mathrm{Pb}$ ground state transition, at bombarding energies below and slightly above the Coulomb barrier. It is found that successive transfer (two-step) processes account for almost all the observed cross section.NUCLEAR REACTIONS Theory of one- and two-step contributions to $^{208}\mathrm{Pb}$($^{16}\mathrm{O}$, $^{18}\mathrm{O}$)$^{206}\mathrm{Pb}$.

One-phonon scattering of atoms in three dimensions by a simplified continuum model of a surface: Thermal desorption

A model of thermal desorption of atoms from surfaces is presented. The treatment is quantum mechanical, and calculations are made using the first-order distorted-wave Born approximation, within the one-phonon approximation. The atom–surface interaction potential is a Morse potential, and the modal properties of the surface are those of a bulk continuum, the work being a natural continuation of some earlier atom–surface scattering work of Goodman. Our conclusions are inconsistent with some of those of Bendow and Ying and Ying and Bendow, who reported pre-exponential factors τ0 of order 10−5 s in the standard Frenkel formula for desorption; our values of τ0 are more in accord with the previously accepted values, of order 10−12 s. We apply the model to the astrophysical system H–C, and to interpretation of some experimental data on the systems He–Ar, He–Kr, and He–Xe; we find satisfactory agreement with experiment.

Measurement of theCo59Quadrupole Moment by Observation of the Deformation Effect in theCo59+nTotal Cross Section

The deformation effect DELTA sigma /sub def/ in the /sup 59/Co + n total cross sect ion has been measured at neutron energies of 1.0, 1.2, 1.4, 1.6, 2.0, and 15.9 MeV employing a single-crystal target with 16% nuclear alignment. The average of the five measurements at energies between 1 and 2 MeV was f/ = - 37 plus or minus 42 mb. These results, when interpreted using the first-order distorted-wave Born-approximation theory, imply a value of 0.39 plus or minus 0.06 b for the quadrupole moment of /sup 59/Co, which is in good agreement with the result of other techniques. (auth)