Distorted Wave Born Approximation Results Research Articles

Analysis of electron induced single ionisation differential cross-section of CO2 molecules in different kinematics

Theoretical investigations of electron-impact ionisation for carbon dioxide (CO2) in low to intermediate energy ranges are presented. In addition to the energy range, we have estimated triple differential cross-section (TDCS) in coplanar and perpendicular plane geometry. We have calculated the TDCS for electron impact using the modified distorted wave formalism up to the second order. Post-collision interaction effects have also been introduced to describe the collision dynamics accurately. There is a good correlation between the distorted-wave Born approximation results and the experimental results in terms of forward and backward scattering regions.

Estimation of the S34(0) S-factor for 3He(α, γ)7Be reaction by using distorted wave born approximation and artificial neural network

The astrophysical S-factor and total cross-section of radiative capture reaction are analyzed using the first-order distorted wave born approximation and artificial neural network. To make estimations of S34(0) at energies going to zero, we have used an artificial neural network model as a new approximation in this area. First, we obtain distorted wave born approximation results using the Gaussian and Woods-Saxon potentials. After, we evaluate artificial neural network approximation to analyze reaction observables of the system. Our results show that artificial neural network model is a powerful candidate as an extrapolation model for astrophysical energies for estimating of the S-factor observable.

Effects of dynamical screening on single ionization of potassium by electron impact in doubly symmetric geometry

The dynamically screened three-Coulomb-wave (DS3C) method is applied to study the single ionization of potassium by electron impact. Triple differential cross-sections (TDCS) are calculated in doubly symmetric geometry at excess energies of 6, 10, 15, 20, 30, 40, 50 and 60 eV. Comparisons are made with recent experimental data and theoretical predictions from a three-Coulomb-wave (3C) and distorted-wave Born approximation (DWBA). The DS3C method is able to reproduce most of the trend of experimental data and in good agreement with DWBA results. It is shown that the DS3C calculation provides much better shape and relative magnitude agreement with experiment.

Differential cross section calculations of positron and electron impact ionization of Ar (3p)

We report the distorted wave Born approximation results of triple differential cross section of Ar (3p) by positron and electron impact. We compare the results of our calculations with the recent available experimental and theoretical results. We also provide a comparison of our positron impact ionization results with the electron impact ionization results to understand the effect of projectile charge on the projectile-target interaction.

Coulomb Effect of Positron for (e,e') Reactions in Quasielastic Region

The static Coulomb field of medium and heavy nuclei has been one of persistent problems in medium energy electron scattering. In particular, in the early 1990’s, Ohio group for the ðe; e0Þ reactions treated exactly the Coulomb distortion using partial wave expansion of the electron wave function, referred to the full distorted wave Born approximation (DWBA) in quasielastic region. This calculation is able to compare various nuclear models and furnish an invaluable check for several approximate methods of the Coulomb distortion. However, it is numerically challenging and computation time increases rapidly with higher incident electron energy. In particular, it is not possible to separate the cross section into the longitudinal and the transverse structure functions. In order to avoid the difficult problems related to the DWBA calculations, there are two approaches to treat approximately the electron Coulomb distortion. The first approach is known as the effective momentum approximation (EMA). This is that the electron momenta are modified by the value of the Coulomb potential at the center of target nucleus. This approximation describes the Coulomb distortion for light nuclei and for high incident electron energies but does not for heavy nuclei and for intermediate incident electron energies. Recently, there were experimental data measured from Saclay for C and Pb with positron beam. They improved the EMA calculation with the effective momentum p0 1⁄4 p ð2=3ÞVð0Þ, where Vð0Þ is the Coulomb potential at the origin. With this method, they claimed that if one uses this new EMA the total structure functions induced by positrons have roughly the same magnitude as those by electrons as a function of the energy transfer. As the other approach, from the middle of 1990’s, Kim and Wright have developed an approximate treatment of the electron Coulomb distortion. This approximation leads to an r-dependent momentum which includes the Coulomb distortion arising from the four potential A . The advantage of this approximation is that the separation of the cross section into a longitudinal term and a transverse term is possible. This approximation of the Coulomb distortion agreed with the full DWBA results (about 1–2%) near the peaks of the cross sections for heavy nucleus like Pb on ðe; e0Þ and ðe; e0pÞ reactions with the momentum transfer greater than approximately 300MeV/c. More recently, Kim and Wright improved the above method of the r-dependent momentum for the electron (or positron) current by averaging the phase shift of the leptons, referred to ad hoc approximation (see ref. 8 in detail). They compared the ad hoc approximation, the full DWBA, and the EMA calculations for the Coulomb distortion with a simple harmonic oscillation model. They showed that the total structure functions did not have the same magnitude because of the phase shift of the leptons even though they used the same kinematics as the Saclay experiments. In this report, we examine the Coulomb distortion effect of the positron for the cross section with the ad hoc approximation. In addition, we also investigate the positron Coulomb distortion effect at high incident positron energy of 2.02 GeV for several nuclei, C, Fe, and Au, which is the same kinematics as the SLAC data for the electron scattering. We use a relativistic single particle model for the bound state based on the –! model and apply the same potential for the outgoing nucleon as the bound state coupled with a free relativistic current operator. Since only electrons are observed in the ðe; e0Þ reaction, we do not take into account whether or not the ejected nucleons are ‘‘lost’’, which is no nucleon flux loss. This assumption guarantees current conservation and contains the final state interaction. In the plane wave Born approximation (PWBA) in which the electrons or the positrons are described as plane waves, the cross section for the inclusive ðe; e0Þ scattering can be written as d d d! 1⁄4 M q q4 RLðq; !Þ þ tan 2 q 2q2 ! RTðq; !Þ # ; ð1Þ

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).

Inner-shell ionization of a neon atom by electron impact

A model is proposed to study the inner-shell (K- shell) ionization of the inert gas atoms (e.g., Ne, Ar, etc.) by fast electron impact in coplanar geometry in the framework of a distorted wave approximation. An independent particle model is employed with a one-electron orbital for the multielectron target atom. Triple differential cross sections (TDCS) are presented for both symmetric and asymmetric kinematics of neon atom. The most salient feature noted in the TDCS structure is the presence of intense recoil peak that for certain dynamics (particularly when the ejected energy is much lower than the K-shell binding energy) is even larger than the binary peak, an unusual feature for the outer-shell ionization process. Results are compared with the relative measurements [P. Bickert and W. Hink, in 2nd European Conference on $(e,2e)$ Collisions and Related Problems (Kaiserslautern, 1989), edited by H. Ehrhardt] and the theoretical distorted-wave Born approximation results, available only for asymmetric kinematics. The qualitative agreement of the present results with the experiment by Bickert and Hink is quite good, particularly in respect to the binary/recoil intensity ratio, the latter being greater than unity in both cases for the particular dynamics at which the measurements by Bickert and Hink were performed. Additional results are also presented for symmetric as well as some other asymmetric kinematics.

Multiple scattering calculation of double and single differential cross sections for ionization of hydrogen atoms by electrons at intermediate energies

The multiple scattering approach of Das and Seal, which was applied earlier to calculate the triple differential cross section for the ionization of atomic hydrogen by electrons is now used to calculate the double and the single differential cross sections for the same system. The range of the incident electron energy is taken to be 100–250 eV. The present results are compared with the measured results of Shyn and with the available distorted wave Born approximation results.

Double differential cross sections in the electron impact ionization of helium

The double differential cross sections for electron impact ionization of helium are evaluated in the framework of a distorted wave approximation that takes into account the effects of initial channel, final channel, and target distortion. The present results are in fair agreement with the measured values and rigorous DWBA (distorted-wave Born approximation) results of McCarthy and Zhang.

Electron impact excitation of the 33P state of helium: coherence parameters

In an electron-photon coincidence experiment the authors have measured the polarization degree of the decay radiation from the electron impact excited 33P to 23S transition in helium. They performed their measurements perpendicular to the scattering plane. To analyse the polarization they used a beam splitting polarizer instead of the usual sheet polarizer. The linear polarization degree was measured at an electron impact energy of 40 eV and the circular polarization degree was measured at 40, 60 and 80 eV. The electron scattering angle ranged from 32.8' to 116'. The experimentally determined degrees of polarization are in good agreement with the theoretical results of the distorted-wave Born approximation (DWBA). The scaling relation of Lin et al. (1989) is in agreement with the DWBA results of the circular polarization for 33P excitation.

Quantum mechanical study of the D+H2→HD+H reaction

A quantum mechanical study is made of the D+H2(vi=0,1)→ HD(vf=0,1,2)+H reactions within the infinite order sudden approximation (IOSA) for the total energy interval 0.28≤Et≤1.28 eV. Results at various stages of the calculation are given ranging from most detailed reactive transition probabilities through opacity functions and γ-dependent cross sections to total and state-to-state integral and differential cross sections, as well as rate constants. The cross sections and rate constants are compared with other available theoretical results and experiments. It is found that the IOSA total cross sections for vi=0,1 overlap very nicely with the corresponding quasiclassical trajectory cross sections, except for the tunneling region. A less satisfactory fit is obtained with the distorted wave born approximation results. The calculated rate constants are compared with experiment and a rather good fit is obtained, in particular for rate constants from the ground state.

Excitation of the ground state rotational band inNe20by 0.8 GeV protons

Angular distributions for the scattering of 0.8 GeV polarized protons from the ground state rotational band in $^{20}\mathrm{Ne}$ are reported. Cross sections and analyzing powers for protons exciting these states were measured with a high resolution spectrometer. Coupled channels and distorted wave Born approximation analyses of scattering data for the ${0}^{+}$, ${2}^{+}$, ${4}^{+}$, and experimentally unresolved ${6}^{+}$ states are presented. The observed cross section data for the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states are reproduced quite well with the coupled channels calculations, and the large hexadecapole deformation reported previously is confirmed. The distorted wave Born approximation results are equally good for the ${0}^{+}$ angular distribution, but are a significantly poorer representation of the cross section data for the ${2}^{+}$ and ${4}^{+}$ states. Both calculations do equally well in explaining the ${0}^{+}$ analyzing power data and both fail to explain the ${4}^{+}$ analyzing power data past the region of the first maximum. The coupled channels results do a better job in explaining the ${2}^{+}$ analyzing power data. The multipole moments of the deformed optical potential used in the coupled channels calculations are related to those of the matter distributions by Satchler's theorem. These are compared to the moments found using other hadronic probes, those of the charge distribution determined by electromagnetic measurements, and to moments from shell model and Hartree-Fock calculations.

Calculation of proton-neutron coincidence cross sections in 56 MeV deuteron-induced breakup reactions by post form distorted-wave Born approximation

Recently measured neutron-proton angular correlations in the deuteron-induced breakup reactions at 56 MeV incident energy have been analyzed in terms of the post form distorted-wave Born approximation theory of breakup reactions. Comparison of the present results is made with those of the prior form distorted-wave Born approximation calculations. It is found that the results of the post form distorted-wave Born approximation calculations are in better agreement with the experimental data than the prior form distorted-wave Born approximation results.

Two-step contributions in thePb206(t→, p)Pb208two-neutron transfer reaction

The /sup 206/Pb(t,p) reaction has been studied over the angular range from 10/sup 0/ to 60/sup 0/ at a triton energy of 17 MeV. Cross sections and analyzing powers were measured for 11 states between 2.6 and 5.0 MeV excitation, including the 4/sup -/ state at 3.475 MeV. The two-neutron transfer reaction to this state was represented by a sequential transfer calculation. Data for three natural parity states, in particular the analyzing powers, were not fitted well by one-step distorted-wave Born approximation calculations. Numerous sequential transfer calculations with different transfer configurations were tried for each of these states. While most of the calculations produced results similar to the distorted-wave Born approximation results, at least one calculation was found for each state which gave an improved representation over that of the distorted-wave Born approximation. The failure of the distorted-wave Born approximation documents the need to apply sequential transfer reaction processes in general descriptions of two-nucleon transfer reactions.

Depolarized rayleigh light scattering in gaseous systems: I. Multilevel description and application to the HD-He system

A multilevel description of depolarized Rayleigh (DPR) light scattering in gases is presented from the point of view of kinetic theory using the linearized Waldmann-Snider kinetic equation as a starting point. Connections between the present description and earlier work are made. A multilevel calculation of the collision broadening of the DPR line for HD infinitely dilute in He is given using both distorted-wave Born approximation results and full close-coupled results for the transformed Shafer-Gordon potential for H 2-He. Various approximations to the full multilevel description are tested and compared for this system.

High spin states inTl206,204,202observed in (d,α) reactions at 80 MeV

The ($d,\ensuremath{\alpha}$) reaction on $^{208,206,204}\mathrm{Pb}$ has been studied at 80 MeV bombarding energy. The experimental angular distributions are structured and the transferred angular momentum $L$ could be determined without ambiguity from a comparison of distorted-wave Born-approximation calculations with the experimental angular distributions. The angular momentum matching conditions greatly favored large values of $L$ and allowed the identification of ${J}^{\ensuremath{\pi}}={12}^{\ensuremath{-}} \mathrm{and} {9}^{+}$ states in $^{206,204,202}\mathrm{Tl}$. Data for the $^{208}\mathrm{Pb}(d,\ensuremath{\alpha})^{206}\mathrm{Tl}$ reaction were compared with shell model calculations. The properties of nine levels could be correlated with very good agreement with those of states predicted in the shell model calculations. Both zero-range and exact finiterange distorted-wave Born-approximation calculations were carried out. Unlike the zero-range distorted-wave Born-approximation results, the exact finite-range angular distributions did not change greatly for different choices of the $\ensuremath{\alpha}$ particle optical potential. Although somewhat better agreement with the relative cross sections was obtained, the exact finite-range calculations underestimated the absolute cross sections by roughly a factor of 50.NUCLEAR REACTIONS $^{208,206,204}\mathrm{Pb}(d,\ensuremath{\alpha})$, ${E}_{d}=80$ MeV. Measured $\ensuremath{\sigma}(\ensuremath{\theta})$; enriched targets; microscopic DWBA analysis; shell model calculations; deduced $J$, $\ensuremath{\pi}$.

DWBA evaluation of relaxation and kinetic theory cross sections

A connection is made between the reorientation collision cross section expressions arising in nuclear magnetic relaxation in the gas phase when described from the point of view of kinetic (using the Waldmann-Snider equation) involving t-matrix elements and from the point of view of traditional correlation function theory involving S-matrix elements. These separate expressions are then used to test the distorted wave Born approximation (DWBA) for one of the Shafer-Gordon H 2-He potentials by comparing the DWBA results for the reorientation cross sections with those obtained from the Shafer-Gordon close-coupled calculations. For H 2-He at room temperature, the DWBA results are found to be systematically 10% higher than the close-coupled results; however, cross section ratios are reproduced to better than 2%.

(Li6,d) Reaction onfp-Shell Nuclei and Alpha-Transfer Distorted-Wave Born-Approximation Analysis

Strongly structured ($^{6}\mathrm{Li}$, $d$) angular distributions exhibiting systematic variations with $A$ for $A=40$ to $A=90$ target nuclei are well reproduced by $\ensuremath{\alpha}$-stripping calculations using a single set of potential parameters. Zero-range and finite-range distorted-wave Born-approximation results are found very similar both in the shapes of the angular distributions and in the relative magnitudes. The question of nuclear-structure dependence in the angular distributions is discussed.

On the evaluation of kinetic-theory collision integrals: III. General distorted-wave born approximation

Expressions are obtained using the Distorted-Wave Born Approximation (DWBA) for a number of kinetic-theory collision cross sections. In particular, DWBA results are given for the (production) collision integrals that couple angular-momentum directional polarizations with the hydrodynamic fluxes. These integrals as well as the full relaxation rate (kinetic-theory collision) matrix of angular-momentum polarizations involve energetically inelastic collisions. Except for this energy inelasticity, the DWBA results can be written as a product of an internal-state dependent factor and a translational factor. The simplest approximation is to ignore the dependence of the translational factor on energy inelasticity, or if the integral vanishes if that is done, to include the energy inelasticity to first order. Such a procedure yields an explicit estimate of the complete dependence of the collision integrals on internal-state quantum numbers. A crude approximation for the translational factors is also investigated. This amounts to assuming that the transition operator depends (translationally) only on the momentum transfer. Some relations between relaxation and production collision integrals then follow. Throughout this work, reduced matrix elements (in the sense of the 3-dimensional rotation group) are stressed, so that the results are applicable to any molecular species and most results are valid for any form of intermolecular potential.

F19(α,t)Ne20reaction at 28.5 MeV

The measured $^{19}\mathrm{F}(\ensuremath{\alpha},t)^{20}\mathrm{Ne}$ angular distributions of Hansen et al. at 28.5 MeV to the first ${0}^{+}$-${2}^{+}$-${4}^{+}$ states have been reanalyzed in terms of the collective-model coupled-channel Born-approximation theory. The "$j$-forbidden" ${4}^{+}$ cross section at 4.247 MeV is well described by the theory, while the allowed transitions show little change from the distorted-wave Born-approximation results. Limited excitation-function measurements of the $^{19}\mathrm{F}(\ensuremath{\alpha},t)^{20}\mathrm{Ne}$ reaction from 25 to 26 MeV show little structure, indicating little compound contribution to the "allowed" and "$j$-forbidden" transitions.[NUCLEAR REACTIONS $^{19}\mathrm{F}(\ensuremath{\alpha},t) ^{20}\mathrm{Ne}$, $E=28.5$ MeV; for first ${0}^{+}$-${2}^{+}$-${4}^{+}$ calculated $\ensuremath{\sigma}(\ensuremath{\theta})$, DWBA and CCBA; deduced $S$.]