Distorted-wave Method Research Articles

Single charge exchange between hydrogen-like projectiles and hydrogen atom: the post version of the BDW-4B approximation

The post version of the four-body Born distorted wave method (BDW-4B) is applied to calculate the total cross section for single electron exchange in the collision of hydrogen-like projectiles with hydrogen atom. The post form of transition amplitude is obtained in terms of two-dimensional real integrals which can be computed numerically. This second-order theory which satisfies the correct boundary conditions is used for the collision of with hydrogen atoms at intermediate and high impact energies. The validity of our results is assessed in comparison with available experimental data and other theories.

Scattering of protons by 9B and 10B isotopes at intermediate energies in the diffraction theory

Differential cross sections of the elastic scattering of protons of intermediate energies by 9B and 10B nuclei are calculated within the Glauber theory. The matrix elements of elastic scattering are derived with a wave function in the three-particle 2αp-model (for 9B) and with an oscillatory wave function (for 10B). The differential cross-sections are calculated with allowance for the triple collisions on 9B nuclei and in the approximation of double collisions on 10B nuclei. The sensitivity of the differential cross-section to the 9B nucleus structure is analyzed. The differential cross section of 10B at E = 197 MeV is compared to the results from calculations using the distorted wave method.

Wannier threshold theory for the description of the two-electron cusp in the ion-induced double ionization of atoms

The double electron capture into the continuum states of the projectile (double ECC) is investigated theoretically in collisions of 100keV He2+ ions with He atoms. The process is described within the framework of the impact parameter and frozen-correlation approximations where the single-electron events are treated by the continuum distorted wave method. On the other hand, the Wannier theory is employed for describing the angular correlation between both ejected electrons. This treatment substantially improved the agreement between the theory and experiment as compared to the previous version of the theory (Gulyás et al., 2010) in which the correlation between the ejected electrons was taken into account by the Coulomb density of states approximation.

Electron-impact single ionization ofW19+ions

Electron-impact single ionization of $\mathrm{W}^{19+}$ ions has been studied both experimentally and theoretically. By employing the crossed-beams method, absolute cross sections have been measured in the energy range from the ionization onset up to 1000 eV. Theoretical calculations of the ionization-cross-section function were performed using the configuration-averaged distorted-wave method for electron-ion collision energies up to 150 keV. Contributions of excited long-lived primary-ion-beam admixtures were taken into account. The role of different competing ionization mechanisms contributing to the studied cross section is discussed. Plasma rate coefficients have been inferred and are presented in parametrized form.

R-matrix calculations of photoionization cross section of Ne-like tungsten

The photoionization cross section calculation for the ground state 1s22s22p6 1S (J = 0) of Ne-like W64+has been performed in the close-coupling approximation using the Dirac–Coulomb R-matrix method. The resonance structures are analysed and described by finding the resonance energy positions of prominent Rydberg series 2s2p6(2S)np1P0for W LXV ion. To calculate fine structure energy levels, multi-configuration Dirac–Fock and relativistic distorted-wave methods have been employed. Wherever possible we have compared our work with the available data. The present results will be useful for diagnostics and modeling of plasma in ITER and other fusion devices.

Study of rlastic and inelastic 11 B +α scattering and search for cluster states of enlarged radius in 11B

The differential cross sections for elastic and inelastic 11B + α scattering were measured at the alpha-particle energy of 65 MeV, the inelastic-scattering processes leading to the excitation of known states of 11B up to excitation energies of about 14 MeV. Data on elastic scattering were analyzed together with those that were published earlier for lower energies. The cross sections for inelastic scattering were analyzed on the basis of the distorted-wave method. A modified diffractionmodel was used to determine the root-mean-square radii of excited states. The radii of states whose excitation energies were below about 7MeV were found to agree with radius of the ground state to within 0.1 to 0.15 fm. This result complieswith the traditional idea that the low-lying states of 11B have a shell structure. The possibility that these states belong to the predicted rotational bands, which, if any, are truncated to three states, cannot be ruled out either. The majority of the observed highly excited states are distributed among four rotational bands. The moments of inertia of these bands are close; for the band based on the 3/2− state at E* = 8.56 MeV, they are even higher than those of the Hoyle state in the 12C nucleus. The measured radii of states associated with these bands of 11B are larger than the ground-state radius by 0.7 to 1.0 fm and are also close to the radius of the Hoyle state. The results of the present study agree with the existing predictions that the cluster structure of the 11B nucleus is diverse at high excitation energies. The hypothesis that the 11B nucleus features a “giant” state of size commensurate with those in heavy nuclei was not confirmed.

Electron-Impact Ionization of Se16+ and Se17+ Ions

SynopsisElectron-impact ionization cross sections for Se16+ and Se17+ ions have been calculated using semirelativistic configuration-average distorted-wave (CADW) method for both the direct and indirect ionization contributions. The excitation-autoionization contributions originating from the excitations of 2s and 2p subshels were calculated using a semirelativistic level to level distorted-wave (LLDW) method. Direct ionization cross section calculations involving 2s,2p,3s, and 3p subshells were also calculated using the LANL collisional atomic code and comparisons are made.

Positronium formation for positron scattering from helium ion

Positronium (Ps) formation processes from helium ions by positron impact are studied using the two-channel two-center eikonal final state–continuum initial distorted wave method. The Ps(n = 1 and 2) and total Ps formation cross sections are calculated from the threshold to the high energy region, and the results are compared with other theoretical calculations available in the literature. It is found that the present results agree reasonably well with the close-coupling calculations, while other predictions, such as the Coulomb–Born approximation, the optical potential method, and the recent classical trajectory Monte Carlo method (Naginey 2014 Phys. Rev. A 89, 062704), are all much higher in the entire energy region. The maximum positions of the Ps(n) formation cross sections in our present work are in good agreement with the wave vector matching model of (Charlton 2014 J. Phys. B: At. Mol. Opt. Phys. 39, 4575). Finally, we discuss the scaling law of the Ps(n) formation cross sections with respect to the principal quantum number n of the Ps atom.

Transfer induced by core excitation within an extended distorted-wave Born approximation method

Background: Dynamic core-excitation effects have been found to be of importance in breakup reactions and may be of relevance when obtaining spectroscopic information from transfer reactions. Purpose: In this paper we extend the distorted-wave Born approximation (DWBA) formalism in order to allow for noncentral components in the core-core term appearing in the transition operator, which allows for dynamic core-excitation effects. Then we study these effects by applying the formalism to different (d,p) reactions. Methods: The expression of the nonlocal kernels required for the evaluation of the DWBA amplitudes has been extended so as to include noncentral parts in the core-core interaction. The DWBA scattering amplitude is then obtained by solving the corresponding inhomogeneous equation, with the new computed kernels, and the usual outgoing boundary conditions. A new DWBA code has been developed for this purpose. Results: For 10 Be(d,p) 11 Be, core-excitation effects are found to be almost negligible (<3%). The importance of this effect has been found to depend to a large extent on the excitation energy of the core. This has been confirmed in the 30 Ne(d,p) 31 Ne case, for which the excitation energy of the first 2 + state is 0.8 MeV, and the effect of core excitation increases to ≈10%. Conclusions: We find dynamic core-excitation effects in transfer reactions to have small contributions to cross sections, in general. However, they should not be neglected, since they may modify the spectroscopic information obtained from these reactions and may become of importance in reactions with nuclei with a core with high deformation and low excitation energy.

Polarization transfer coefficients and partial differential cross sections for the 16O $$(\bar p,\bar p')$$ 16O (4–, T = 0 and 1) reactions at intermediate energies

Linear combinations of polarization transfer coefficients (D K ) or their products with differential cross sections (i.e., partial differential cross sections σ K ) for the 16O $$(\bar p,\bar p')$$ 16O (4–, T = 0 and 1) reactions are systematized in experiments at 200 and 350 MeV. Various data for three 4– stretched states in 16O are compared to the corresponding calculations performed with impulse approximations using the distorted wave method in several theoretical models. A considerable isospin dependence of the spin-orbit amplitude strength is demonstrated. The reference process of excitation in 12C $$(\bar p,\bar p')$$ 12C is used in comparing the nuclear response functions (spin-longitudinal and spin-transversal) for the reaction under study.

Fast atom diffraction of H and He from a LiF(001) surface: semi-quantum approach

SynopsisFor fast atom diffraction (FAD) from crystal surfaces we introduce a distorted wave method, based on the semi-quantum approach of the quantum evolution operator, in order to improve the description of rainbow effects given by the Surface Eikonal (SE) model. The theory, named Surface Initial Value Representation (SIVR) approximation, is applied to H and He atoms colliding with a LiF(001) surface, using pair-wise additive and DFT-derived potentials. The SIVR approach provides a very good representation of the experimental distributions, even in the angular region around classical rainbow angles where the SE method diverges. In addition, the influence of the incident wave-packet is analyzed.

Fast calculation of cross sections using graphics processing units

SynopsisContinuum Distorted Wave methods are adapted to new heterogeneous computing architectures, exhibiting excellent speed ups in performance.

Influence of Breit interaction on the cross section and circular polarization of radiation emitted by longitudinally-polarized electron impact excitation of highly charged Be-like ions

SynopsisWe investigated the contributions of the Breit interaction to the longitudinally-polarized electron impact excitation cross sections and circular polarizations of the 1s2s22p3/2(J = 2) → 1s22s2(J = 0) line of highly charged Be-like ions using a fully relativistic distorted-wave method. It is found that the Breit interaction can modify the Mf = -1 and -2 sublevels cross sections by several orders of magnitude. These dramatic influences also lead to a remarkable decrease in the circular polarization of radiation, which characters becomes more evident as the incident energy and/or atomic number increases. And all these features are different from the conclusions for the linear polarization of radiation.

Cascades effects on the polarization properties of x-ray radiation emitted by electron-impact excitation of highly charged He-like Fe24+ ions

SynopsisDetailed calculations using a fully relativistic distorted-wave method are carried out for the electron-impact excitation cross sections from the ground state 1s2 (J= 0) to the individual magnetic sublevels of the excited state 1s2s1/2 (J= 1) of highly charged He-like Fe24+ ions. The cascades effects to the cross sections and the linear polarizations of the 1s2s1/2(J= 1) → 1s2 (J=0) line are investigated systematically. Our results show that the 1s2p, 1s3l, and 1s4l (l = s, p, d) excited states have significant effects and make the cross sections increase. These influences also lead to a remarkable decrease in the linear polarization of subsequent x-ray radiation. The present results agree with the previous theoretical results and the polarization measurements very well.

Measurement of the electron-impact excitation rate coefficients from argon 1s states to 3p states

The apparent rate coefficients for the electron-impact excitation from argon 1s to 3p states are determined in the electron temperature (Te) range of 0.8 to 1.2 eV, in the afterglow of a capacitive argon discharge by using the temporal behavior of different state densities. The measured parameters include the densities of the 3p states (by optical emission), the densities of the four argon 1s states (by diode laser absorption) and Te (by a Langmuir probe and a line-ratio technique). Among the 24 rate coefficients obtained in this work, the results for excitation from the two resonance states (1s2 and 1s4) are reported here for the first time. As for the excitation from the two metastable states (1s3 and 1s5), the measured rate coefficients are compared with the available values from the distorted wave method and the electron beam experiment.

Circular polarization of the Lyman-α 1 line radiation emitted by longitudinally-polarized electron impact excitation: effects of Breit interaction and radiation multipoles

Detailed calculations are carried out for the longitudinally-polarized electron impact excitation cross sections from the ground state 1s 1/2 to the individual magnetic sublevels of the excited state 2p 3/2 of highly charged H-like ions using a fully relativistic distorted-wave method. The influence of the Breit interaction and radiation multipoles on the circular polarization of X-ray radiation are investigated systematically. Our results show that the Breit interaction, as the dominant correction to the Coulomb interaction, may lead to a considerable change in the magnetic sublevels cross sections and circular polarizations of Lyman-α 1 (2p 3/2 → 1s 1/2) line radiation with a more pronounced effect at higher incident energies and/or atomic numbers. Moreover, the interference between the electric dipole (E1) decay and the magnetic quadrupole (M2) decay may significantly alter the circular polarizations of the emitted X-rays. The circular polarizations of the Lyman-α 1 line are exhibit a different behavior than the linear polarizations for the same transition line regarding the radiative electron capture [Weber et al., Phys. Rev. Lett. 105, 243002 (2010)], radiative recombination [Bettadj et al., J. Phys. B 47, 105205 (2014)], and electron-impact excitation processes [Chen et al., Phys. Rev. A. 90, 012703 (2014)].

Influence of Debye plasma on the cross section and linear polarization of x-ray radiation following inner-shell electron-impact excitation of highly charged Be-like Sc17+ ions

Detailed calculations using a fully relativistic distorted-wave method incorporating the Debye–Hückel potential are carried out for the electron-impact excitation cross sections from the ground state 1s22s2 (J = 0) to the individual magnetic sublevels of 1s2s22p and states of highly charged Be-like ions in the presence of a plasma environment. The effects of plasma screening on the cross section and linear polarization of the corresponding x-ray emission are investigated. For the line, it is found that the plasma screening has a pronounced effect and causes the cross section to decrease over the whole energy range considered. This dramatic influence also leads to a remarkable decrease in the linear polarization of subsequent x-ray radiation. However, for the line, the plasma screening effect on the cross sections is relatively larger than for the excitations, while its influence on the linear polarization of the radiation is very small.

The contribution of the magnetic quadrupole to the angular distribution and polarization of electron-impact excitation and dielectronic recombination in highly charged ions

The degree of linear polarization and angular distribution of the x-ray photoemission of highly charged He-like and Li-like uranium ions following electron-impact excitation and dielectronic recombination processes are calculated using a fully relativistic distorted-wave method. A detailed investigation is carried out regarding the contribution of the magnetic quadropole (M2) term to the subsequent characteristic x-ray emission from the above two different processes. It is found that while the M2 term has a slight effect on the angular distribution and linear polarization of electron-impact excitation, it has a substantial effect on the same properties of dielectronic recombination.

Influence of radiative cascades on the polarization and angular distribution of radiation following electron-impact excitation of He-like Fe24+ ions

Detailed calculations are carried out for the electron-impact excitation cross sections from the ground state 1s2(J = 0) to the individual magnetic sublevels of the excited state 1s2s1/2 (J = 1) of highly charged He-like Fe24+ ions using a fully relativistic distorted-wave method. The cascades contributions from high-lying levels 1s2p, 1snl (n = 3, 4, 5, 6; l = s, p, d) to the cross sections and the polarization properties of the 1s2s(J = 0) line are investigated systematically. It is found that the 1s2p, 1s3l, and 1s4l (l = s, p, d) excited states have significant effects and make the cross sections increase evidently. These dramatic influences also lead to a remarkable decrease in the linear polarization and angular distribution of subsequent x-ray radiation. The present results are in good agreement with the previous theoretical results and the polarization measurements performed at the Livermore electron beam ion trap.

Relativistic effects on the cross section and circular polarization of x-ray radiation following longitudinally-polarized electron impact excitation of highly charged ions

Detailed calculations using a fully relativistic distorted-wave method are carried out for the cross sections of longitudinally polarized electron impact excitation from the ground state to the magnetic sublevels of the 1s2p state of highly charged He-like ions. The relativistic effects on the cross sections and circular polarization of the x-ray photoemission are investigated in detail. For the excitation process, results show that the relativistic effects may become important leading to considerable enhancements in the cross sections. The inclusion of the relativistic effects can modify the cross sections by several orders of magnitude, especially to the Mf = and magnetic sublevels. For the de-excitation process, the relativistic effects make the degree of circular polarization decreases, these features are more pronounced when the incident electron energy and/or atomic number increase. The relativistic effects are found to be much larger compared to the case of the linear polarization of radiation.