Relativistic Distorted-wave Born Approximation Research Articles

Spin asymmetries in the electron-impact ionization of Ar(2p)

Spin- and fine-structure resolved results for the inner-shell ionization of argon are presented. By performing measurements and relativistic scattering calculations under kinematical conditions where the contribution from the exchange between the scattered electrons and the electrons in the residual ion is small, the effect of target fine structure on the measured spin asymmetry has been highlighted. Fully relativistic distorted wave Born approximation calculations are found to be in good agreement with both the spin asymmetry and branching ratio measurements.

Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

The relativistic distorted-wave Born approximation is used to calculate differential and total cross sections for inner shell ionization of neutral atoms by electron and positron impact. The target atom is described within the independent-electron approximation using the self-consistent Dirac-Fock-Slater potential. The distorting potential for the projectile is also set equal to the Dirac-Fock-Slater potential. For electrons, this guarantees orthogonality of all the orbitals involved and simplifies the calculation of exchange T-matrix elements. The interaction between the projectile and the target electrons is assumed to reduce to the instantaneous Coulomb interaction. The adopted numerical algorithm allows the calculation of differential and total cross sections for projectiles with kinetic energies ranging from the ionization threshold up to about ten times this value. Algorithm accuracy and stability are demonstrated by comparing differential cross sections calculated by our code with the distorting potential set to zero with equivalent results generated by a more robust code that uses the conventional plane-wave Born approximation. Sample calculation results are presented for ionization of K- and L-shells of various elements and compared with the available experimental data.

Spin asymmetries in spatially resolved processes of ionization of heavy atoms by relativistic electrons

The triple-differential cross section for ionization of a heavy atom is shown to depend on the spin of the incident electron even if this is polarized entirely parallel or antiparallel to its direction of propagation, the atom is unpolarized, and the spins of the ejected electrons are not resolved. Quantitative predictions for the spin asymmetry are presented in a relativistic distorted-wave Born approximation. Simple physical models are introduced to understand both these results and further symmetry properties involving the reversal of a spatial momentum component also.

Analysis of relativistic (e,2e) experiments in coplanar asymmetric geometry

Triply differential cross sections and spin asymmetries for (e, 2e) reactions on the 1s1/2 state of intermediate- and high-Z atoms in coplanar asymmetric geometries are analyzed within the framework of the relativistic distorted wave Born approximation. Specific signatures of the relativistic nature of the electron-electron interaction, and of the electron-residual ion interaction, are identified.

Recoil-free relativistic (e,2e) collisions

We report here on (e,2e) measurements at relativistic electron energies (up to 500 keV) under 'bound-electron Bethe ridge' conditions. Absolute triple differential cross sections for K-shell ionization of silver (E bind =25.5 keV) have been measured. Appreciable discrepancies are found with calculations in the relativistic distorted-wave Born approximation whereas results of the Coulomb-Born approximation give better accord with the experimental data. At the highest incident energy (500 keV) the Coulomb-Born approximation is in perfect agreement with the experimental results.

Relativistic (e,2e) experiments with polarized and unpolarized electron beams

(e,2e) experiments at a relativistic electron energy (300 keV) on the K shells of copper, silver, and gold are reported. Using coplanar asymmetric kinematics the angular distributions of the relative triply differential cross sections and the corresponding spin asymmetries were measured. The experimental results are compared with calculations in a relativistic distorted-wave Born approximation. The results show an increasing influence of the electron-nucleus interaction in the recoil regime with increasing atomic number. Also reported are distinct spin asymmetries in this region increasing with the nuclear charge of the target atom.

Interpretation of relativistic(e,2e)experiments in coplanar asymmetric geometry: Atomic-number-dependent effects

Triply differential cross sections and spin asymmetries for $(e,2e)$ reactions of the ${1s}_{1/2}$ state of intermediate- and high-$Z$ atoms in coplanar asymmetric geometry are analyzed within the framework of the relativistic distorted wave Born approximation. Specific signatures of the relativistic nature of the electron-electron interaction, and of the atomic-number-dependent electron-residual ion interaction, are identified.

Low-energy(e,2e)spectroscopy from the W(001) surface: Experiment and theory

The simultaneous ejection of two electrons from the (001) surface of W due to the collision of incident low-energy electrons with valence electrons has been studied experimentally and theoretically. Energy and momenta of the ejected electrons were measured simultaneously by a combination of coincidence and time-of-flight techniques. Calculations were performed in a relativistic distorted-wave Born approximation including exchange, in which the primary electron and the two emitted electrons are described by quasiparticle multiple scattering states. The valence electron is represented by linear combinations of Bloch waves matched at the surface. Screened Coulomb interaction matrix elements between these four states are evaluated. Experimental and calculated energy distributions from W(001) for very-low-energy primary electrons at normal and grazing incidence are in fairly good overall agreement. Although some features of one-dimensional bulk densities of states are roughly reflected, Coulomb matrix elements with low-energy-electron-diffraction-type states play a vital role. Further analysis reveals in detail the importance of elastic scattering of the primary electron and of the two ejected electrons. Some observed features can be attributed to occupied surface states.

Fine-structure effect in the relativistic(e,2e)process

Using a transversely polarized electron beam a relativistic $(e,2e)$ experiment has been performed to look for a spin-up--spin-down asymmetry in the electron-impact ionization process caused by the fine-structure effect. An incident energy of 300 keV, coplanar asymmetric kinematics, and the ${2p}_{3/2}$ shell of uranium $(Z=92)$ have been used. We found clear evidence for the fine-structure effect in the relativistic regime and a qualitative agreement with theoretical results of the relativistic distorted-wave Born approximation, including a change of sign in the angular distribution of the asymmetry near the Bethe ridge.

Influence of Coulomb boundary conditions for (e, 2e) processes on the K-shell of high- Z atoms

We study the relevance of physical boundary conditions for relativistic (e, 2e) processes on the K-shell of high-Z atoms. The relativistic distorted-wave Born approximation is extended to include the long-range Coulomb interaction in the final channel, allowing the two outgoing electrons to escape in the field of a singly charged positive ion. Besides the physical description we also construct the first fully relativistic Coulomb-Born approximation for (e, 2e) processes, which is the appropriate one to assess the validity of calculations based on semirelativistic Coulomb wavefunctions. The theoretical investigation is illustrated with calculated triple-differential cross sections for (e, 2e) processes on silver and gold, in both coplanar symmetric and asymmetric geometries. The comparison of the results obtained in the modified relativistic distorted-wave Born approximation with previous calculations indicates that the inclusion of asymptotic physical boundary conditions has only a limited effect. On the other hand, the fully relativistic Coulomb-Born approach is seen to yield results in very good agreement with the absolute experimental data, and demonstrates how the use of approximate semi-relativistic wavefunctions can be misleading.

Coincident two-electron emission from surfaces by low-energy electrons

The simultaneous ejection of two electrons from non-magnetic surfaces due to the collision of incident low-energy electrons with valence electrons is treated in a relativistic distorted-wave Born approximation including exchange. The primary electron and the two emitted electrons are described by quasi-particle multiple scattering states. The valence electron is represented by linear combinations of Bloch waves matched at the surface. Screened Coulomb interaction matrix elements between these four states are evaluated. Numerical results for W(0 0 1) are presented and compared with one-dimensional bulk densities of states. Energy-integrated spectra and general features of the 2 e-distribution are in good agreement with recent experimental data.

Relativistic-energy-sharing (e,2e) collisions in coplanar constant Theta 1,2 geometry.

We present a geometry for the investigation of the coplanar energy sharing ({ital e},2{ital e}) collision processes at relativistic energies. In the coplanar constant {Theta}{sub 1,2} geometry the angle between the detectors is held fixed, while both detectors are rotated around the normal to the scattering plane. This geometry is particularly suited for the investigation of the interaction between the heavy atom and the electrons in the incident and final channels. We present a systematic study of the {ital K}-shell ionization of gold at 300 keV using the relativistic distorted-wave Born approximation, investigate the relative importance of different spin channels and the variation of the triple differential cross section with the relative angle between the two outgoing electrons. Even though we are considering the unpolarized beam incident on unpolarized targets, we are able to demonstrate clearly the role of Pauli blocking. We identify those features in the cross section which are most sensitive to distortion and demonstrate their enhancement with the increasing nuclear charge. Finally, we discuss their dependence on impact energies. {copyright} {ital 1996 The American Physical Society.}

Theory of (e,2e) processes with spin-polarized relativistic electrons.

A general formalism for the description of spin and angular momentum projection sensitive (e,2e) processes valid for all electron energies is proposed. Using the relativistic distorted-wave Born approximation, a reasonable description of a recent (e,2e) experiment with spin-polarized relativistic electrons [H.-Th. Prinz, K.-H. Besch, and W. Nakel, Phys. Rev. Lett. 74, 243 (1995)] is obtained. A detailed numerical study of spin-sensitive (e,2e) processes on inner-shell states of high-Z atoms is presented. \textcopyright{} 1996 The American Physical Society.

Analyzing powers and cross sections of inclusive polarized proton scattering on 208Pb

Inclusive polarized proton-nucleus scattering on 208Pb has been studied at 290 and 500 MeV. The measurements cover a broad range (0–250 MeV) of excitation energy over the 4°–27° angular range. The measured analyzing powers and cross sections for the continuum were compared with recent relativistic and nonrelativistic distorted-wave impulse approximation calculations. The cross section in the continuum region is found to be dominated by single-step quasi-free scattering. Differences of up to 40% between the analyzing powers measured at the quasi-free peak as opposed to free NN values strongly support the relativistic impulse approximation predictions for the quasi-free region, and indicate the presence of relativistic medium effects. Analyzing powers and cross sections of several low-lying states were compared with both nonrelativistic and relativistic distorted-wave Born approximation predictions.

Relativistic DWBA calculations for medium energy photonuclear reactions

A one nucleon model for the photoejection of intermediate energy protons based on Dirac phenomenology is proposed. The t- matrix element for the process is written in the distorted wave Born approximation (DWBA) using distorted Dirac spinors to describe the proton dynamics. The calculated cross sections for the 16O(γ, p) 15N and 40Ca(γ, p) 39K reactions exhibit reasonable agreement with forward angle data as well as qualitative agreement with the measured energy dependence.

Relativistic impulse approximation description of polarized proton elastic scattering from polarized 13C.

The elastic scattering of intermediate energy polarized protons from polarized /sup 13/C is studied within the framework of the relativistic distorted wave Born approximation using the relativistic impulse approximation to describe the projectile--target nucleon interaction. Sensitivities of observables to (1) the upper and lower components of the valence nucleon wave function, (2) the Lorentz form of the two-body interaction, (3) isoscalar three-vector currents, and (4) the individual strengths of the separate Lorentz terms in the two-body interaction are calculated and discussed. The bound state wave functions for the 1p/sub 1/2 valence neutron used in the calculations are taken from relativistic mean field theory and from traditional, nonrelativistic Woods-Saxon eigenstate solutions. Predictions obtained using either pseudoscalar or pseudovector projectile-nucleon coupling forms are compared. Possible effects on the p-arrow-right+/sup 13/C-arrow-right polarized target spin observables due to contributions of the core nucleons to the effective isoscalar three-vector current are discussed and investigated using a simple model. What can be learned from normal (i.e., perpendicular to scattering plane) and transverse (i.e., approximately perpendicular to beam, in the scattering plane) polarized target spin observables, as well as unpolarized p-arrow-right+/sup 13/C elastic scattering observables are discussed. The results suggest that new nuclear structure information, additional effectivemore » interaction phenomenology, and further constraints on the Lorentz character of the effective two-body interaction can in principle be obtained from analyses of p-arrow-right+/sup 13/C-arrow-right elastic scattering data. Experiments to obtain such data are encouraged« less

Relativistic effects in electron-atom collisions

Relativistic effects in electron-atom collision cross sections are discussed. According to the results obtained using the relativistic distorted-wave Born approximation, relativistic cross sections for electron-impact excitations of Li-like ions are smaller than corresponding nonrelativistic cross sections. This reduction results mostly relativistic contraction of bound orbitals and from spin-orbit splitting. We also found that electron exchange and orthogonality between bound and continuum orbitals did not significantly alter cross sections for highly charged ions.

Observation of Lambda -hypernuclei in the reaction 12C( pi +,K+) 1 Lambda 2C.

The observation of $\ensuremath{\Lambda}$-hypernuclear levels in $_{\ensuremath{\Lambda}}^{12}\mathrm{C}$ by associated production through the (${\ensuremath{\pi}}^{+}, {K}^{+}$) reaction is reported. The $_{\ensuremath{\Lambda}}^{12}\mathrm{C}$ excitation-energy spectra were recorded at laboratory scattering angles of 5.6\ifmmode^\circ\else\textdegree\fi{}, 10.3\ifmmode^\circ\else\textdegree\fi{}, and 15.2\ifmmode^\circ\else\textdegree\fi{}. They show two major peaks---one attributed to the ground state, and one about 11 MeV higher. These results are compared to the strangeness-exchanging (${K}^{\ensuremath{-}}, {\ensuremath{\pi}}^{\ensuremath{-}}$) reaction. The measured cross sections are compared to relativistic distorted-wave Born-approximation calculations.

Distortion effects in a relativistic one-nucleon model for the (p,π+) reaction

A relativistic distorted-wave Born approximation model is developed for (p,..pi../sup +/) reactions within the framework of the one-nucleon mechanism. The nucleon motion is described by solutions to the Dirac equation with appropriate nuclear potentials. Distortion effects in both the proton and pion channels are taken into account and are found to be important. Both pseudovector and pseudoscalar forms of the ..pi..NN vertex are considered. The former is found to lead invariably to better agreement with the data. Calculations have been carried out for proton energies < or =200 MeV. Good agreement is obtained with the cross section data for reactions on /sup 40/Ca and /sup 16/O leading to the ground state of the residual nucleus. For reactions on /sup 12/C, the cross section shapes, but not their magnitudes, are reproduced. The calculated analyzing powers are found to be in good agreement with the forward angle data.