Positron-atom Collisions Research Articles

Kinematically complete scattering cross sections in collisions between positron and hydrogen atom

SynopsisA three-body classical trajectory Monte Carlo (CTMC) method is used to describe positron and hydrogen atom collisions. The total and multi-differential ionization and charge exchange cross sections are calculated and compared with experimental data and other theoretical results.

Configuration space method to calculate rearrangement matrix elements

A new method has been developed for calculating rearrangement matrix elements within the two-centre convergent close-coupling theory and applied to Ps formation in positron–atom collisions. The method utilises partial wave expansion of the Ps wavefunction that separates dependencies on coordinates of electron and positron. Resulting expressions contain slowly converging series which have been accelerated with use of the Euler–Wijngaarden transformation. The integrals in the method are free of the Coulomb singularity that appears in previously used momentum-space methods and therefore more straightforward to apply to complex and charged targets. The results are compared with the existing benchmark calculations for positron scattering on H and He+ targets.

Vortex rings in the ionization of atoms by positron impact

We uncovered the morphology of quantum vortex structures in positron-atom ionization collisions. By performing an exhaustive calculation of the position of vortices in the final momentum space of the problem with only one kinematic restriction, we could elucidate that quantum vortices form a closed structure, which is one of the two possible scenarios for their emergence in three dimensions. This is the first time that these structures are fully calculated for positron atom collisions.

Vortex rings in the ionization of atoms by positron impact

SynopsisWe uncovered the morphology of quantum vortex structures in positron-atom ionization collisions. By performing an exhaustive calculation of the position of vortices in the final momentum space of the problem with only one kinematic restriction, we could elucidate that quantum vortices form a closed structure, which is one of the two possible scenarios for their emergence in three dimensions. This is the first time that these structures are fully calculated for positron-atom collisions.

State selective electron capture in low energy positron and argon collisions

A three-body classical trajectory Monte Carlo method is applied in the study of positron and argon atom collisions at impact energies between 10 and 60eV. The calculations are based on the independent particle model. We present state selective and total positronium formation cross sections as a function of the impact energy. Our results are compared with recent experimental data.

Threshold effects in the ionization of atoms by positron impact

We employ different theoretical models, both classical and quantum-mechanical, to explore the recoil-ion momentum distribution in positron–atom collisions. We pay special attention to the vicinity of the kinematical threshold between ionization and positronium formation. We demonstrate that it is intertwined by dynamical constraints to the formation of highly excited and low-lying continuum electron–positron states. Finally we discuss how the study of recoil-ion momentum distribution, which is characteristic of a reaction microscopy technique, might represent an alternative approach to the standard spectroscopy of electrons and positrons.

The role of projectile double scattering in positron–atom collisions

We present the doubly differential cross sections of the ionization for positron and hydrogen atom collisions at 50 eV impact energy. We treat the collision problem in the framework of the full and reduced three-body classical trajectory Monte Carlo (CTMC) model. The role of projectile double scattering in light projectile and atom collisions are discussed.

Theory of ionization processes in positron–atom collisions

We review past and present theoretical developments in the description of ionization processes in positron–atom collisions. Starting from an analysis that incorporates all the interactions in the final state on an equal footing and keeps an exact account of the few-body kinematics, we perform a critical comparison of different approximations, and how they affect the evaluation of the ionization cross section. Finally, we describe the appearance of fingerprints of capture to the continuum, saddle-point and other kinematical mechanisms.

A wave function for three charged particles with arbitrary masses

In this work we present a fully correlated wave function to describe the continuum of the three-body spectra for particles with arbitrary masses interacting with Coulomb potentials. We show that this function can be related with the Φ 2 correlated model introduced few years ago for ion–atom collisions processes. The function includes important properties such as correct asymptotic conditions and Kato's cusp conditions. We discuss the properties of the wave function for one heavy and two light particles, focusing in the case of positron–electron–proton systems. A comparison between the properties of the new model and the C3 one is also performed. This analysis suggests that this function can be a successful alternative choice for the description of positron–atom collisions.

Low-energy positron scattering from atoms and molecules using positron accumulation techniques

Positron scattering from atoms and molecules is studied at low values of incident positron energy. The experiments use a cold magnetized positron beam formed in a positron accumulator. A discussion of positron scattering in a magnetic field is presented along with differential cross-sections (DCS) for positron–atom collisions and positron–molecule total vibrational excitation cross-sections. Absolute values of the DCS for elastic scattering from argon and krypton are measured at energies ranging from 0.4 to 2.0 eV. The first low-energy positron–molecule vibrational excitation cross-sections have been measured (i.e., for carbon tetrafluoride at energies ranging from 0.2 to 1 eV). Using information gained from these experiments a second generation scattering apparatus is described, which was designed and built specifically for scattering experiments using a magnetized positron beam. This apparatus has a number of improvements, including an order of magnitude higher throughput, better energy separation between elastic and inelastic scattering events, and improved measurement of the absolute pressure of the test-gases. Analysis techniques for the data taken in these experiments using a retarding potential energy analyzer and possible extensions of these experiments are also discussed.

Differential ionization measurements for electron and positron impact on atoms

A progress report is presented on a new experimental program at the University of Missouri Rolls which is investigating the dynamics of inelastic lepton-atom collisions. By employing recoil ion momentum spectroscopic techniques, differential ionization cross sections are being studied for electron-atom and positron-atom collisions in the energy range from 50 to 1000 eV. The apparatus is configured to measure the transverse and longitudinal momentum components of the recoil target ion and of the ejected electrons. In addition, projectile scattering into θ and φ angles up to 20 degrees can be measured. The goal is to study isotachic electron and positron impact in order to investigate charge effects on the interaction dynamics. In addition, by comparing these data with existing proton impact data, mass effects can be investigated. A summary of progress to date and experiments planned for the near future are given.

Electron ejection from ionising positron–atom collisions

Recent progress in the differential study of ionization in positron–atom collisions is reviewed. In particular, experimental and theoretical results concerning electron-capture-to the continuum are discussed, outstanding questions highlighted and current efforts indicated.

A theoretical prediction on laser assisted Ps formation including multiphoton processes

In the first Born approximation, a theoretical prediction on positronium formation in laser assisted positron-atom collisions is made. It is found that the collisions are accompanied by multiphoton processes. The cross sections are notably modified by the laser.

Recent development in the theory of fast positron-atom collisions

We will review some recent high energy theories of positronium formation in positron-hydrogen collisions, and compare these theories to the recent experimental measurements. We will also present high energy theories of positron-impact ionization of hydrogen. A comparison of these theories with the two sets of experimental measurements clearly shows that positron-impact ionization of hydrogen is not completely understood. In particular, the role of positronium formation to the continuum in positron-hydrogen ionization is presently not known. Structures arising from the interference between two double-binary collision processes in the triply differential cross section of positron-impact ionization of hydrogen will be discussed.

Elaborate treatment of the inelastic collisions of positrons with alkali atoms and alkaline-earth positive ions using a restricted coupled-static approximation

We present the results of a very elaborate investigation of the inelastic collisions of positrons with the ground states of the first four alkali atoms (3Li,11Na,19K and38Rb) and their electronically resemblant alkaline-earth positive ions,i.e.4Be+,12Mg+,20Ca+ and39Sr+, respectively, using a restricted coupled-static approximation in which the reactance matrices are adjusted to be symmetrical. Our interest is concentrated on the calculation of the total elastic and positronium formation cross-sections and their behaviour in the low-energy region (below 10 eV for the atoms) or the regions above the positronium formation thresholds (when the ions are considered). Our results are the most accurate cross-sections expected from the approximation employed. They reveal, within their limits, the most important characteristics of these cross-sections and provide us with a satisfactory comparison between the main features of positron-atom and positron-ion collisions.

Elastic and inelastic scattering of electrons and positrons by atomic hydrogen at intermediate and high energies in the unitarised eikonal-Born series method

The eikonal-Born series approximation is unitarised by using an improved Wallace-type amplitude to construct the direct scattering amplitude. The new unitarised eikonal-Born series (UEBS) direct amplitude obtained in this way is first tested successfully in potential scattering. It is then generalised to electron- and positron-atom collisions, and applied to elastic (1s-1s), 1s-2s and 1s-2p transitions in atomic hydrogen. The large momentum transfer properties of the UEBS direct amplitude are analysed for these three transitions, and the structure of the third term of the Born series is investigated by using the unitarity relations. Exchange effects are also discussed. The theoretical results are compared with those obtained from other theories and with recent measurements, for impact energies ranging from 54.4 to 400 eV.

A systematic search for a realistic SU(N) Tumbling gauge model: Gönül Süalp. Middle East Technical University, Physics Department, Ankara, Turkey; and Sinan Kaptanoglu. Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794

We discuss three aspects of the analysis of the quasi-bound-state (QBS) or resonance-state effects on multichannel continuum wavefunctions for few-body atomic systems. Section 1 is devoted to a brief introductory account of the basic concept necessary for understanding the later sections. General properties of the scattering matrix S and a related time-delay matrix Q are discussed in Section 2. Both isolated and overlapping resonances are treated, starting from single-channel problems and extending the theory for multichannel cases. Useful relations are derived in detail on the basis of linear algebra. The concept of the resonance channel and nonresonance channel spaces, separated from each other, is introduced via the Q-matrix diagonalization. Outstanding examples of resonance analysis by the inspection of the eigenvalues of the Q matrix are presented. They include the extraction of resonances from a monotonically decreasing phase shift due to a strong background, the detection of a weak resonance, seemingly a nearly constant background behind a strong resonance, and the decomposition of several overlapping resonances into the individual components, some of which are difficult to identify by the conventional methods.Section 3 examines effective potentials for understanding QBSs. First, the information obtainable from the asymptotic long-range potentials is summarized. This includes the analysis of infinite series of QBSs supported by an attractive Coulomb or dipole potential, the latter appearing in charged-particle collisions with hydrogen-like atoms. The infinite series of dipole-supported QBSs is terminated to only a few resonances, sometimes to one or two, by correcting for relativistic and quantum electrodynamic effects. The dipole potential can also cause the background phase shift to diverge as the energy tends to a channel threshold from above, complicating a resonance structure.The hyperspherical coordinate approach is then briefly discussed. Accurate numerical calculations for three-body systems are possible by solving coupled-channel equations in terms of these coordinates. The resultant resonance structures can be visually and qualitatively interpreted by inspecting the adiabatic potentials with the hyperradius adopted as the adiabatic parameter. Sometimes the adiabatic correction or diabatic connection, or both are necessary for proper resonance analysis. By combining with the knowledge of the long-range potentials, resonances can often be ascribed to particular adiabatic or diabatic hyperspherical potentials out of an intertwined set of potential curves. In particular, when two or more adiabatic potentials exhibit strongly avoided crossings, some resonances appear as if they were associated with no hyperspherical potentials, even though a careful diabatic interpretation can clearly explain them. A shift in hyperspherical potentials with a continuous change in some parameter(s) in the system can result in a sudden change from a bound state to QBS or from a Feshbach to shape resonance without any essential change in the main part of the wavefunction.Section 4 analyzes the energy dependence of the cross sections near the threshold for the formation of a QBS. The Wigner threshold law breaks down close to the threshold since the threshold itself has an uncertainty due to the finite lifetime of the QBS. The modifications, due to Baz', for a blurred threshold are explained. Positron–atom collisions are discussed as a prototype, where a bound electron–positron pair (positronium, Ps) can be formed. It is a QBS since it annihilates eventually. Pair annihilation, or positron absorption, can also occur during the collision. The conventional theory leads to a divergent positron absorption cross section at the Ps formation threshold Eth, and to a Ps formation cross section starting from zero and rapidly increasing above Eth. Both of these processes have a common final channel of pair annihilation and should be treated collectively. This is possible by phenomenologically modeling pair annihilation as particle loss due to an imaginary potential in the Schrödinger equation. This approach proves the continuous and smooth transition from positron absorption to Ps formation across Eth, following the Baz' threshold law. Thus, the two processes are indistinguishable in the energy region of this transition.

The potential harmonic expansion method: M. Fabre de la Ripelle. Division de Physique Theorique, Institut de Physique Nucléaire, F-91406 Orsay Cedex, France

We discuss three aspects of the analysis of the quasi-bound-state (QBS) or resonance-state effects on multichannel continuum wavefunctions for few-body atomic systems. Section 1 is devoted to a brief introductory account of the basic concept necessary for understanding the later sections. General properties of the scattering matrix S and a related time-delay matrix Q are discussed in Section 2. Both isolated and overlapping resonances are treated, starting from single-channel problems and extending the theory for multichannel cases. Useful relations are derived in detail on the basis of linear algebra. The concept of the resonance channel and nonresonance channel spaces, separated from each other, is introduced via the Q-matrix diagonalization. Outstanding examples of resonance analysis by the inspection of the eigenvalues of the Q matrix are presented. They include the extraction of resonances from a monotonically decreasing phase shift due to a strong background, the detection of a weak resonance, seemingly a nearly constant background behind a strong resonance, and the decomposition of several overlapping resonances into the individual components, some of which are difficult to identify by the conventional methods.Section 3 examines effective potentials for understanding QBSs. First, the information obtainable from the asymptotic long-range potentials is summarized. This includes the analysis of infinite series of QBSs supported by an attractive Coulomb or dipole potential, the latter appearing in charged-particle collisions with hydrogen-like atoms. The infinite series of dipole-supported QBSs is terminated to only a few resonances, sometimes to one or two, by correcting for relativistic and quantum electrodynamic effects. The dipole potential can also cause the background phase shift to diverge as the energy tends to a channel threshold from above, complicating a resonance structure.The hyperspherical coordinate approach is then briefly discussed. Accurate numerical calculations for three-body systems are possible by solving coupled-channel equations in terms of these coordinates. The resultant resonance structures can be visually and qualitatively interpreted by inspecting the adiabatic potentials with the hyperradius adopted as the adiabatic parameter. Sometimes the adiabatic correction or diabatic connection, or both are necessary for proper resonance analysis. By combining with the knowledge of the long-range potentials, resonances can often be ascribed to particular adiabatic or diabatic hyperspherical potentials out of an intertwined set of potential curves. In particular, when two or more adiabatic potentials exhibit strongly avoided crossings, some resonances appear as if they were associated with no hyperspherical potentials, even though a careful diabatic interpretation can clearly explain them. A shift in hyperspherical potentials with a continuous change in some parameter(s) in the system can result in a sudden change from a bound state to QBS or from a Feshbach to shape resonance without any essential change in the main part of the wavefunction.Section 4 analyzes the energy dependence of the cross sections near the threshold for the formation of a QBS. The Wigner threshold law breaks down close to the threshold since the threshold itself has an uncertainty due to the finite lifetime of the QBS. The modifications, due to Baz', for a blurred threshold are explained. Positron–atom collisions are discussed as a prototype, where a bound electron–positron pair (positronium, Ps) can be formed. It is a QBS since it annihilates eventually. Pair annihilation, or positron absorption, can also occur during the collision. The conventional theory leads to a divergent positron absorption cross section at the Ps formation threshold Eth, and to a Ps formation cross section starting from zero and rapidly increasing above Eth. Both of these processes have a common final channel of pair annihilation and should be treated collectively. This is possible by phenomenologically modeling pair annihilation as particle loss due to an imaginary potential in the Schrödinger equation. This approach proves the continuous and smooth transition from positron absorption to Ps formation across Eth, following the Baz' threshold law. Thus, the two processes are indistinguishable in the energy region of this transition.

The classical trajectory study of e++A to A++e-+e+reaction near the threshold

Numerical investigations of the positron-atom ionisational collisions near the threshold have been carried out within the classical trajectory method. It is found that for an infinitely heavy target the threshold law reads: I approximately E2.49, whereas recent analytical calculations predict a value of 2.65 for the exponent. However, in the case of a hydrogen-atom target, the value 1.64 has been obtained, indicating that the resting target mass assumption, as employed in all previous analytical investigations of e+or--A processes near the ionisation threshold breaks down in the case of the positron-light-atom collisions. The energy distribution of the outgoing particles appears non-zero and uniform in larger parts of available energy regions: e+(E/2, E), e-(0, E/2), but turns out, surprisingly, to be zero around E/2. The calculated energy dependence of the mutual angle is consistent with the analytically predicted theta +- approximately E1/4 behaviour.

Unitarisation of the eikonal-Born series method for electron-atom and positron-atom collisions

A systematic study is made of the unitarisation method which the authors recently proposed for the eikonal-Born series approximation, in the case of fast electron-atom and positron-atom collisions. The authors' unitarisation procedure is based on a generalisation of the potential scattering eikonal expansion of Wallace to the multiparticle case, suitably modified to take the long-range polarisation effects and absorption effects at small angles into account correctly. They also develop a new non-perturbative approximation for the exchange scattering amplitude, which is appropriate to use with the authors' unitarised EBS direct scattering amplitude for electron-atom collisions. The authors' then apply their unitarised EBS method to the elastic scattering of electrons and positrons by atomic hydrogen in the energy range 100-400 eV. A detailed comparison is made with other related theoretical methods and with recent absolute measurements of (e--H) elastic differential cross sections. Total (integrated) elastic and total (complete) cross sections for both electron and positron impact are also discussed.