Of atomic collisions with positrons and positronium

Recent progress in the study of atomic collisions using positronic projectiles is outlined and advances which might ensue from the production of more intense positron beams are indicated. Material in this paper was contained in a lecture delivered at the Workshop on Intense Positron Beams in Europe held at UCL on the 18th and 19th September, 1995.     

Spin-orbit potential in heavy-ion collisions

The spin-orbit potentials between heavy-ion projectiles and ¹²C target are calculated by the folding method. The projectile mass number dependence of the spin-orbit potential is presented. The contributions of the spin-orbit potential to the elastic and inelastic scatterings of the ⁶Li and ¹⁴N projectiles from the ¹²C target are calculated. The theoretical elastic polarization of the ⁶Li scattered from ¹²C is found to be appreciable.     

Magnetic quenching of positronium in semiconductors

The positronium-determined characteristics of electron-positron annihilation in semiconductors in the presence of an external magnetic field are calculated. It is assumed that the positronium atoms can be in one of two states, delocalized or localized (at defects), and undergo not only pick-off annihilation but also orthoparaconversion (³S₁ ¹S₀) on free carriers. Numerical calculations were made for a field H=15 kG. The field has very different effects on localized and delocalized positronium, and in the first case the effect depends strongly on the nature of the defect.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.11, pp. 75–78, November, 1980.     

Resonant positronium formation in atomic gases

A method is presented for calculation of quasistationary excited states of positronium ions. These states are treated as bound positron states in the quadrupole field of an excited valence electron, which are capable of decaying both with positron emission into the continuous spectrum, and with positronium emission. The existence of such states should manifest itself in resonances in the positronium formation section upon motion of positrons with energy in the eV range. The resonant section parameters are calculated for a number of atoms.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 6–12, March, 1984.     

Anisotropic magnetic quenching of positronium states in oriented crystals

We have carried out a theoretical analysis of the anisotropy of magnetic quenching of positronium states in noncubic crystals oriented relative to the direction of the external magnetic field. We show that an initial polarization of the positrons amplifies the anisotropy of magnetic quenching of positronium and lowers the magnitude of the magnetic field in which the anisotropy is maximum. We have obtained numerical estimates of the magnitude of the experimentally observed effect for quasipositronium in a single crystal of crystalline quartz and for a positronium complex in a single crystal of naphthalene. Fiz. Tverd. Tela (St. Petersburg) 41, 999–1002 (June 1999)     

Bromine and oxygen quenching of positronium in silica gel

Positron lifetime spectra for various concentrations of bromine and oxygen adsorbed on silica gel are investigated. Two-photon angular correlation experiments were also performed on some of these samples to study the quenching process of bromine and oxygen. The cross section for bromine quenching of orthopositronium in silica gel is about two orders of magnitude larger than that for oxygen quenching. The process of bromine quenching of positronium is found to be chemical quenching. Oxygen quenching of positronium in silica gel is found to be conversion quenching. The interaction between positronium and bromine or oxygen in silica gel is found to be similar to that found in the gaseous state. The energy of Ps annihilating in the pores of silica gels is found to be 0.25±0.10 eV.     

Exchange collisions between positronium and Cu2+ ions

Summary The fate and properties of the ortho-Ps in aqueous solutions of CuSO₄ and CuCl₂ have been investigated through lifetime measurements and through a magnetic-quenching experiment. The obtained results are interpreted in terms of exchange collisions between Ps and unpaired electron. An upper limit is given for the chemical-quenching rate. Our measurements have shown that the presence of paramagnetic centres determines a strong shift of the levels of the Ps hyperfine structure. This work was entirely supported by CISM (Centro Interuniversitario di Struttura della Materia) of the Ministero della Publica Istruzione and by GNSM (Gruppo Nazionale di Struttura della Materia) of CNR.     

Low energy atomic collisions

The Schrödinger equation for the system H⁺-H developed in a previous paper is considered using new expansion functions for electronic states obtained from H₂ ⁺ molecular ion electronic eigenfunctions by a unitary transformation. These new functions have the advantage of remaining orthonormal at all internuclear separations and asymptotically becoming symmetrized atomic hydrogen states. Although they are eigenfunctions of the H₂ ⁺ hamiltonian only in the limit of large internuclear distance, the effect of the H₂ ⁺ hamiltonian on these functions is readily found.

Due to coupling which remains non-zero in the limit of large interproton distance, each independent formal solution of the H⁺-H equations involves more than one expansion state in this limit. These solutions may be expressed asymptotically as column vectors multiplied by incoming or outgoing spherical waves.

The formal theory of scattering as developed by Gell-Mann and Goldberger has been utilized along with the projection formalism of Feshbach to obtain the correct asymptotic form of the scattering wave function. The procedure employed involves formulating the problem in terms of two-potential scattering and requires application of renormalization techniques for treating level shifts produced by the infinite-ranged coupling. This asymptotic form may be used in imposing scattering boundary conditions on numerical solutions of coupled equations for H⁺-H scattering.

Finally, it is shown that one cannot interpret coefficients of all outgoing spherical waves as scattering amplitudes. In addition, new interference phenomena are found to result from the presence of the infinite-ranged coupling. The present formalism is shown to reduce to the usual perturbed stationary-states method in the approximation that the infinite-ranged coupling is neglected.     

Antihydrogen formation in low-energy antiproton collisions with excited-state positronium atoms

The convergent close-coupling method is used to obtain cross sections for antihydrogen formation in low-energy antiproton collisions with positronium (Ps) atoms in specified initial excited states with principal quantum numbers n_i ≤?5. The threshold behaviour as a function of the Ps kinetic energy, E, is consistent with the 1/E law expected from threshold theory for all initial states. We find that the increase in the cross sections is muted above n_i =?3 and that here their scaling is roughly consistent with \({n_{i}^{2}}\), rather than the classically expected increase as \({n_{i}^{4}}\).     

Collective effects in atomic collisions

As a first step towards a collective treatment of charge flow in atomic collisions, we constructab initio potential energy surfaces as a function of the internuclear distance and the charge asymmetry between the two atomic species. To this end, the charge asymmetry off its stability value for a given nuclear separation is imposed upon the system by a suitable constraint within a two-centre Hartree-Fock calculation. Energy surfaces are presented for the systems LiH, HF, LiF, and CO. This representation offers a conceptual framework for visualising ionic or covalent molecular states and trajectories describing charge-changing collisions.     

Nonadiabatic transitions upon atomic collisions

The standard interpretation of the adiabatic approach and the t matrix method for the calculation of the probabilities of nonadiabatic transitions and inelastic cross sections in atomic collisions is analyzed, and a model problem of collisions of hydrogen atoms with neutrons is considered. It is shown that the application of the standard approach results in a physically inconsistent result—considerable values of the excitation cross sections of hydrogen atoms by neutrons. The application of the t matrix method improves the result by two to three orders of magnitude even for a restricted basis set.     

Physics of atomic collisions in retrospect

The classic work by Mott and Massey, in which the scope of the physics of atomic collisions was defined, was published about 65 years ago. Since then, this field has undergone considerable development. In fact, all the theoretical methods named by Mott and Massey have been implemented to some extent. As for experiment, the measurements performed, which are differential with respect to several parameters, have provided for reliable testing of the mechanisms proposed. The physics of atomic collisions has been developed to the point that we can look back on the road taken and discover many achievements which have promoted its development. Progress in science is usually associated with highly concentrated efforts on the part of a critical number of investigators to solve a specific problem, which is widely regarded as being of great importance. Such a “breakthrough” is usually followed by rapid development of the field. In this respect, the physics of atomic collisions is no exception. It has known periods of highly concentrated efforts aimed at solving specific problems and breakthroughs followed by rapid development and subsequent periods of stagnation. The cycles have repeated: a new area for concentrated efforts is discovered, a breakthrough occurs, and a new concept is established. Some of these cycles are analyzed from the standpoint of their significance to atomic physics as a whole. Zh. Tekh. Fiz. 69, 22–26 (September 1999)     

Theoretical studies of antihydrogen formation in collisions between positronium atoms and antiprotons

The current state of the theoretical methods that are used in calculations of cross sections for the production of antihydrogen in collisions between antiprotons and positronium atoms is reviewed. A broad outline of available methods together with the results of recent computations are presented. The main emphasis is made on the general close-coupling approach that allows any reaction channel to be taken as the initial state of the collision system. In this way, and on account of charge-conjugation invariance, the formation of antihydrogen in collisions between antiprotons and positronium atoms becomes linked to positron-hydrogen scattering and the same computational methods can be applied to either reaction. The review gives references to recent papers on the subject.     

Feynman diagram approach to atomic collisions

A quantum field theoretic formulation of atomic collision phenomena involving non-relativistic free and bound systems is developed and a calculational procedure in terms of Feynman diagrams is prescribed. Matrix elements of several atomic collision processes have been calculated. In most cases standard quantum mechanical results are reproduced. But in some cases new terms appear in the scattering matrix whose contribution though negligibly small in the low energy region, become important at higher energies. A large portion of this work formed material for an invited talk delivered by one of us (T.P.) at the Second National Workshop on Atomic and Molecular Physics at Visva-Bharati, Santiniketan (India) held from 18–23 November 1979.     

Feynman diagram method for atomic collisions

Feynman diagram method of treating atomic collision problems in perturbation theory is presented and matrix elements are calculated for a number of processes. The result for the resonant charge transfer in hydrogen is identical to the well known OBK value. However, in processes like collisional ionisation, the results are different from those obtained by conventional methods.     

Rovibrational in ultracold quenching of BH 3He collisions

The interaction potential of a He-BH complex is investigated by the coupled-cluster single-double plus perturbative triples （CCSD （T）） method and an augmented correlation consistent polarized valence （aug-cc-pV）5Z basis set extended with a set of （3s3p2dlflg） midbond functions. Using the five two-dimensional model potentials, the first three-dimensional interaction potential energy surface is constructed by interpolating along （r-re） by using a fourth-order polynomial. The cross sections for the rovibrational relaxation of BH in cold and ultracold collisions with 3He atom are calculated based on the three-dimensional potential. The results show that the △v =-1 transition is more efficient than the △v=-2 transition, and that the process of relaxation takes place mainly between rotational energy levels with the same vibration state and the △j=-1 transition is the most efficient. The zero temperature quenching rate coefficient is finite as predicted by Wigner＇s law. The resonance is found to take place around 0.1-1 cm^-1 translational energy, which gives rise to a step in the rate coefficients for temperatures around 0.1-1 K. The final rotational distributions in the state v = 0 resulting from the quenching of state （v = 1,j = 0） at three energies corresponding to the three different regimes are also given.     

Control of atomic collisions by laser polarization

Atomic collision pairs in a light field form a microscopic interferometer. The light acts as the beam splitter and controls at the same time the amplitudes and phases of the interfering waves. We demonstrate the complete tunability using linear and elliptic polarization.