Joseph Macek

Collisions near threshold in atomic and molecular physics

We review topics of current interest in the physics of electronic, atomic and molecular scattering in the vicinity of thresholds. Starting from phase space arguments, we discuss the modifications of the Wigner law that are required to deal with scattering by Coulomb, dipolar and dispersion potentials, as well as aspects of threshold behaviour observed in ultracold atomic collisions. We employ the tools of quantum defect and semiclassical theories to bring out the rich variety of threshold behaviours. The discussion is then turned to recent progress in understanding threshold behaviour of many-body break-ups into both charged and neutral species, including both Wannier double ionization and three-body recombination in ultracold gases. We emphasize the dominant role that hyperspherical coordinate methods have played in understanding these problems. We assess the effects of external fields on scattering, and the corresponding modification of phase space that alters the Wigner law. Threshold laws in low dimensions and examples of their applications to specific collision processes are discussed.

The production of K shell vacancies in symmetric ion-atom collisions

The electron-promotion model of Fano and Lichten (1965) has been applied to the calculation of the cross section for production of K shell vacancies in symmetric ion-atom collisions. The promotion is assumed to occur via rotational coupling between the 2p sigma and 2p pi molecular orbitals. Certain statistical factors which govern the probability of a vacancy occurring initially in the 2p pi molecular orbital have been derived. A peak in the vacancy production probability at small impact parameters is predicted and is shown to correspond to deflection through 90 degrees . Good agreement with experiment is obtained when the method is applied to the Ne+-Ne system and an approximate scaling law is suggested by which the cross section for K shell vacancy production in other symmetric collisions may be deduced.

The Theory of Fast Ion-Atom Collisions

Publisher Summary This chapter describes the theory of fast ion-atom collisions that are based upon high-energy, Born-type expansions, or their distorted-wave generalization. The chapter focuses on Born theories of processes involving only one active electron. The collisions of multi-electron species exhibit all of the features of the one electron prototype, but also include new types of motion arising from the electron–electron interaction. Effects because of this electron–electron interaction are even dominant in some ranges of ion charge, collision velocity, or secondary-electron energy. Collisions involving only one or two active electrons have been considered to isolate the separate effects of electron–nucleus and electron–electron interactions as clearly as possible. For one-electron collisions, the first Born approximation has been analyzed in terms of the qualitative features of differential excitation and ionization cross sections that it predicts. For ionization, the first Born approximation, either in direct or capture form, is fundamentally inadequate. The influence of higher-order processes, in particular double-binary collisions of the Thomas type, is emphasized in the chapter.

Theory of emission-angle-dependent Auger transitions in ion-atom collisions

By means of a continuum distorted-wave approximation of the post-collision state the authors derive an analytical equation for the Auger emission amplitude in ion-atom collisions. This theory includes previous models as particular cases. The authors further show that the presence of the projectile strongly affects the intensity profile, giving rise to a dependence on the emission angle that is missed in previous theories. In particular, a sharp enhancement in the forward direction is computed.

Hyperspherical adiabatic eigenvalues for zero-range potentials

The scattering length a associated with two-body interactions is the relevant parameter for near threshold processes in cold atom-atom collisions. For this reason zero-range potentials are traditionally used to model collective behaviour of dilute collections of bosons. The model is also used to compute three-body recombination rates, where it gives an a4 law. In this paper we examine the applicability of the zero-range model to real physical systems. Hyperspherical adiabatic potentials obtained from the zero-range model are compared with published potentials based on realistic two-body interactions. From these comparisons it is possible to determine the regions where the model applies.

Valence-bond calculation of energy curves for XeH+

The lowest five energies of the XeH+ system have been calculated using the valence-bond method. The effects of spin-orbit coupling are introduced by a semi-empirical procedure. These results serve to interpret qualitatively processes involved in collisions between protons and xenon atoms and, in particular, the polarization of spin on the hydrogen atoms formed by charge exchange is discussed.

Nth order perturbation theory for hydrogen

This paper presents a simple reformulation of second order perturbation theory for hydrogen. We calculate first the perturbed wavefunction and then the perturbed matrix element. This procedure is repeated to obtain the nth order matrix element in terms of n−1 integrals. The parameters in the nth order matrix element are defined recursively. Schwinger’s representation of the Coulomb Green’s function follows immediately from our expression for the second order matrix element.

Scattering of charged particles

Different methods of avoiding the known difficulties of the Coulomb potential scattering theory are reviewed. Mulherin and Zinnes’ [J. Math. Phys. 11, 1402 (1976)] ‘‘distorted’’ free waves and van Haeringen’s [J. Math. Phys. 17, 995 (1976)] Coulomb asymptotic states are considered. The equivalence of both approaches on the energy shell is shown. Actually the possibility of deriving the first method within van Haeringen’s formalism by means of a distorted wave procedure is demonstrated.

The electron impact spectrum of He in the vicinity of the n=2 thresholds

The derivative of the electron transmission spectrum of helium has been directly measured for electron energies between about 19.2 and 21.2 eV. Effective range theory has been used to extrapolate the 22S state of He- across the 23S threshold of He. Such extrapolation produces a peak in the energy derivative of the transmitted current at the 23S threshold which was used to calibrate the electron energy scale. This calibration technique has been used to identify the positions of the other n=2 thresholds. The position of the dip in the elastic cross section due to the 22S state of He- is thus established at 19.35+or-0.02 eV. Two additional structures have been observed between (He- (22S)) and (He (23S)) and three between (He (23S)) and (He (21S)) in agreement with the results of Golden and Zecca (1970). Several additional features in the spectrum are also discussed.

Integral representation of one-dimensional three particle scattering for δ function interactions

The Schrodinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The interactions are replaced by appropriate boundary conditions. This leads then to requiring the solution of a free-particle Schrodinger equation subject to these boundary conditions. A generalized Kontorovich–Lebedev transformation is used to write this solution as an integral involving a product of Bessel functions and pseudo-Sturmian functions. The coefficient of the product is obtained from a three-term recurrence relation, derived from the boundary condition. The contours of the Kontorovich–Lebedev representation are fixed by the asymptotic conditions. The scattering matrix is then derived from the exact solution of the recurrence relation. The wavefunctions that are obtained are shown to be equivalent to those derived by McGuire. The method can clearly be applied to a larger n...