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Journal of Physics Conference Series

Exchange-assisted tunneling and enhancement of positron annihilation with inner-shell ellectrons

V. V. Flambaum, M. G. Kozlov

Published Sep 7, 2015• 0 citations
Publisher

Abstract

Exchange interaction and correlations radically change behaviour of of a quantum particle in a classically forbidden region. Exchange produces a power-law decay instead of the usual exponential decrease of the wave function. Exchange-assisted tunneling enhances annihilation of positron with inner-shell electrons and produces other observable effects.

DOI
10.1088/1742-6596/635/5/052026

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Exchange interaction and correlations radically change behaviour of of a quantum particle in a classically forbidden region. Exchange produces a power-law decay instead of the usual exponential decrease of the wave function. Exchange-assisted tunneling enhances annihilation of positron with inner-shell electrons and produces other observable effects.
Electron-positron annihilation rates calculated directly from the electron and positron densities are known to underestimate the true annihilation rate. A correction factor, known as the enhancement factor, allows for the local increase of the electron density around the positron caused by the attractive electron-positron interaction. Enhancement factors are given for positrons annihilating with the 1s1s1s electron in H, He+{\mathrm{He}}^{+}He+, He, Li2+{\mathrm{Li}}^{2+}Li2+, and Li+{\mathrm{Li}}^{+}Li+. The enhancement factor for a free positron annihilating with He+{\mathrm{He}}^{+}He+ and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of 1.47a01.47{a}_{0}1.47a0​ for Ps-He scattering. Further, enhancement factors for e+{e}^{+}e+-Ne and e+{e}^{+}e+-Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of 1.46a01.46{a}_{0}1.46a0​ for Ps-Ne scattering and 1.75a01.75{a}_{0}1.75a0​ for Ps-Ar scattering.
Everyday macroscopic objects follow the laws of classical mechanics. For microscopic objects, such as atoms or nuclei, the wave character of their dynamics has to be taken into account within the framework of quantum mechanics. While wave-like behaviour can show up in various ways, one of the most striking is the tunnelling effect: some events that are classically forbidden for energetic reasons happen because the quantum particles can tunnel under a potential barrier. Similarly, events that are prohibited due to some other dynamical constraints can occur via a process known as dynamical tunnelling. Indeed, tunnelling plays a major role in a variety of physical phenomena, ranging from α-particle radioactivity to the current–voltage characteristics of transistors.
Exchange interaction has been studied for electrons in coupled quantum dots (QDs) by a configuration interaction method using confinement potentials with different profiles. The confinement potential has been parametrized by a two-centre power-exponential function, which allows us to investigate various types of QDs described by either soft or hard potentials of different ranges. For the soft (Gaussian) confinement potential the exchange energy decreases with increasing interdot distance due to the decreasing interdot tunnelling. For the hard (rectangular-like) confinement potential we have found a non-monotonic behaviour of the exchange interaction as a function of distance between the confinement potential centres. In this case, the exchange interaction energy exhibits a pronounced maximum for the confinement potential profile which corresponds to the nanostructure composed of the small inner QD with a deep potential well embedded in the large outer QD with a shallow potential well. This effect results from the strong localization of electrons in the inner QD, which leads to the large singlet–triplet splitting. Implications of this finding for quantum logic operations have been discussed.
We consider pseudogap effects for electrons interacting with gapless modes. We study both generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of the photo electron or tunneling spectroscopy. Within the formalism of functional integration and the adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by presence of gapless phonons which change the usual dynamics to the regime of the quantum dissipation. Below the free particle edge the pseudogap starts with the exponential (stretched exponential for gapful phonons) decrease of transition rates. Deeply within the pseudogap they are dominated by a power law, in contrast with nearly exponential law for gapful modes.
Since the early days of quantum mechanics, tunneling has been recognized as one of the hallmarks of the wave character of microscopic physics. The possibility of a quantum particle to penetrate an energetic barrier represents certainly one of the most spectacular implications of quantum theory and has led to various applications in nuclear, atomic, and molecular physics as well as in mesoscopic science. Typical scenarios in which tunneling manifests are the escape route of a quantum particle from a quasibounded region, the transition between two or more symmetry-related, but classically disconnected wells (which we shall focus on in the following), as well as scattering or transport through potential barriers. The spectrum of scenarios becomes even richer when the concept of tunneling is generalized to any kind of classically forbidden transitions in phase space, that is, to transitions that are not necessarily inhibited by static potential barriers but by some other constraints of the underlying classical dynamics (such as integrals of motion). Such “dynamical tunneling” processes arise frequently in molecular systems [1] and were realized with cold atoms propagating in periodically modulated optical lattices [2-4]. Moreover, the electromagnetic analog of dynamical tunneling was also obtained with microwaves in billiards [5].