Quantum Monte Carlo Study of a Positron in an Electron Gas

Abstract

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects.PACS numbers: 78.70. Bj, 71.60.+z, 71.10.Ca, 02.70.Ss Electron-positron annihilation underlies both medical imaging with positron emission tomography (PET) and studies of materials using positron annihilation spectroscopy (PAS) [1]. Positrons entering a material rapidly thermalize and the majority annihilate with oppositespin electrons to yield pairs of photons at energies close to 0.511 MeV. In a PET scan, positrons are emitted by radionuclides in biologically active tracer molecules and the resulting annihilation radiation is measured to image the tracer concentration. The interaction of low-energy positrons with molecules is therefore of substantial experimental and theoretical interest [2]. PAS is used to investigate microstructures in metals, alloys, semiconductors, insulators [1], polymers [3], and nanoporous materials [4]. Positrons are repelled by the positively charged nuclei and tend to become trapped in voids within the material. The positron lifetime is measured as the interval between the detection of a photon emitted in the β + radioactive decay that produces the positron and the detection of the annihilation radiation [1]. The lifetime is characteristic of the region in which the positron settles, and PAS is a sensitive, nondestructive technique for characterizing the size, location, and concentration of voids in materials. Measuring the Doppler broadening of the annihilation radiation or the angular correlation between the two 0.511 MeV photons yields information about the momentum density (MD) of the electrons in the presence of the positron. These techniques may be used to investigate the Fermi surfaces of metals [5].The aim of PAS experiments is to investigate a host material without the changes induced by the positron. The positron is, however, an invasive probe which polarizes the electronic states of the material. Disentangling the properties of the host from the changes induced by the positron is a major theoretical challenge. Positrons in condensed matter may be modeled with two-component density functional theory (DFT) [6], in which the correlations are described by a functional of the electron and positron density components. Within the local density approximation (LDA), this functional is obtained from the difference ∆Ω between the energy of a homogeneous electron gas (HEG) with and without an immersed positron. ∆Ω is known as the relaxation energy, and is equal to the electron-positron correlation energy. Two-component DFT gives reasonable electron and positron densities, bu...

Experimental and theoretical cross sections for positron scattering from the pentane isomers

“…Given that our IAM-SCAR formalism may not be so accurate at incident energies below 30 eV or so, ab initio positron-molecule calculations, such as those based on density functional theory (DFT) or self-consistent field with configuration interaction (SCF-CI), might be more precise at those very low energies. In particular, we acknowledge the recent fundamental improvements in the electron-positron scattering potential within the DFT framework, both in the local density approximation (LDA) (Drummond et al, 2011) and the generalized gradient approximation (GGA) (Barbiellini and Kuriplach, 2015) methods. Although these theoretical approaches do not explicitly account for Ps formation, which is an important scattering channel at such low energies, they might lead to a clearer picture of the isomer effect.…”

Метод Определения Работы Выхода Электронов И Позитронов Из Металла, Содержащего Вакансии

“…где первое слагаемое соответствует электростатиче-скому взаимодействию позитрона с металлом, второе представляет вклад позитрон-электронных корреляций в приближении локальной плотности [8], третий член описывает неэлектростатическое позитрон-ионное взаи-модействие в каждой из атомных ячеек Вигнера−Зейтца. Вакансионная поправка к работе выхода позитрона так-же выражается через характеристики металла в отсут-ствие вакансий…”

Probing the Fermi surface by positron annihilation and Compton scattering

“…2 The problem of dealing with enhancement is an important one (and one which is still the subject of current studies 3,4 ), but a proper treatment is beyond the scope of this review and discussions can be found elsewhere. 2,5,6 The application of the LCW theorem becomes X…”

“…These precipitates are in fact highly ordered L1 2 Al 3 Li which is coherent with the parent fcc Al matrix with only a small lattice mismatch. 81,82 Using the positron's affinity for the precipitates, the Fermi surface of Al 3 Li was determined using positron annihilation on an Al-9 at. % Li sample by Laverock et al 83 Four different crystallographic projections were measured (see Fig.…”