Many-body aspects of positron annihilation in the electron gas

We investigate positron annihilation in electron liquid as a case study for many-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL) method. We examine several approximation schemes and show that one has to go up to the most sophisticated implementation of the theory available at the moment in order to get annihilation rates that agree reasonably well with experimental data. Even though there is basically just one number to look at, the electron-positron pair distribution function at zero distance, it is exactly this number that dictates how the full pair distribution behaves: In most cases, it falls off monotonously towards unity as the distance increases. Cases where the electron-positron pair distribution exhibits a dip are precursors to the formation of bound electron--positron pairs. The formation of electron-positron pairs is indicated by a divergence of the FHNC-EL equations, from this we can estimate the density regime where positrons must be localized. This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is the dimensionless density parameter of the electron liquid.Comment: To appear in Phys. Rev. B (2003

Investigation of Electron-Positron Correlations by Monte Carlo Simulation

Earlier theoretical studies, as well as recent calculations of positron annihilation rates in metals, show that some basic problems concerning electron-positron (e-p) interaction have not been solved satisfactorily, even for homogeneous media (the electron gas). In turn, the "computer experiments" e.g. quantum Monte Carlo simulations applied to these problems by several authors yielded only fragmentary, inaccurate and even incorrect results for smaller electron densities. It is shown in the present paper that the quantum Monte Carlo method may be useful in investigations of positron interactions with electrons. Reasonable annihilation rates have been obtained owing to appropriate construction of the trial function and taking into account the 3-particle correlations (i.e. dependence of the electron-electron (e-e) interaction on the distance from the positron). Moreover, the method of "exact determination" (without any fitting) of positron annihilation rates on the basis of the variational trial function was proposed. One also found the way of calculating the momentum dependent enhancement factors, the quantities not achievable within the Monte Carlo method until now

Momentum distributions in positron annihilation with tightly bound electrons in Al

An approach based on Carbotte, Salvadori and Chiba two-body schemes for calculation of electron-positron (e-p) momentum densities ro(p) for core electrons in solids is developed. The approach allows to avoid such common approximations as the local density approximation (LDA) etc. in determination of ro(p) of deeper atomic shells and reduces the contribution to ro(p) for higher momenta. Thus, the final calculations of the Doppler spectra of annihilation radiation yield lower values for greater momenta than those obtained within the LDA scheme. The exemplary calculations for Al are presented

Positron lifetime calculations for some elements on the base of the GGAPHNC approximation

In studies of several interesting materials by positron annihilation technique the theoretical values of positron lifetimes in bulk and defected elements are useful. These lifetimes are often calculated within the GGA approximation. In this approximation the results of Arponen and Pajanne calculations for the positron in an electron gas are used. It is known, however, that when using the LDA approximation for the calculations of positron lifetime in real metals, Arponen and Pajanne values yield worse agreement with experimental data than the results obtained on the basis of PHNC formalism. Therefore, in this paper the appropriate PHNC formulas are incorporated into the GGA approximation and the calculations have been performed for some metals: bulk as well as containing monovacancies. The comparison of the lifetimes found in this way to the ones based on the previous method is promising for the applicability of the new algorithm

A New Project for Calculations of e+\text{}^{+}-e−\text{}^{-} Interaction in Real Metals

A method based on numerical relaxation technique is proposed for solving directly the three-dimensional Euler-Lagrange equation for the density amplitude of conduction electrons in real metals disturbed by the positron. The method has been tested with good results for the positron in an inhomogeneous electron gas. The preliminary calculations of positron screening in lithium give hope for effective applications to real systems

Effect of electronelectron correlations on positron-electron momentum density distributions

The calculations of the influence of the self-energy effects on the electron-positron (e-p) enhancement factors and the e-p momentum distributions are presented. The approach bases on the novel formulation of the Bethe- -Goldstone (B-G) equation for the positron in an electron gas where the scattering of the electrons into the states below the Fermi surface due to the self-energy effects is allowed. This equation has been solved and the corresponding e-p enhancement factors and momentum distributions have been found. The agreement between the absolute values of the theoretical calculations and experimental data has improved noticeably

Investigation of Electron-Positron Correlations by Monte Carlo Simulation

Earlier theoretical studies, as well as recent calculations of positron annihilation rates in metals, show that some basic problems concerning electron-positron (e-p) interaction have not been solved satisfactorily, even for homogeneous media (the electron gas). In turn, the "computer experiments" e.g. quantum Monte Carlo simulations applied to these problems by several authors yielded only fragmentary, inaccurate and even incorrect results for smaller electron densities. It is shown in the present paper that the quantum Monte Carlo method may be useful in investigations of positron interactions with electrons. Reasonable annihilation rates have been obtained owing to appropriate construction of the trial function and taking into account the 3-particle correlations (i.e. dependence of the electron-electron (e-e) interaction on the distance from the positron). Moreover, the method of "exact determination" (without any fitting) of positron annihilation rates on the basis of the variational trial function was proposed. One also found the way of calculating the momentum dependent enhancement factors, the quantities not achievable within the Monte Carlo method until now