Electron-positron overlap function

Studies on other high-temperature superconductors Positron annihilation measurements across Tc, coupled with the calculations of PDD have been carried out in a variety of hole-doped superconductors that include YBa2Cu40g [48], Bi-Sr-Ca-Cu-0 [49], and Tl-Ba-Ca-Cu-0 [50, 51] systems. We will not labor with the details here, except to state that a variety of temperature dependencies are seen and these can be rationalized when the results are analysed in terms of positron density distribution and the electron-positron overlap function [39]. These calculations show that the positron s sensitivity to the superconducting transition arises primarily from the ability to probe the Cu-O network in the Cu-0 layer. The different temperature dependencies of lifetime, i.e., both the increase and decrease, can be understood in terms of a model of local electron transfer from the planar oxygen atom to the apical oxygen atom, after taking into account the correct positron density distribution within the unit cell of the cuprate superconductor. 

The interpolation formula that gives the electron-positron correlation energy functional was found by Borohski and Nieminen [98]. The positron annihilation rate A is proportional to the overlap between the positron and electron densities. In the LDA approximation [72],... 

Positroniums (Ps) have two spin states ortho (o-Ps) (triplet) and para (p-Ps) (singlet). In condensed matter 75% of the Ps formed will be o-Ps and 25% p-Ps and their existence will depend on the existence of regions with low electron density [4]. The lifetime of positrons depends on the overlap integral of the wave functions of the positron and local electrons and, thus, it is related with the electronic structure of the material [5]. Since the positrons thermalize after a few ps, and the subsequent lifetime is roughly two orders of magnitude higher than the thermalization time, the lifetime of positrons within the matter will effectively depend upon the local electron density [5]. Thus, PALS implies the measurement of the lifetime, t, which is the inverse of the annihilation rate, X, defined by [ 1 ] C p r)p r)dr (1)... 

Quantum chemistry predicts that the annihilation lifetime of a positron species is generally determined by the degree of overlapping of positron and electron wave functions, which leads e.g. to the intrinsic lifetime of the ortho-Ps of 1.4 x 10 sec. In a condensed matter it is obvious that the electron density at the position of the positron will greatly depend on the macroscopic and microscopic (mass) density and thus on parameters such as phase and temperature. This rather simple approach has led to the development of the "free volume" or "excluded volume" model (20, 28-29), whose basic feature it is that the lifetime of a positron or Ps trapped in such a material will depend on the free volume which it has available. 

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