Positron-annihilation characteristics in an electron gas from low to high densities

1999

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.

Section: Methodsmentioning

confidence: 99%

“…This yields a prescription for normalization of w, if the integral (14) gives a constant α instead of 1 then…”

Section: Methodsmentioning

confidence: 99%

A New Project for Calculations of e⁺-e^-Interaction in Real Metals

1999

“…(12,13) and v(s) is a small correction computed self-consistently. This approach allowed us to obtain the annihilation rate as a function of r s , the momentum distribution of annihilation quanta and the correlation energy [3][4][5].…”

Section: The Two-particle Approximationmentioning

confidence: 99%

“…[3][4][5] in the hope that a better theory would lead to lower annihilation rates. At the same time such calculations would help to find how good is the self-consistent Born approximation used in the PHNC approach.…”

Section: Introductionmentioning

confidence: 99%

Electron-Positron Interaction in Jellium: Optimization of the Perturbed Hypernetted-Chain Approach

Stachowiak

2006

The perturbed hypernetted-chain approach to electron-positron interaction in jellium consists in assuming the wave function of the system in the form of a Slater determinant built of single-electron functions presented as. s is the distance between the electron and the positron. The function w(s) is obtained by solving the equation of Gondzik and Stachowiak. The function ϕ k (s) is computed by applying a self-consistent Born approximation. The idea of the paper is to modify the function w(s) in such a way as to obtain from the Born approximation as precise results as possible. It is shown that the influence of such modifications on physical predictions is small. This shows how good is the perturbed hypernetted-chain approach. The annihilation rates obtained in such a way decrease somewhat, becoming closer to experimental expectations.

“…[16] and [17] it was assumed that the form (17) of the wave function where w(s) is obtained by solving the Gondzik-Stachowiak equation…”

Section: The Perturbed Hnc Approachmentioning

confidence: 99%

Electron-Positron Interaction in Metals. Theory and Experiment

Stachowiak

2005

The electron-positron interaction greatly complicates the interpretation of positron annihilation data. The two-detector Doppler measurements of Mijnarends et al. as well as our theoretical calculations point at the conclusion that the local density approximation to e + −e − interaction is a good way of treating this problem in real metals, at least the simplest ones. This shows that e + −e − interaction in an electron gas is the key to understanding this phenomenon also in inhomogeneous systems. On the basis of dozens of experiments one comes to the conclusion that the well known formula of Boroński and Nieminen for the electron accumulation on the positron in jellium describes the best the positron lifetimes in metals. However, it is based on the calculations of Lantto which start from a physically oversimplified trial function. The results of Arponen and Pajanne, of Rubaszek and Stachowiak, and of Stachowiak and Lach lead to too short positron lifetimes in spite of using less controversial assumptions. The discrepancy is of the order of 8 to 15% for r s = 2. This shows that we still do not fully understand e + −e − interaction even in an electron gas.