Calculation of positron states and annihilation in solids: A density-gradient-correction scheme

Abstract

The generalized gradient correction method for positron-electron correlation effects in solids ͓B. Barbiellini et al., Phys. Rev. B 51, 7341 ͑1995͔͒ is applied in several test cases. The positron lifetime, energetics, and momentum distribution of the annihilating electron-positron pairs are considered. The comparison with experiments shows systematic improvement in the predictive power of the theory compared to the local-density approximation results for positron states and annihilation characteristics. ͓S0163-1829͑96͒03824-6͔

First-principles calculation of positron annihilation characteristics at metal vacancies

“…The use of a LDA interpolation form based on the many-body calculations by Arponen and Pajanne 12 leads to lifetimes consistently shorter than the experimental ones and the corresponding GGA would then improve the agreement. 14,15 The LMTO-ASA and FP-LMTO methods, which use self-consistent electronic structures, give almost the same lifetimes. Therefore the ASA seems to work quite well for the positron in bulk metals, as it does for the electrons.…”

“…14 In order to improve the agreement between theory and experiment Barbiellini et al 14 have introduced a generalized gradient approximation ͑GGA͒ in which the enhancement factor in a given point depends both on the electron density and its gradient at that point. It has been found 15 that the ratio between the experimental and the LDA lifetimes is nearly constant for a wide range of materials. Therefore, a simple scaling would correct the LDA lifetimes to agree well with experiments.…”

Modeling the momentum distributions of annihilating electron-positron pairs in solids

“…The value ␣ = 0.22 has been found to give with the Arponen-Pajanne enhancement lifetimes in good agreement with the experiment. 26,27 One must note that also the correlation potential for the positron is gradient corrected in the scheme by Barbiellini et al However, the different enhancement factors cause directly most of the differences compared to the BN-LDA. The LDA parametrization of the correlation potential is the same in both schemes.…”

“…28 The LDA systematically underestimates positron lifetimes in materials because it overestimates the annihilation with core electrons for which the correlation effects are less important. 26,27 Therefore, Barbiellini et al 26,27 have presented a gradient-corrected scheme in which the enhancement factor ␥ is interpolated between the LDA ͑␥ = ␥ LDA , zero gradient͒ and the IPM values ͑␥ ϵ 1, infinite gradient͒ as a function of the charge density gradient ٌn − . Effectively, the interpolation means that the annihilation with valence electrons in the interstitial region is described using the LDA but when the density gradient is high ͑as near nuclei where the rapid oscillations of core and valence wave functions take place͒ the enhancement factor decreases and approaches the IPM limit ͑␥ ϵ 1͒.…”

Energetics of positron states trapped at vacancies in solids

“…For delocalized positron states in perfect bulk solids, there exist several systematic comparisons, [15][16][17][18] but for positron states trapped at vacancy defects, comparisons treating several materials and systems on the same footing are scarce. The reason may be in difficulties arising in the theoretical description, e.g., in the density-functional theory 19,20 ͑DFT͒, the local-density approximation ͑LDA͒ for the electron exchange and correlation underestimates the energy band gap in semiconductors which may have severe consequences on the localized electron states and the ionic structure at defects.…”