Solid State Communications, Vol. 21, pp. 293-296,1977. Pergamon Press. Printed in Great Britain POSITRON ANNIHILATION IN SMALL METAL VOIDS* P. Jena and A.K. Gupta Physics Department, Northwestern University, Evanston, IL 60201, U.S.A. and K.S. Singwi Physics Department, Northwestern University, Evanston, IL 60201, U.S.A. and Argonne National Laboratory, Argonne, IL 60439, U.S.A. (Received 4 October 1976 by L. Hedin) The electron density profile around small voids of varying radii in Al is calculated in a fully self-consistent manner using the density-functional formalism of Hohenberg-Kohn-Sham. The results are then used to calculate positron lifetimes and angular correlation between annihilation photons as a function of the size of the void. THE STUDY of voids in materials used in fast reactor technology has assumed great importance during the last few years.le3 An important tool of investigation in this area is the study of the characteristics of positron annhil- ation in voids, e.g. the positron lifetime and angular cor- relation between annihilation photons. Further, voids smaller than 100 A diameter can only be probed by positron annihilation technique since the conventional electron microscopy is inadequate. To date, the experi- mental work has established the broad fact2 that there exists a correlation between the size of a void and the above mentioned two characteristics. To our knowledge, no quantitative theoretical work has been done in this area. In this letter we present a fully self-consistent cal- culation, based on Hohenberg-Kohn-Sham (HKS) density-functional formalism,4 of the electron charge densities around voids of varying sizes in a simple metal. The effective positron-defect potential and positron wave functions have been calculated from first principles. This then enables us to compute positron lifetimes and angular-correlation curves for voids of different sizes. The results are in good agreement with experimental data where available. From our calculations we are led to conclude that for a sufficiently large void (radius > 10 A), the electron density profile would resemble closely that of a surface profile. We have chosen, for obvious reasons of simplicity, * Research supported by the National Science Foun- dation through Northwestern University Materials Research Center and in part by the U.S. Energy Research and Development Administration. aluminum metal for our study. Our model is to replace Al-metal by a jellium of r, = 2.07. A void of radius a is then created by scooping a spherical hole in the uniform positive background. This lead to an ion density, n+(r) = n&r - a) The electron density is given by (1) n(r) = 1 Ircli(r)12, i (2) where $i’S are the solutions, within the HKS formalism,4 of an effective one-particle equation r-V” + ~effCr)l+i(r) = eitii(r), (3) ei being the energy of the occupied state i. We have used Rydberg atomic units throughout this paper. V,,,(r) can be written as v,ff(r) = -Q(r) + &bE,dn)l - i-4~0) [ I . (4) The electrostatic potential Q(r) is obtained from the charge density by solving the Poisson’s equation. The second term in Equation (4) is the exchange-correlation potential in the local-density approximation defined with respect to cc,,(nO) for the average density no of Al metal. For eXc(n) we took the values of Vashishta and Singwi.5 The electron charge density n(r) is given by n(r) = f kF s dkk’ 2 (21+ 1) (5) 0 I=0 where the radial part u,,(r) of the electron wave function 293