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Recent interesting experiments used scanning tunneling microscopy to studysystems involving Kondo impurities in quantum corrals assembled on Cu or noblemetal surfaces. The solution of the two-dimensional one-particle Schrodingerequation in a hard wall corral without impurity is useful to predict theconditions under which the Kondo effect can be projected to a remote location(the quantum mirage). To model a soft circular corral, we solve this equationunder the potential W*delta(r-r0), where r is the distance to the center of thecorral and r0 its radius. We expand the Green's function of electron surfacestates Gs0 for r<r0 as a discrete sum of contributions from single poles atenergies epsilon_i-I*delta_i. The imaginary part delta_i is the half-width ofthe resonance produced by the soft confining potential, and turns out to be asimple increasing function of epsilon_i. In presence of an impurity, we solvethe Anderson model at arbitrary temperatures using the resulting expression forGs0 and perturbation theory up to second order in the Coulomb repulsion U. Wecalculate the resulting change in the differential conductance Delta dI/dV as afunction of voltage and space, in circular and elliptical corrals, fordifferent conditions, including those corresponding to recent experiments. Themain features are reproduced. The role of the direct hybridization betweenimpurity and bulk, the confinement potential, the size of the corral andtemperature on the intensity of the mirage are analyzed. We also calculatespin-spin correlation functions.Comment: 13 pages, 12 figures, accepted for publication in Phys. Rev. B.  Calculations of spin correlations within an additional approximation adde

One- and many-body effects on mirages in quantum corrals