Critical size of small particles for the development of resonances

It has been often claimed that the formation of a Kondo ground state requires a minimum particle radius of r{}ζR={}vF/{Δ}, where {Δ}=kB{T}K$ is the width of the Kondo resonance. We suggest that this minimum size is an artifact of the high symmetry of the sphere for which these calculations have been performed. A similar argument applies to other resonances. This question of minimal size is investigated for a Friedel resonance in two geometries, a sphere and a parallelepiped with a noninteger ratio of its edge lengths. A numerical calculation shows that the minimum linear size of the sample can be much smaller than ζR.