Optical non-linear response of small metal particles: A complete self-consistent calculation including exchange and correlation

We report a fully self-consistent calculation of the third-order Kerr polarisation in small metal spheres embedded in a dielectric medium. The random phase approximation with exchange is used leading to a fully symmetric expression accounting for the non-locality of the electronic response as well as exchange and correlation. This treatment generalises the results reported in a previous paper by Hache et al. The expression of the octupolar component of the charge density is also given.