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We present a numerically efficient and accurate Multiple Scattering formalism, which is a generalization of the Multiple Scattering method with a truncated basis set [X. -G. Zhang and W. H. Butler, Phys. Rev. B 46,7433 (1992)]. Compared to the latter method, we keep the phase shifts of high angular momenta but apply approximations in the elements of the scattering matrix which is the subtraction of the unit matrix and the product of transition operator matrix and structure constant matrix. The detailed behaviour of our formalism for different types of calculations, where not full information of Green's function is needed, are discussed. We apply our formalism to study density of states of fcc Cu and silicon and C K-edge X-ray absorption spectra of graphene, in order to check the efficiency and accuracy of our formalism. We find that compared to Zhang's method, the accuracy is greatly improved by our method., Comment: 14 pages, 7 figures

6 pages, 5 figures.-- PACS number(s) : 78.70.Dm, 61.10.Ht.-- ArXiv pre-print: http://arxiv.org/abs/0706.4370, This work reports a theoretical study of the x-ray absorption near-edge structure spectra at both the Cu and the Mn K-edge in several Cu2MnM (M=Al, Sn, and In) Heusler alloys. Our results show that ab initio single-channel multiple-scattering calculations are able to reproduce the experimental spectra. Moreover, an extensive discussion is presented concerning the role of the final state potential needed to reproduce the experimental data of these half-metallic alloys. In particular, the effects of the cluster size and of the exchange and correlation potential needed in reproducing all the experimental x-ray absorption near edge structure features are discussed, This work was partially supported by the Spanish CICYT Grant No. MAT2005-06806-C04-04 . K.H. acknowledges a grant from Aragón DGA research mobility program , and J.C. acknowledges the Japanese Society for the Promotion of Science, Japan.