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We give a new, short proof of the regularity away from the nuclei of theelectronic density of a molecule obtained in [1,2]. The new argument is basedon the regularity properties of the Coulomb interactions underlined in [3,4]and on well-known elliptic technics. [1] S. Fournais, M. Hoffmann-Ostenhof, T.Hoffmann-Ostenhof, T. Oe stergaard Soerensen: The electron density is smoothaway from the nuclei. Comm. Math. Phys. 228, no. 3 (2002), 401-415. [2] S.Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oestergaard Soerensen:Analyticity of the density of electronic wave functions. Ark. Mat. 42, no. 1(2004), 87-106. [3] W. Hunziker: Distortion analyticity and molecularresonances curves. Ann. Inst. H. Poincar{\'e}, s. A, t. 45, no 4, 339-358(1986). [4] M. Klein, A. Martinez, R. Seiler, X.P. Wang: On theBorn-Oppenheimer expansion for polyatomic molecules. Comm. Math. Phys. 143, no.3, 607-639 (1992). The paper is published in Letters in Mathematical Physics93, number 1, pp. 73-83, 2010. The original publication is available at"www.springerlink.com".

A new proof of the analyticity of the electronic density of molecules