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Merz, Konstantin; Siedentop, Heinz (2019): THE ATOMIC DENSITY ON THE THOMAS-FERMI LENGTH SCALE FOR THE CHANDRASEKHAR HAMILTONIAN. In: Reports on Mathematical Physics, Vol. 83, No. 3: pp. 387-391
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We consider a large neutral atom of atomic number Z, modelled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably resealed one-particle ground state density on the Thomas-Fermi length scale Z(-1/3). Using an observation by Fefferman and Seco, we find that the density on this scale converges to the minimizer of the Thomas-Fermi functional of hydrogen as Z -> infinity when Z/c is fixed to a value not exceeding 2/pi. This shows that the electron density on the Thomas-Fermi length scale does not exhibit any relativistic effects.