Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case

In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.

HAJAIEJ, H., MARKOWICH, P. A., & TRABELSI, S. (2013). MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE. Mathematical Models and Methods in Applied Sciences, 24(03), 599–626. doi:10.1142/s0218202513500619

The authors would like to thank warmly the anonymous referees for their careful reading and criticism of the original manuscript which led to several changes and improvements. H. H. extends his appreciation to the Deanship of Scientific Research at King Saud University for funding the work through the research group project No. RGP-VPP-124.

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