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Lipkin translational-symmetry restoration in the mean-field and energy-density-functional methods

Jacek Dobaczewski
Institute of Theoretical Physics, University of Warsaw, Hoza 69, PL-00681 Warsaw, Poland
Department of Physics, P.O. Box 35 (YFL), FI-40014 University of Jyväskylä, Finland


Based on the 1960 idea of Lipkin, the minimization of energy of a symmetry-restored mean-field state is equivalent to the minimization of a corrected energy of a symmetry-broken state with the Peierls-Yoccoz mass. It is interesting to note that the "unphysical" Peierls-Yoccoz mass, and not the true mass, appears in the Lipkin projected energy. The Peierls-Yoccoz mass can be easily calculated from the energy and overlap kernels, which allows for a systematic, albeit approximate, restoration of translational symmetry within the energy-density formalism. Analogous methods can also be implemented for all other broken symmetries.

Jacek Dobaczewski 2009-06-28