Impact of the Center of Mass Fluctuations on the Ground State Properties of Nuclei

Abstract

Ground state properties across the entire nuclear chart are described predominantly and rather accurately within the density functional theory (DFT). DFT however breaks many symmetries, among them the most important being the translational, rotational, and gauge symmetries. The translational symmetry breaking is special, since it is broken for all nuclei, unlike the rotational and gauge symmetries. The center-of-mass (CoM) correction most commonly used in the literature [see Vautherin and Brink, Phys. Rev. C {\bf 5}, 626 (1972) and Bender {\it et al.}, Rev. Mod. Phys. {\bf 75}, 121 (2003)] leads to a gain of 15,...,19 MeV, which varies rather weakly for medium and heavy mass nuclei. A better approximation to the CoM correction was suggested by Butler {\it et al.}, Nu cl. Phys. A {\bf 422}, 157 (1984) and its magnitude varies between 10 and 5 MeV from light to heavy nuclei, a correction which is also significantly larger than the RMS energy error in the Bethe-Weizsäcker mass formula, initially proposed by Gamow, Proc. Phys. Soc. A {\bf 126}, 157 (1930), which is at most 3.5 MeV, and which for heavy nuclei corresponds to about 0.2\% of their mass. ....