Shell and isospin effects in nuclear charge radii

The shell effect and isospin effect in nuclear charge radii are systematically investigated and a four-parameter formula is proposed for the description of the root-mean-square (rms) charge radii by combining the shell corrections and deformations of nuclei obtained from the Weizs\"acker-Skyrme mass model. The rms deviation with respect to the 885 measured charge radii falls to 0.022 fm. The proposed formula is also applied for the study of the charge radii of super-heavy nuclei and nuclear symmetry energy. The linear relationship between the slope parameter L of the nuclear symmetry energy and the rms charge radius difference of 30S - 30Si mirror pair is clearly observed. The estimated slope parameter is about $L=54 \pm 19$ MeV from the coefficient of the isospin term in the proposed charge radius formula.Comment: 7 figures, 1 table, accepted for publication as a Rapid Communication in Physical Review

Conserved Quantities of harmonic asymptotic initial data sets

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is rather difficult in general. We found a large family of initial data sets on which such a calculation can be carried out effectively. These are initial data sets of harmonic asymptotics, first proposed by Corvino and Schoen to solve the full vacuum constraint equation. In the second half of this article, the new total angular momentum and center of mass for these initial data sets are computed explicitly.Comment: 20 pages. Invited article for the volume "Surveys in Differential Geometry", a Jubilee Volume on General Relativity and Mathematics celebrating 100 Years of General Relativity, edited by L. Bieri and S.T. Ya