Qualitative feature of the low-lying spectrum of intrashell states of 4-valence-electron atoms derived from symmetry consideration

Inherent nodal surfaces existing in the wavefunctions of intrashell states of 4-valence-electron atoms have been investigated. The decisive effect of these surfaces has been demonstrated, the ordering of low-lying levels has been predicted, a primary classification scheme has been proposed, the existence of three rotation bands has been suggested.Comment: 10 pages, no figure

Deduction of the quantum unmbers of low-lying states of the (e+e+e-e-) system from symmetry consideration

The feature of the low-lying spectrum and a complete set of quantum numbers of the (e+e+e-e-) system have been deduced based on symmetry consideration. The existence of a low odd-parity L=1 excited state with the spins of the two electrons coupled to s1=1 and the two positrons coupled to s2=0 (or s1=0 and s2=1) and a low even-parity L=0 excited state with s1=s2=1 have been predicted. The discussion is generalized to 2-dimensional (e+e+e-e-) systems.Comment: 12 pages, 5 tables, no figure

Nucleon Effective E-Mass in Neutron-Rich Matter from the Migdal-Luttinger Jump

The well-known Migdal-Luttinger theorem states that the jump of the single-nucleon momentum distribution at the Fermi surface is equal to the inverse of the nucleon effective E-mass. Recent experiments studying short-range correlations (SRC) in nuclei using electron-nucleus scatterings at the Jefferson National Laboratory (JLAB) together with model calculations constrained significantly the Migdal-Luttinger jump at saturation density of nuclear matter. We show that the corresponding nucleon effective E-mass is consequently constrained to $M_0^{\ast,\rm{E}}/M\approx2.22\pm0.35$ in symmetric nuclear matter (SNM) and the E-mass of neutrons is smaller than that of protons in neutron-rich matter. Moreover, the average depletion of the nucleon Fermi sea increases (decreases) approximately linearly with the isospin asymmetry $\delta$ according to $\kappa_{\rm{p}/\rm{n}}\approx 0.21\pm0.06 \pm (0.19\pm0.08)\delta$ for protons (neutrons). These results will help improve our knowledge about the space-time non-locality of the single-nucleon potential in neutron-rich nucleonic matter useful in both nuclear physics and astrophysics.Comment: Discussions added. Version accepted by PL

H(2)-Unknotting Operation Related to 2-Bridge Links

This paper concerns the H(2)-unknotting numbers of links related to 2-bridge links. It consists of three parts. In the first part, we consider a necessary and sufficient condition for a 2-bridge link to have H(2)-unknotting number one. The second part concerns an explicit form of composite links with H(2)-unknotting number one. In the last part, we develop a method of studying the H(2)-unknotting numbers of some tangle unknotting number one knots via 2-bridge knots.Comment: 14 pages, 9 figure

Convergence rate of dimension reduction in Bose-Einstein condensates

In this paper, we study dimension reduction of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) modelling Bose-Einstein condensation under different limiting interaction and trapping frequencies parameter regimes. Convergence rates for the dimension reduction of 3D ground state and dynamics of the GPE in the case of disk-shaped condensation and cigar-shaped condensation are reported based on our asymptotic and numerical results. In addition, the parameter regimes in which the 3D GPE cannot be reduced to lower dimensions are identified.Comment: 27pages; 9 figure