Relativistic effect of spin and pseudospin symmetries

Dirac Hamiltonian is scaled in the atomic units $\hbar =m=1$, which allows us to take the non-relativistic limit by setting the Compton wavelength $\rightarrow 0$. The evolutions of the spin and pseudospin symmetries towards the non-relativistic limit are investigated by solving the Dirac equation with the parameter $\lambda$. With $\lambda$ transformation from the original Compton wavelength to 0, the spin splittings decrease monotonously in all spin doublets, and the pseudospin splittings increase in several pseudospin doublets, no change, or even reduce in several other pseudospin doublets. The various energy splitting behaviors of both the spin and pseudospin doublets with $\lambda$ are well explained by the perturbation calculations of Dirac Hamiltonian in the present units. It indicates that the origin of spin symmetry is entirely due to the relativistic effect, while the origin of pseudospin symmetry cannot be uniquely attributed to the relativistic effect.Comment: 15 pages, 7 figures, accepted by PR

Searching for dark matter via mono-ZZ boson production at the ILC

High energy colliders provide a new unique way to determine the microscopic properties of the dark matter (DM). Weakly interacting massive particles (WIMPs) are widely considered as one of the best DM candidates. It is usually assumed that the WIMP couples to the SM sector through its interactions with quarks and leptons. In this paper, we investigate the DM pair production associated with a $Z$ boson in an effective field theory framework at the International Linear Collider (ILC), which can be used to study the interactions between the DM and leptons. For illustrative purposes, we present the integrated and differential cross sections for the $e^+ e^- \rightarrow \chi \bar{\chi} Z$ process, where the $Z$ boson is radiated from the initial state electron or positron. Meanwhile, we analyze the neutrino pair production in association with a $Z$ boson as the SM background.Comment: 12 pages, 5 figure

Molecular separation by thermosensitive hydrogelmembranes

A new method for separation of molecules of different size is presented. The method is a useful addition to conventional separation methods which depend mainly on gel permeation chromatography using size exclusion. In the new method, hydrogel membranes are used which swelling level can be thermally controlled. In this study, a crosslinked poly(N-isopropylacrylamide¿co-butylmethacrylate 95:5mol%) membrane is used and three solutes of distinct molecular size: two dextrans with molecular weights of 150,000 and 4,400 g/mol respectively and uranine with a molecular weight of 376 g/mol. The swelling of the membranes as function of temperature was measured as well as the influence of the swelling level on the permeability of the three solutes. the influence of the swelling level and the solute size on the permeability was as expected from the free-volume theory. Based on these permeability phenomena, separation was performed in a continuous way by varying the membrane swelling at the appropriate time. A linear relationship between inverse membrane hydration and solute diffusion was found for uranine and dextran (MW=4,400), indicating the validity of the free-volume theory