The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormalization group (SRG) method. The Schrödinger equation is taken as an example, corresponding to the lowest-order approximation in transforming a Dirac equation into a diagonal form by using the SRG. It is shown that while the spin-symmetry-conserving term appears in the single-particle Hamiltonian H, the PSS-conserving term appears naturally in its SUSY partner HamiltonianH.The eigenstates of Hamiltonians H andH are exactly one-to-one identical except for the so-called intruder states. In such a way, the origin of PSS deeply hidden in H can be traced in its SUSY partner HamiltonianH. The perturbative nature of PSS in the present potential without spin-orbit term is demonstrated by the perturbation calculations, and the PSS-breaking term can be regarded as a very small perturbation on the exact PSS limits. A general tendency that the pseudospinorbit splittings become smaller with increasing single-particle energies can also be interpreted in an explicit way.

Perturbation theory is used systematically to investigate the symmetries of the Dirac Hamiltonian and their breaking in atomic nuclei. Using the perturbation corrections to the single-particle energies and wave functions, the link between the single-particle states in realistic nuclei and their counterparts in the symmetry limits is discussed. It is shown that the limit of S-V=const and relativistic harmonic oscillator (RHO) potentials can be connected to the actual Dirac Hamiltonian by the perturbation method, while the limit of S+V=const cannot, where S and V are the scalar and vector potentials, respectively. This indicates that the realistic system can be treated as a perturbation of spin-symmetric Hamiltonians, and the energy splitting of the pseudospin doublets can be regarded as a result of small perturbation around the Hamiltonian with RHO potentials, where the pseudospin doublets are quasidegenerate.Comment: 5 pages, 4 figures, Phys. Rev. C in pres

Droplet microfluidics technology is recently a highly interesting platform in material fabrication. Droplets can precisely monitor and control entire material fabrication processes and are superior to conventional bulk techniques. Droplet production is controlled by regulating the channel geometry and flow rates of each fluid. The micro-scale size of droplets results in rapid heat and mass-transfer rates. When used as templates, droplets can be used to develop reproducible and scalable microparticles with tailored sizes, shapes and morphologies, which are difficult to obtain using traditional bulk methods. This technology can revolutionize material processing and application platforms. Generally, microparticle preparation methods involve three steps: (1) the formation of micro-droplets using a microfluidics generator; (2) shaping the droplets in micro-channels; and (3) solidifying the droplets to form microparticles. This review discusses the production of microparticles produced by droplet microfluidics according to their morphological categories, which generally determine their physicochemical properties and applications.

A novel class of ZnSalens (ZnL(1-10)) with lipophilic and cationic conjugates as optical probes in single and two-photon fluorescence microscopy images of living cells were prepared, which exhibited chemo- and photostability, low cytotoxicity and high subcellular selectivity.