Approximate k-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number {\kappa}. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C_{s} from the valence energy spectrum of particle and also for pseudospin symmetry constant C_{ps} from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter {\alpha}. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when {\alpha} becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.Comment: 21 pages, 6 figure

Global pattern of leaf litter nitrogen and phosphorus in woody plants

Forest ecosystems exert an important influence on global biogeochemical cycles. A global dataset of nitrogen (N) and phosphorus (P) concentrations in leaf- litter of woody plants was compiled from the literature. Among the 677 data sets, 482 included P concentrations and the N:P ratio. At a global scale, the mean leaf-litter N and P and N:P ratio were 10.9 mg g-1, 0.85 mg g-1 and 18.3, respectively. Leaf-litter N and P were significantly correlated. When the data was grouped by continents, the highest mean N was found in Africa (19.5 mg g-1), and the lowest in North America (8.18 mg g-1). P was significantly smaller in the Asian Islands (Japan and Malaysia, 0.44 mg g-1) than on the Asian mainland. For the global dataset, leaf-litter N increased linearly with mean annual temperature and annual precipitation and decreased with latitude. Although leaf- litter P showed no significant relationship with temperature, it declined linearly with precipitation and there was a convex quadratic relationship with latitude. For the global dataset and also for different functional groups (e.g. shrubs, evergreen broadleaf, deciduous broadleaf, and conifers) the leaf-litter N:P ratio generally followed a positive linear relationship with temperature and precipitation, and showed a concave quadratic response with latitude. The differences in leaf-litter N:P ratio among functional groups and among continents should be taken into account when modeling biogeochemical cycles in different regions as well as on a global scale