The leader operators of the (d+1)(d+1)-dimensional relativistic rotating oscillators

The main pairs of leader operators of the quantum models of relativistic rotating oscillators in arbitrary dimensions are derived. To this end one exploits the fact that these models generate P\"{o}schl-Teller radial problems with remarkable properties of supersymmetry and shape invariance.Comment: 11 page

Relativistic Hartree-Bogoliubov theory with finite range pairing forces in coordinate space: Neutron halo in light nuclei

The Relativistic Hartree Bogoliubov (RHB) model is applied in the self-consistent mean-field approximation to the description of the neutron halo in the mass region above the s-d shell. Pairing correlations and the coupling to particle continuum states are described by finite range two-body forces. Finite element methods are used in the coordinate space discretization of the coupled system of Dirac-Hartree-Bogoliubov integro-differential eigenvalue equations, and Klein-Gordon equations for the meson fields. Calculations are performed for the isotopic chains of Ne and C nuclei. We find evidence for the occurrence of neutron halo in heavier Ne isotopes. The properties of the 1f-2p orbitals near the Fermi level and the neutron pairing interaction play a crucial role in the formation of the halo. Our calculations display no evidence for the neutron halo phenomenon in C isotopes.Comment: 7 pages, Latex, 5 P.S. Figures, To appear in Phys. Rev. Let

Relativistic Hartree-Bogoliubov description of ground-state properties of Ni and Sn isotopes

The Relativistic Hartree Bogoliubov (RHB) theory is applied in the description of ground-state properties of Ni and Sn isotopes. The NL3 parameter set is used for the effective mean-field Lagrangian, and pairing correlations are described by the pairing part of the finite range Gogny interaction D1S. Fully self-consistent RHB solutions are calculated for the Ni ($28\leq N\leq 50$) and Sn ($50\leq N\leq 82$) isotopes. Binding energies, neutron separation energies, and proton and neutron $rms$ radii are compared with experimental data. The model predicts a reduction of the spin-orbit potential with the increase of the number of neutrons. The resulting energy splittings between spin-orbit partners are discussed, as well as pairing properties calculated with the finite range effective interaction in the $pp$ channel.Comment: 11 pages, RevTex, 12 p.s figures, submitted to Phys. Rev.

Relativistic shape invariant potentials

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected and replaced by two new statement

Proton drip-line nuclei in Relativistic Hartree-Bogoliubov theory

Ground-state properties of spherical even-even nuclei $14\leq Z \leq 28$ and $N=18,20,22$ are described in the framework of Relativistic Hartree Bogoliubov (RHB) theory. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite range Gogny interaction D1S. Binding energies, two-proton separation energies, and proton $rms$ radii that result from fully self-consistent RHB solutions are compared with experimental data. The model predicts the location of the proton drip-line. The isospin dependence of the effective spin-orbit potential is discussed, as well as pairing properties that result from the finite range interaction in the $pp$ channel.Comment: 12 pages, RevTex, 10 p.s figures, submitted to Phys. Rev.

Lattice Gauge Description of Colliding Nuclei

We propose a novel formalism for simultaneously describing both, the hard and soft parton dynamics in ultrarelativistic collisions of nuclei. The emission of gluons from the initially coherent parton configurations of the colliding nuclei and low-$p_t$ color coherence effects are treated in the framework of a Yang-Mills transport equation on a coupled lattice-particle system. A collision term is added to the transport equation to account for the remaining intermediate and high-$p_t$ interactions in an infrared finite manner.Comment: 8 page

Seasonal cycle and temperature dependence of pinene oxidation products, dicarboxylic acids and nitrophenols in fine and coarse air particulate matter

Filter samples of fine and coarse air particulate matter (PM) collected over a period of one year in central Europe (Mainz, Germany) were analyzed for water-soluble organic compounds (WSOCs), including the α- and β-pinene oxidation products pinic acid, pinonic acid and 3-methyl-1,2,3-butanetricarboxylic acid (3-MBTCA), as well as a variety of dicarboxylic acids and nitrophenols. Seasonal variations and other characteristic features in fine, coarse, and total PM (TSP) are discussed with regard to aerosol sources and sinks in comparison to data from other studies and regions. The ratios of adipic acid and phthalic acid to azelaic acid indicate that the investigated aerosol samples were mainly influenced by biogenic sources. A strong Arrhenius-type correlation was found between the 3-MBTCA concentration and inverse temperature (<i>R</i><sup>2</sup> = 0.79, <i>n</i> = 52, <i>E</i><sub>a</sub> = 126 ± 10 kJ mol<sup>−1</sup>, temperature range 275–300 K). Model calculations suggest that the temperature dependence observed for 3-MBTCA can be explained by enhanced photochemical production due to an increase of hydroxyl radical (OH) concentration with increasing temperature, whereas the influence of gas-particle partitioning appears to play a minor role. The results indicate that the OH-initiated oxidation of pinonic acid is the rate-limiting step in the formation of 3-MBTCA, and that 3-MBTCA may be a suitable tracer for the chemical aging of biogenic secondary organic aerosol (SOA) by OH radicals. An Arrhenius-type temperature dependence was also observed for the concentration of pinic acid (<i>R</i><sup>2</sup> = 0.60, <i>n</i> = 56, <i>E</i><sub>a</sub> = 84 ± 9 kJ mol<sup>−1</sup>); it can be tentatively explained by the temperature dependence of biogenic pinene emission as the rate-limiting step of pinic acid formation

Spherical Relativistic Hartree theory in a Woods-Saxon basis

The Woods-Saxon basis has been suggested to replace the widely used harmonic oscillator basis for solving the relativistic mean field (RMF) theory in order to generalize it to study exotic nuclei. As examples, relativistic Hartree theory is solved for spherical nuclei in a Woods-Saxon basis obtained by solving either the Schr\"odinger equation or the Dirac equation (labelled as SRHSWS and SRHDWS, respectively and SRHWS for both). In SRHDWS, the negative levels in the Dirac Sea must be properly included. The basis in SRHDWS could be smaller than that in SRHSWS which will simplify the deformed problem. The results from SRHWS are compared in detail with those from solving the spherical relativistic Hartree theory in the harmonic oscillator basis (SRHHO) and those in the coordinate space (SRHR). All of these approaches give identical nuclear properties such as total binding energies and root mean square radii for stable nuclei. For exotic nuclei, e.g., $^{72}$Ca, SRHWS satisfactorily reproduces the neutron density distribution from SRHR, while SRHHO fails. It is shown that the Woods-Saxon basis can be extended to more complicated situations for exotic nuclei where both deformation and pairing have to be taken into account.Comment: 12 pages, 9 figure