Recurrence and differential relations for spherical spinors

We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) $\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic atomic, molecular, and solid state physics, as well as in relativistic quantum chemistry. First, we list finite expansions in the spherical spinor basis of the expressions $\mathbf{A}\cdot\mathbf{B}\,\Omega_{\kappa\mu}(\mathbf{n})$ and {$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\, \Omega_{\kappa\mu}(\mathbf{n})$}, where $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{C}$ are either of the following vectors or vector operators: $\mathbf{n}=\mathbf{r}/r$ (the radial unit vector), $\mathbf{e}_{0}$, $\mathbf{e}_{\pm1}$ (the spherical, or cyclic, versors), $\boldsymbol{\sigma}$ (the $2\times2$ Pauli matrix vector), $\hat{\mathbf{L}}=-i\mathbf{r}\times\boldsymbol{\nabla}I$ (the dimensionless orbital angular momentum operator; $I$ is the $2\times2$ unit matrix), $\hat{\mathbf{J}}=\hat{\mathbf{L}}+1/2\boldsymbol{\sigma}$ (the dimensionless total angular momentum operator). Then, we list finite expansions in the spherical spinor basis of the expressions $\mathbf{A}\cdot\mathbf{B}\,F(r)\Omega_{\kappa\mu}(\mathbf{n})$ and $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\, F(r)\Omega_{\kappa\mu}(\mathbf{n})$, where at least one of the objects $\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$ is the nabla operator $\boldsymbol{\nabla}$, while the remaining ones are chosen from the set $\mathbf{n}$, $\mathbf{e}_{0}$, $\mathbf{e}_{\pm1}$, $\boldsymbol{\sigma}$, $\hat{\mathbf{L}}$, $\hat{\mathbf{J}}$.Comment: LaTeX, 12 page

New exact solution of Dirac-Coulomb equation with exact boundary condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z > 137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.Comment: 12 pages,no figure

A comparative study on q-deformed fermion oscillators

In this paper, the algebras, representations, and thermostatistics of four types of fermionic q-oscillator models, called fermionic Newton (FN), Chaichian-Kulish-Ng (CKN), Parthasarathy-Viswanathan-Chaichian (PVC), Viswanathan-Parthasarathy-Jagannathan-Chaichian (VPJC), are discussed. Similarities and differences among the properties of these models are revealed. Particular emphasis is given to the VPJC-oscillators model so that its Fock space representation is analyzed in detail. Possible physical applications of these models are concisely pointed out.Comment: 32 pages, 2 figures, to appear in Int. J. Theor. Phys. (IJTP

The warm, the excited, and the molecular gas: GRB 121024A shining through its star-forming galaxy★

We present the first reported case of the simultaneous metallicity determination of a gamma-ray burst (GRB) host galaxy, from both afterglow absorption lines as well as strong emission-line diagnostics. Using spectroscopic and imaging observations of the afterglow and host of the long-duratio

Effect of event selection on jetlike correlation measurement in d+Au collisions at sNN=200 GeV

AbstractDihadron correlations are analyzed in sNN=200 GeV d+Au collisions classified by forward charged particle multiplicity and zero-degree neutral energy in the Au-beam direction. It is found that the jetlike correlated yield increases with the event multiplicity. After taking into account this dependence, the non-jet contribution on the away side is minimal, leaving little room for a back-to-back ridge in these collisions

Beam-energy Dependence Of Charge Balance Functions From Au + Au Collisions At Energies Available At The Bnl Relativistic Heavy Ion Collider

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Balance functions have been measured in terms of relative pseudorapidity (Δη) for charged particle pairs at the BNL Relativistic Heavy Ion Collider from Au + Au collisions at sNN=7.7GeV to 200 GeV using the STAR detector. These results are compared with balance functions measured at the CERN Large Hadron Collider from Pb + Pb collisions at sNN=2.76TeV by the ALICE Collaboration. The width of the balance function decreases as the collisions become more central and as the beam energy is increased. In contrast, the widths of the balance functions calculated using shuffled events show little dependence on centrality or beam energy and are larger than the observed widths. Balance function widths calculated using events generated by UrQMD are wider than the measured widths in central collisions and show little centrality dependence. The measured widths of the balance functions in central collisions are consistent with the delayed hadronization of a deconfined quark gluon plasma (QGP). The narrowing of the balance function in central collisions at sNN=7.7 GeV implies that a QGP is still being created at this relatively low energy. © 2016 American Physical Society.942CNPq, Conselho Nacional de Desenvolvimento Científico e TecnológicoMinistry of Education and Science of the Russian FederationMOE, Ministry of Education of the People's Republic of ChinaMOST, Ministry of Science and Technology of the People's Republic of ChinaNRF-2012004024, National Research FoundationNSF, National Stroke FoundationConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Mid-rapidity anti-proton to proton ratio from Au+Au collisions at sNN=130 \sqrt{s_{NN}} = 130 GeV

We report results on the ratio of mid-rapidity anti-proton to proton yields in Au+Au collisions at \rts = 130 GeV per nucleon pair as measured by the STAR experiment at RHIC. Within the rapidity and transverse momentum range of $|y|<0.5$ and 0.4 $<p_t<$ 1.0 GeV/$c$, the ratio is essentially independent of either transverse momentum or rapidity, with an average of $0.65\pm 0.01_{\rm (stat.)} \pm 0.07_{\rm (syst.)}$ for minimum bias collisions. Within errors, no strong centrality dependence is observed. The results indicate that at this RHIC energy, although the $p$-\pb pair production becomes important at mid-rapidity, a significant excess of baryons over anti-baryons is still present.Comment: 5 pages, 3 figures, accepted by Phys. Rev. Let

Multiplicity dependence of inclusive J/psi production at midrapidity in pp collisions at root s=13 TeV

Measurements of the inclusive J/psi yield as a function of charged-particle pseudorapidity density dN(ch)/d eta in pp collisions at root s = 13 TeV with ALICE at the LHC are reported. The J/psi meson yield is measured at midrapidity (vertical bar y vertical bar <0.9) in the dielectron channel, for events selected based on the charged-particle multiplicity at midrapidity (vertical bar eta vertical bar <1) and at forward rapidity (-3.7 <eta <-1.7 and 2.8 <eta <5.1); both observables are normalized to their corresponding averages in minimum bias events. The increase of the normalized J/psi yield with normalized dN(ch)/d eta is significantly stronger than linear and dependent on the transverse momentum. The data are compared to theoretical predictions, which describe the observed trends well, albeit not always quantitatively. (C) 2020 European Organization for Nuclear Research. Published by Elsevier B.V.Peer reviewe

Energy dependence of acceptance-corrected dielectron excess mass spectrum at mid-rapidity in Au + Au collisions at s NN = 19.6 and 200 GeV

The acceptance-corrected dielectron excess mass spectra, where the known hadronic sources have been subtracted from the inclusive dielectron mass spectra, are reported for the first time at mid-rapidity |yee|&lt;1 in minimum-bias Au+Au collisions at √sNN=19.6 and 200 GeV. The excess mass spectra are consistently described by a model calculation with a broadened ρ spectral function for Mee&lt;1.1 GeV/c2. The integrated dielectron excess yield at √sNN=19.6 GeV for 0.

Dielectron Azimuthal Anisotropy At Mid-rapidity In Au+au Collisions At Snn =200 Gev

We report on the first measurement of the azimuthal anisotropy (v2) of dielectrons (e+e- pairs) at mid-rapidity from sNN=200 GeV Au+Au collisions with the STAR detector at the Relativistic Heavy Ion Collider (RHIC), presented as a function of transverse momentum (pT) for different invariant-mass regions. In the mass region Mee<1.1 GeV/c2 the dielectron v2 measurements are found to be consistent with expectations from π0,η,ω, and φ decay contributions. In the mass region 1.1<Mee<2.9GeV/c2, the measured dielectron v2 is consistent, within experimental uncertainties, with that from the cc¯ contributions.906Adams, J., (2005) Nucl. Phys. A, 757, p. 102. , NUPABL 0375-9474Arsene, I., (2005) Nucl. Phys. A, 757, p. 1. , NUPABL 0375-9474Adcox, K., (2005) Nucl. Phys. A, 757, p. 184. , NUPABL 0375-9474Back, B.B., (2005) Nucl. Phys. A, 757, p. 28. , NUPABL 0375-9474Rapp, R., Wambach, J., (2002) Adv. Nucl. Phys., 25, p. 1. , 0065-2970David, G., Rapp, R., Xu, Z., (2008) Phys. 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