The reactions γp → ηp and γp → η 0 p are measured from their thresholds up to the center-of-mass energy W ¼ 1.96 GeV with the tagged-photon facilities at the Mainz Microtron, MAMI. Differential cross sections are obtained with unprecedented statistical accuracy, providing fine energy binning and full production-angle coverage. A strong cusp is observed in the total cross section for η photoproduction at the energies in the vicinity of the η 0 threshold, W ¼ 1896 MeV (E γ ¼ 1447 MeV). Within the framework of a revised ηMAID isobar model, the cusp, in connection with a steep rise of the η 0 total cross section from its threshold, can only be explained by a strong coupling of the poorly known Nð1895Þ1=2 − state to both ηp and η 0 p. Including the new high-accuracy results in the ηMAID fit to available η and η 0 photoproduction data allows the determination of the Nð1895Þ1=2 − properties.

The Hellmann potential, which is a superposition of an attractive Coulomb potential −a/r and a Yukawa potential b e−δr/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov—Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.

No abstract

We study the D-dimensional Schrödinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov (NU) method, we calculate the corresponding eigenfunctions and eigenvalues.

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov method, we obtain approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.

The Tietz‐Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Measurement of the ω → π 0 e + e − and η → e + e − γ Dalitz decays with the A2 setup at MAMI The Dalitz decays η → e + e − γ and ω → π 0 e + e − have been measured in the γp → ηp and γp → ωp reactions, respectively, with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The value obtained for the slope parameter of the electromagnetic transition form factor of η, Λ −2 η = (1.97 ± 0.11tot ) GeV −2 , is in good agreement with previous measurements of the η → e + e − γ and η → µ + µ − γ decays. The uncertainty obtained in the value of Λ −2 η is lower than in previous results based on the η → e + e − γ decay. The value obtained for the ω slope parameter, Λ −2 ωπ 0 = (1.99 ± 0.21tot) GeV −2 , is somewhat lower than previous measurements based on ω → π 0 µ + µ − , but the results for the ω transition form factor are in better agreement with theoretical calculations, compared to earlier experiments.

The spin polarizabilities of the nucleon describe how the spin of the nucleon responds to an incident polarized photon. The most model-independent way to extract the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the Δð1232Þ region using circularly polarized incident photons and a transversely polarized proton target at the Mainz Microtron. Fits to asymmetry data were performed using a dispersion model calculation and a baryon chiral perturbation theory calculation, and a separation of all four proton spin polarizabilities in the multipole basis was achieved. The analysis based on a dispersion model calculation yields γ E1E1 ¼ −3.5 AE 1.2, γ M1M1 ¼ 3.16 AE 0.85, γ E1M2 ¼ −0.7 AE 1.2, and γ M1E2 ¼ 1.99 AE 0.29, in units of 10 −4 fm 4 . DOI: 10.1103/PhysRevLett.114.112501 PACS numbers: 25.20.Lj, 13.40.-f, 13.60.Fz, 13.88.+e Electromagnetic polarizabilities are fundamental properties of composite systems such as molecules, atoms, nuclei, and hadrons [1]. Whereas magnetic moments provide information about the ground-state properties of a system, polarizabilities provide information about the excited states of the system. For atomic systems, polarizabilities are of the order of the atomic volume. For hadrons, polarizabilities are much smaller than the volume, typically of order PRL 114,