Approximate solution of the pairing Hamiltonian in the Berggren basis

We derive the approximate solution for the pairing Hamiltonian in the Berggren ensemble of single particle states including bound, resonance and non-resonant scattering states. We show that this solution is reliable in the limit of a weak pairing interaction

Nuclear three-body problem in the complex energy plane: Complex-Scaling-Slater method

The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape towards the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. To describe open quantum systems, we introduce a Complex Scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow Shell Model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an $\alpha$+ n + n cluster system. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly-bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method, if it can be applied, can provide an additional information about partial energy widths associated with individual thresholds.Comment: 15 pages, 16 figure

Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave

Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive analytical asymptotic formulas valid for arbitrary energies and partial waves. Moreover, it is possible to extend these formulas for complex values of parameters.Comment: 5 pages, 2 figure

Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs and Alkali-mediated Interactions

Starting from a model of rigid interacting C60 polymer chains on an orthorhombic lattice, we study the mutual orientation of the chains and the stability of the crystalline structures Pmnn and I2/m. We take into account i) van der Waals interactions and electric quadrupole interactions between C60 monomers on different chains as well as ii) interactions of the monomers with the surrounding alkali atoms. The direct interactions i) always lead to an antiferrorotational structure Pmnn with alternate orientation of the C60 chains in planes (001). The interactions ii) with the alkalis consist of two parts: translation-rotation (TR) coupling where the orientations of the chains interact with displacements of the alkalis, and quadrupolar electronic polarizability (ep) coupling, where the electric quadrupoles on the C60 monomers interact with induced quadrupoles due to excited electronic d states of the alkalis. Both interactions ii) lead to an effective orientation-orientation interaction between the C60 chains and always favor the ferrorotational structure I2/m where C60 chains have a same orientation. The structures Pmnn for KC60 and I2/m for Rb- and CsC60 are the result of a competition between the direct interaction i) and the alkali-mediated interactions ii). In Rb- and CsC60 the latter are found to be dominant, the preponderant role being played by the quadrupolar electronic polarizability of the alkali ions.Comment: J.Chem.Phys., in press, 14 pages, 3 figures, 8 table

Access to improve the muon mass and magnetic moment anomaly via the bound-muon gg factor

A theoretical description of the $g$ factor of a muon bound in a nuclear potential is presented. One-loop self-energy and multi-loop vacuum polarization corrections are calculated, taking into account the interaction with the binding potential exactly. Nuclear effects on the bound-muon $g$ factor are also evaluated. We put forward the measurement of the bound-muon $g$ factor via the continuous Stern-Gerlach effect as an independent means to determine the free muons magnetic moment anomaly and mass. The scheme presented enables to increase the accuracy of the mass by more than an order of magnitude

Accretion of Ghost Condensate by Black Holes

The intent of this letter is to point out that the accretion of a ghost condensate by black holes could be extremely efficient. We analyze steady-state spherically symmetric flows of the ghost fluid in the gravitational field of a Schwarzschild black hole and calculate the accretion rate. Unlike minimally coupled scalar field or quintessence, the accretion rate is set not by the cosmological energy density of the field, but by the energy scale of the ghost condensate theory. If hydrodynamical flow is established, it could be as high as tenth of a solar mass per second for 10MeV-scale ghost condensate accreting onto a stellar-sized black hole, which puts serious constraints on the parameters of the ghost condensate model.Comment: 5 pages, 3 figures, REVTeX 4.0; discussion expande

Chaotic motion of charged particles in toroidal magnetic configurations

We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a non generic perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to a axi-symmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics

Dipole-active optical phonons in YTiO_3: ellipsometry study and lattice-dynamics calculations

The anisotropic complex dielectric response was accurately extracted from spectroscopic ellipsometry measurements at phonon frequencies for the three principal crystallographic directions of an orthorhombic (Pbnm) YTiO_3 single crystal. We identify all twenty five infrared-active phonon modes allowed by symmetry, 7B_1u, 9B_2u, and 9B_3u, polarized along the c-, b-, and a-axis, respectively. From a classical dispersion analysis of the complex dielectric functions \tilde\epsilon(\omega) and their inverses -1/\tilde\epsilon(\omega) we define the resonant frequencies, widths, and oscillator strengths of the transverse (TO) and longitudinal (LO) phonon modes. We calculate eigenfrequencies and eigenvectors of B_1u, B_2u, and B_3u normal modes and suggest assignments of the TO phonon modes observed in our ellipsometry spectra by comparing their frequencies and oscillator strengths with those resulting from the present lattice-dynamics study. Based on these assignments, we estimate dynamical effective charges of the atoms in the YTiO_3 lattice. We find that, in general, the dynamical effective charges in YTiO_3 lattice are typical for a family of perovskite oxides. By contrast to a ferroelectric BaTiO_3, the dynamical effective charge of oxygen related to a displacement along the c-axis does not show the anomalously large value. At the same time, the dynamical effective charges of Y and ab-plane oxygen exhibit anisotropy, indicating strong hybridization along the a-axis.Comment: 8 pages, 7 figure