Molecular vibration in cold collision theory

Cold collisions of ground state oxygen molecules with Helium have been investigated in a wide range of cold collision energies (from 1 $\mu$K up to 10 K) treating the oxygen molecule first as a rigid rotor and then introducing the vibrational degree of freedom. The comparison between the two models shows that at low energies the rigid rotor approximation is very accurate and able to describe all the dynamical features of the system. The comparison between the two models has also been extended to cases where the interaction potential He - O$_2$ is made artificially stronger. In this case vibration can perturb rate constants, but fine-tuning the rigid rotor potential can alleviate the discrepancies between the two models.Comment: 11 pages, 3 figure

Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states II: calculation of the glueball spectrum

In the preceding paper, a rigorous three-dimensional relativistic equation for two-gluon bound states was derived from the QCD with massive gluons and represented in the angular momentum representation. In order to apply this equation to calculate the glueball spectrum, in this paper, the equation is recast in an equivalent three-dimensional relativistic equation satisfied by the two-gluon positive energy state amplitude. The interaction Hamiltonian in the equation is exactly derived and expressed as a perturbative series. The first term in the series describes the one-gluon exchange interaction which includes fully the retardation effect in it. This term plus the linear confining potential are chosen to be the interaction Hamiltonian and employed in the practical calculation. With the integrals containing three and four spherical Bessel functions in the QCD vertices being analytically calculated, the interaction Hamiltonian is given an explicit expression in the angular momentum representation. Numerically solving the relativistic equation with taking the contributions arising from the retardation effect and the longitudinal mode of gluon fields into account, a set of masses for the $0^{++},0^{-+},1^{++},1^{-+},2^{++}$ and $2^{-+\text{}}$ glueball states are obtained and are in fairly good agreement with the predictions given by the lattice simulatio

Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states I: Derivation of the relativistic equation

A rigorous three-dimensional relativistic equation satisfied by two-gluon bound states is derived from the QCD with massive gluons. With the gluon fields and the quark fields being expanded in terms of the gluon multipole fields and the spherical Dirac spinors respectively, the equation is well established in the angular momentum representation and hence is much convenient for solving the problem of two-gluon glueball spectra. In particular, the interaction kernel in the equation is exactly derived and given a closed expression which includes all the interactions taking place in the two-gluon glueballs. The kernel contains only a few types of Green's functions and commutators. Therefore, it is not only easily calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations

Hadron resonances generated from the dynamics of the lightest scalar ones

We have studied the interactions of the scalar resonances f_0(980) and a_0(980) with the vector resonance \phi(1020) and with the lightest pseudoscalars \pi, K, \eta and \eta'. We first obtain the interaction kernels without including any new free parameter. Afterwards, the interaction kernels are unitarized and the final S-wave amplitudes result. We find that these interactions are very rich and generate a large amount of pseudoscalar resonances including the K(1460), \pi(1300), \pi(1800), \eta(1475) and X(1835) resonances. The f_0(980)\phi(1020) self-interactions give rise to the \phi(2170) resonance. For realistic choices of the parameters we also obtain an isovector companion in the same mass region from the a_0(980) \phi(1020) interactions.Comment: 4 pafes, 4 figures. Invited talk at QCD 10 (25th anniversary), 15th International QCD Conference, 28th June - 3rd July 2010 Montpellier (France). To be published in Nucl. Phys. B (Proc. Suppl.

THE INTERPLAY OF THE K+K- ATOM AND THE f_0(975) RESONANCE

We predict that production of the K+K- atom in pd-3^HeX and similar reactions exhibits a drastic missing mass spectrum due to the interplay with f_0(975) resonance. We point out that high precision studies of the K+K- atom may shed a new light on the nature of f_0(975).Comment: 13 page

No Dynamics in the Extremal Kerr Throat

Motivated by the Kerr/CFT conjecture, we explore solutions of vacuum general relativity whose asymptotic behavior agrees with that of the extremal Kerr throat, sometimes called the Near-Horizon Extreme Kerr (NHEK) geometry. We argue that all such solutions are diffeomorphic to the NHEK geometry itself. The logic proceeds in two steps. We first argue that certain charges must vanish at all times for any solution with NHEK asymptotics. We then analyze these charges in detail for linearized solutions. Though one can choose the relevant charges to vanish at any initial time, these charges are not conserved. As a result, requiring the charges to vanish at all times is a much stronger condition. We argue that all solutions satisfying this condition are diffeomorphic to the NHEK metric.Comment: 42 pages, 3 figures. v3: minor clarifications and correction

Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases

We analyze the ground-state properties and the excitation spectrum of Bose-Einstein condensates of trapped dipolar particles. First, we consider the case of a single-component polarized dipolar gas. For this case we discuss the influence of the trapping geometry on the stability of the condensate as well as the effects of the dipole-dipole interaction on the excitation spectrum. We discuss also the ground state and excitations of a gas composed of two antiparallel dipolar components.Comment: 12 pages, 9 eps figures, final versio

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).Comment: 45 page

Probing the high momentum component of the deuteron at high Q^2

The d(e,e'p) cross section at a momentum transfer of 3.5 (GeV/c)^2 was measured over a kinematical range that made it possible to study this reaction for a set of fixed missing momenta as a function of the neutron recoil angle theta_nq and to extract missing momentum distributions for fixed values of theta_nq up to 0.55 GeV/c. In the region of 35 (deg) <= theta_nq <= 45 (deg) recent calculations, which predict that final state interactions are small, agree reasonably well with the experimental data. Therefore these experimental reduced cross sections provide direct access to the high momentum component of the deuteron momentum distribution in exclusive deuteron electro-disintegration.Comment: 5 pages, 2 figure

Realistic Model of the Nucleon Spectral Function in Few- and Many- Nucleon Systems

By analysing the high momentum features of the nucleon momentum distribution in light and complex nuclei, it is argued that the basic two-nucleon configurations generating the structure of the nucleon Spectral Function at high values of the nucleon momentum and removal energy, can be properly described by a factorised ansatz for the nuclear wave function, which leads to a nucleon Spectral Function in the form of a convolution integral involving the momentum distributions describing the relative and center-of-mass motion of a correlated nucleon-nucleon pair embedded in the medium. The Spectral Functions of $^3He$ and infinite nuclear matter resulting from the convolution formula and from many-body calculations are compared, and a very good agreement in a wide range of values of nucleon momentum and removal energy is found. Applications of the model to the analysis of inclusive and exclusive processes are presented, illustrating those features of the cross section which are sensitive to that part of the Spectral Function which is governed by short-range and tensor nucleon-nucleon correlations.Comment: 40 pages Latex , 16 ps figures available from the above e-mail address or from [email protected]