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I discuss the investigation of heavy exotic mesons using lattice QCD static potentials and the Born-Oppenheimer approximation. I summarize selected recent results for b¯b¯qq tetraquarks, for I = 0 bottomonium and for I = 1 bottomonium. [ABSTRACT FROM AUTHOR]

Through the Born-Oppenheimer Approximation, we have performed a comprehensive investigation of the DD∗K, D D ¯ $ \overline D $ *K, BB∗ K ¯ $ \overline K $ and B B ¯ $ \overline B $ * K ¯ $ \overline K $ molecular states. In the framework of One-Pion Exchange model as well as the treatments of the coupled-channel effects and S-D wave mixing, we find a loosely bound tri-meson molecular state these systems with the isospin configuration |0, 1 2 $ {1 \over 2} $ , ± 1 2 $ {1 \over 2} $ > and quantum number I(JP) = 1/2(1−), where the, 1 2 $ {1 \over 2} $ is the total isospin of the three-body system, the 0 is the isospin of the D∗K, D ¯ $ \overline D $ *K, B∗ K ¯ $ \overline K $ and B ¯ $ \overline B $ ∗ K ¯ $ \overline K $. With the estimated error, the mass of the DD∗K or D D ¯ $ \overline D $ ∗K molecule is 4317.92 − 4.32 + 3.66 $ 4317.92_{ - 4.32}^{ + 3.66} $ MeV or 4317.92 − 6.55 + 6.13 $ 4317.92_{ - 6.55}^{ + 6.13} $ MeV. We also extend our calculations to the bottom sector and find tri-meson bound states for the BB∗ K ¯ $ \overline K $ and B B ¯ $ \overline B $ * K ¯ $ \overline K $ with the mass 11013.65 − 8.84 + 8.49 $ 11013.65_{ - 8.84}^{ + 8.49} $ MeV and 11013.65 − 9.02 + 8.68 $ 11013.65_{ - 9.02}^{ + 8.68} $ MeV respectively. [ABSTRACT FROM AUTHOR]

We analyze two shallow resonance states below the antiproton hydrogen dissociation threshold with a non-adiabatic three-body calculation. Rearrangement correlation between initial channel and protonium formation channel is explicitly included in the total wavefunction. The lower resonance state is in good agreement with the resonance position and width calculated with the R-matrix theory. The higher resonance state which is newly found is closer to the threshold and much narrower than the former resonance. A polarization effect of the hydrogen atom is found to be indispensable to support the resonance state. The accuracy of the present calculation is evaluated by the extended virial theorem. The resonance states calculated in the present work gives shallower relative energy below the dissociation threshold than the Born-Oppenheimer calculation, suggesting that the electron motion which is ignored in latter calculation would give positive energy because the electron is unbound inside the distance. [ABSTRACT FROM AUTHOR]

We report on the results of [1] for the calculations of quarkonium hybrids. We have developed and Effective Field Theory (EFT) for quarkonium hybrids that systematically incorporates an expansion with respect to the adiabatic limit. We matched the potentials in our EFT to the static energies computed on the lattice. We discuss our results and compare them with direct lattice calculations and possible experimental candidates. [ABSTRACT FROM AUTHOR]

The dynamics of the interaction between intense laser field and one-electron molecule H+2 is investigated by solving three-dimensional time-dependent Schrödinger equation (3D TDSE) in the Born-Oppenheimer approximation. It is assumed that the laser field is polarized along the internuclear axis. The wave function is expanded in finite series using B-spline functions and spherical harmonics in prolate spheroidal coordinates. The results for the high-order harmonic generation and above-threshold ionization are presented. [ABSTRACT FROM AUTHOR]

The XYZ mesons are mesons that contain a heavy quark and antiquark but have properties that seem to require additional constituents. Some of them are electrically charged, so they must be tetraquark mesons whose additional constituents are a light quark and antiquark. The list of XYZ mesons has grown to about two dozen over the last decade. A promising approach to understanding these mesons within QCD is the Born-Oppenheimer approximation, which reduces the problem to the solution of the Schrödinger equation in potentials that can be calculated using lattice QCD. The Born- Oppenheimer approximation has not yet revealed the pattern of the XYZ mesons, but it provides a compelling framework for understanding them from the fundamental theory. [ABSTRACT FROM AUTHOR]

We report on the calculation of the Quarkomum Hybnd masses for the cgc, bgc and bgb systems [1]. A QCD analog of the Born-Oppenheimer approximation including the A-doubling terms has been used. The gkiomc static energies are obtained combining the short range description from potential non-relativistic QCD (pNRQCD) and lattice QCD calculations. The effect Δ-doubling terms is to mix the contributions of the static energies to the hybrid states leading to the break of the degeneracy between spin symmetry multiplets with opposite parity. The spin symmetry multiplets with mixed contributions from different static energies have a lower mass with respect to the parity opposite that remains without mixed contributions. We compare with direct lattice calculations and discuss several experimental candidates. [ABSTRACT FROM AUTHOR]

Baryons containing two heavy quarks (QQ'q) are treated in the Born-Oppenheimer approximation. Two nonrelativistic potential models are proposed, in which the Schrödinger equation admits a separation of variables in prolate and oblate spheroidal coordinates, respectively. In the first model, the potential is equal to the sum of Coulomb potentials of the two heavy quarks, separated from each other by a distance - R and linear potential of confinement. In the second model the center distance parameter R is assumed to be purely imaginary. In this case, the potential is defined by the two-sheeted mapping with singularities being concentrated on a circle rather than at separate points. Thus, in the first model diquark appears as a segment, and in the second - as a circle. In this paper we calculate the mass spectrum of double heavy baryons in both models, and compare it with previous results. [ABSTRACT FROM AUTHOR]

We report on the calculation of the Quarkonium Hybrid masses for the cgc, bgc and bgb systems [1]. A QCD analog of the Born-Oppenheimer approximation including the A-doubling terms has been used. The gluonic static energies are obtained combining the short range description from potential non-relativistic QCD (pNRQCD) and lattice QCD calculations. The effect A-doubling terms is to mix the contributions of the static energies to the hybrid states leading to the break of the degeneracy between spin symmetry multiplets with opposite parity. The spin symmetry multiplets with mixed contributions from different static energies have a lower mass with respect to the parity opposite that remains without mixed contributions. We compare with direct lattice calculations and discuss several experimental candidates. [ABSTRACT FROM AUTHOR]

To calculate the rovibronic energies of a triatomic molecule in an electronic state that is degenerate at linear nuclear configurations, it is necessary to allow for the breakdown of the Born-Oppenheimer approximation. This is because the electronic degeneracy is resolved at bent configurations and there is a nonnegligible coupling between the two states caused by molecular rotation. This is termed the Renner (or Renner-Teller) effect. To calculate the rovibronic term values and wavefunctions in this situation, we have developed a variational computational procedure and we have included the effect of spin-orbit coupling for nonsinglet states. The wavefunctions can be used to predict and interpret the results of Coulomb explosion imaging experiments. We can also calculate spectral line intensities so that absorption and emission spectra can be simulated. We review the work and our application to the CH2+ and FeOH molecules. [ABSTRACT FROM AUTHOR]

We deal here with the application of the Nuclear Born Oppenheimer (NBO) method to the description of nuclear rotations. As an edifying illustration, we apply the NBO formalism to study the rotational motion of nuclei which are axially-symmetric and even, but whose shells are not closed. We focus, in particular, on the derivation of expressions for the rotational energy and for the moment of inertia. Additionally, we examine the connection between the NBO method and the self-consistent cranking (SCC) model. Finally, we compare the moment of inertia generated by the NBO method with the Thouless-Valantin formula and hence establish a connection between the NBO method and the large body of experimental data. [ABSTRACT FROM AUTHOR]

These lectures review some advances in the algebraic description of molecules from two point of views: structure and dynamics. We start by presenting the basic ideas involved in the traditional description of molecular structure in configuration space, where the Born-Oppenheimer and rotor-rigid approximations are assumed to be valid. We then focus on the vibrational degrees of freedom in order to introduce the traditional algebraic realization in terms of bosonic operators of harmonic oscillators. This analysis allows the algebraic methods based on dynamical unitary groups to be introduced as a anharmonization procedure where the local bosonic operators are translated into operators satisfying the su(2) commutation relations. Some examples of the vibrational spec-troscopic description are presented. Concerned with the dynamical point of view an algebraic model to describe collinear collisions in the semiclassical approximation is presented. [ABSTRACT FROM AUTHOR]

I review some results for annihilation and rearrangement processes in low-energy antihydrogen-hydrogen and antihydrogen-helium scattering. For the strong nuclear force results using a δ-function potential are compared to a scattering length approach. It is found that the δ-function potential does not give correct annihilation cross sections in the case of antihydrogen-helium scattering. Problem associated with the use of the Born-Oppenheimer approximation for rearrangement calculations are reviewed. [ABSTRACT FROM AUTHOR]

In this contribution we report first-principle all-electron density functional theory (DFT) calculations on small sodium clusters with less than 10 atoms employing the linear combination of Gaussian type orbital DFT program deMon2k. Born-Oppenheimer molecular dynamics (BOMD) simulations over more than 200 ps (>100,000 time steps) with gradient corrected functionals in combination with DFT optimized all-electron double-zeta valence polarization are presented. In order to study the temperature dependency of the cluster polarizabilities BOMD trajectories from 50 to 900 K are recorded for each cluster. The polarizability tensor is then calculated along these trajectories employing all-electron triple-zeta valence polarization basis sets augmented with field induced polarization functions. The analysis of the BOMD results shows that the temperature dependency of the sodium cluster polarizability varies strongly with cluster size. Moreover, characteristic changes in the polarizability per atom as a function of temperature are observed. The mismatch between theoretical and experimental polarizabilities will be discussed in the light of these new results. [ABSTRACT FROM AUTHOR]

Recent findings on the spectrum of heavy-quark mesons from computer simulations of quarks and gluons in lattice QCD are summarized, with particular attention to quark-antiquark states bound by an excited gluon field. The validity of a Born-Oppenheimer treatment for such systems is discussed. Recent results on glueball masses, the light-quark 1-+ hybrid meson mass, and the static three-quark potential are summarized. © 2003 American Institute of Physics [ABSTRACT FROM AUTHOR]

We study the effect of nuclear-electron coupling on time-resolved photo-electron spectra, employing a model system which allows to directly comparing spectra resulting from the adiabatic approximation with those obtained within a non-Born-Oppenheimer description [ABSTRACT FROM AUTHOR]