Radiative charge transfer lifetime of the excited state of (NaCa)+^+

New experiments were proposed recently to investigate the regime of cold atomic and molecular ion-atom collision processes in a special hybrid neutral-atom--ion trap under high vacuum conditions. The collisional cooling of laser pre-cooled Ca$^+$ ions by ultracold Na atoms is being studied. Modeling this process requires knowledge of the radiative lifetime of the excited singlet A$^1\Sigma^+$ state of the (NaCa)$^+$ molecular system. We calculate the rate coefficient for radiative charge transfer using a semiclassical approach. The dipole radial matrix elements between the ground and the excited states, and the potential curves were calculated using Complete Active Space Self-Consistent field and M\"oller-Plesset second order perturbation theory (CASSCF/MP2) with an extended Gaussian basis, 6-311+G(3df). The semiclassical charge transfer rate coefficient was averaged over a thermal Maxwellian distribution. In addition we also present elastic collision cross sections and the spin-exchange cross section. The rate coefficient for charge transfer was found to be $2.3\times 10^{-16}$ cm$^3$/sec, while those for the elastic and spin-exchange cross sections were found to be several orders of magnitude higher ($1.1\times 10^{-8}$ cm$^3$/sec and $2.3\times 10^{-9}$ cm$^3$/sec, respectively). This confirms our assumption that the milli-Kelvin regime of collisional cooling of calcium ions by sodium atoms is favorable with the respect to low loss of calcium ions due to the charge transfer.Comment: 4 pages, 5 figures; v.2 - conceptual change

Collective Modes of Quantum Hall Stripes

The collective modes of striped phases in a quantum Hall system are computed using the time-dependent Hartree-Fock approximation. Uniform stripe phases are shown to be unstable to the formation of modulations along the stripes, so that within the Hartree-Fock approximation the groundstate is a stripe crystal. Such crystalline states are generically gapped at any finite wavevector; however, in the quantum Hall system the interactions of modulations among different stripes is found to be remarkably weak, leading to an infinite collection of collective modes with immeasurably small gaps. The resulting long wavelength behavior is derivable from an elastic theory for smectic liquid crystals. Collective modes for the phonon branch are computed throughout the Brillouin zone, as are spin wave and magnetoplasmon modes. A soft mode in the phonon spectrum is identified for partial filling factors sufficiently far from 1/2, indicating a second order phase transition. The modes contain several other signatures that should be experimentally observable.Comment: 36 pages LaTex with 11 postscript figures. Short animations of the collective modes can be found at http://www.physique.usherb.ca/~rcote/stripes/stripes.ht

Commensurate-incommensurate transitions of quantum Hall stripe states in double-quantum-well systems

In higher Landau levels (N>0) and around filling factors nu =4N+1, a two-dimensional electron gas in a double-quantum-well system supports a stripe groundstate in which the electron density in each well is spatially modulated. When a parallel magnetic field is added in the plane of the wells, tunneling between the wells acts as a spatially rotating effective Zeeman field coupled to the ``pseudospins'' describing the well index of the electron states. For small parallel fields, these pseudospins follow this rotation, but at larger fields they do not, and a commensurate-incommensurate transition results. Working in the Hartree-Fock approximation, we show that the combination of stripes and commensuration in this system leads to a very rich phase diagram. The parallel magnetic field is responsible for oscillations in the tunneling matrix element that induce a complex sequence of transitions between commensurate and incommensurate liquid or stripe states. The homogeneous and stripe states we find can be distinguished by their collective excitations and tunneling I-V, which we compute within the time-dependent Hartree-Fock approximation.Comment: 23 pages including 8 eps figure

Continuous star cluster formation in the spiral NGC 45

We determined ages for 52 star clusters with masses < 10^6 solar masses in the low surface brightness spiral galaxy NGC 45. Four of these candidates are old globular clusters located in the bulge. The remaining ones span a large age range. The cluster ages suggest a continuous star/cluster formation history without evidence for bursts, consistent with the galaxy being located in a relatively unperturbed environment in the outskirts of the Sculptor group.Comment: 4 pages, 3 figures. To appear in "Island Universes - Structure and Evolution of Disk Galaxies", Terschelling (Netherlands), July 200

Macrodimers: ultralong range Rydberg molecules

We study long range interactions between two Rydberg atoms and predict the existence of ultralong range Rydberg dimers with equilibrium distances of many thousand Bohr radii. We calculate the dispersion coefficients $C_{5}$, $C_{6}$ and $C_{8}$ for two rubidium atoms in the same excited level $np$, and find that they scale like $n^{8}$, $n^{11}$ and $n^{15}$, respectively. We show that for certain molecular symmetries, these coefficients lead to long range potential wells that can support molecular bound levels. Such macrodimers would be very sensitive to their environment, and could probe weak interactions. We suggest experiments to detect these macrodimers.Comment: 4 pages, submitted to PR

Surface Contribution to Raman Scattering from Layered Superconductors

Generalizing recent work, the Raman scattering intensity from a semi-infinite superconducting superlattice is calculated taking into account the surface contribution to the density response functions. Our work makes use of the formalism of Jain and Allen developed for normal superlattices. The surface contributions are shown to strongly modify the bulk contribution to the Raman-spectrum line shape below $2\Delta$, and also may give rise to additional surface plasmon modes above $2\Delta$. The interplay between the bulk and surface contribution is strongly dependent on the momentum transfer $q_\parallel$ parallel to layers. However, we argue that the scattering cross-section for the out-of-phase phase modes (which arise from interlayer Cooper pair tunneling) will not be affected and thus should be the only structure exhibited in the Raman spectrum below $2\Delta$ for relatively large $q_\parallel\sim 0.1\Delta/v_F$. The intensity is small but perhaps observable.Comment: 14 pages, RevTex, 6 figure

Anisotropic states of two-dimensional electrons in high magnetic fields

We study the collective states formed by two-dimensional electrons in Landau levels of index $n\ge 2$ near half-filling. By numerically solving the self-consistent Hartree-Fock (HF) equations for a set of oblique two-dimensional lattices, we find that the stripe state is an anisotropic Wigner crystal (AWC), and determine its precise structure for varying values of the filling factor. Calculating the elastic energy, we find that the shear modulus of the AWC is small but finite (nonzero) within the HF approximation. This implies, in particular, that the long-wavelength magnetophonon mode in the stripe state vanishes like $q^{3/2}$ as in an ordinary Wigner crystal, and not like $q^{5/2}$ as was found in previous studies where the energy of shear deformations was neglected.Comment: minor corrections; 5 pages, 4 figures; version to be published in Physical Review Letter

The Rich Globular Cluster System of Abell 1689 and the Radial Dependence of the Globular Cluster Formation Efficiency

We study the rich globular cluster (GC) system in the center of the massive cluster of galaxies Abell 1689 (z=0.18), one of the most powerful gravitational lenses known. With 28 HST/ACS orbits in the F814W bandpass, we reach magnitude I_814=29 with >90% completeness and sample the brightest ~5% of the GC system. Assuming the well-known Gaussian form of the GC luminosity function (GCLF), we estimate a total population of N(GC_total) = 162,850 GCs within a projected radius of 400kpc. As many as half may comprise an intracluster component. Even with the sizable uncertainties, which mainly result from the uncertain GCLF parameters, this is by far the largest GC system studied to date. The specific frequency S_N is high, but not uncommon for central galaxies in massive clusters, rising from S_N~5 near the center to ~12 at large radii. Passive galaxy fading would increase S_N by ~20% at z=0. We construct the radial mass profiles of the GCs, stars, intracluster gas, and lensing-derived total mass, and we compare the mass fractions as a function of radius. The estimated mass in GCs, M(GC_total)=3.9x10^10 Msun, is comparable to ~80% of the total stellar mass of the Milky Way. The shape of the GC mass profile appears intermediate between those of the stellar light and total cluster mass. Despite the extreme nature of this system, the ratios of the GC mass to the baryonic and total masses, and thus the GC formation efficiency, are typical of those in other rich clusters when comparing at the same physical radii. The GC formation efficiency is not constant, but varies with radius, in a manner that appears similar for different clusters; we speculate on the reasons for this similarity in profile.Comment: 13 pages, 11 figures; accepted for publication in Ap