Spectra generated by a confined softcore Coulomb potential

Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator potential terms, and also through `hard confinement' by means of an impenetrable spherical box. A byproduct of this work is the construction of polynomial solutions for a number of linear differential equations with polynomial coefficients, along with the necessary and sufficient conditions for the existence of such solutions. Very accurate approximate solutions for the general problem with arbitrary potential parameters are found by use of the asymptotic iteration method.Comment: 17 pages, 2 figure

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision

Spectral characteristics for a spherically confined -1/r + br^2 potential

We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential $V(r)$ is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure

Interferometric Constraints on Quantum Geometrical Shear Noise Correlations

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.Comment: Matches the journal accepted versio

Photosystem II Peripheral Accessory Chlorophyll Mutants in Chlamydomonas reinhardtii. Biochemical Characterization and Sensitivity to Photo-Inhibition

In addition to the four chlorophylls (Chls) involved in primary charge separation, the photosystem II (PSII) reaction center polypeptides, D1 and D2, coordinate a pair of symmetry-related, peripheral accessory Chls. These Chls are axially coordinated by the D1-H118 and D2-H117 residues and are in close association with the proximal Chl antennae proteins, CP43 and CP47. To gain insight into the function(s) of each of the peripheral Chls, we generated site-specific mutations of the amino acid residues that coordinate these Chls and characterized their energy and electron transfer properties. Our results demonstrate that D1-H118 and D2-H117 mutants differ with respect to: (a) their relative numbers of functional PSII complexes, (b) their relative ability to stabilize charge-separated states, (c) light-harvesting efficiency, and (d) their sensitivity to photo-inhibition. The D2-H117N and D2-H117Q mutants had reduced levels of functional PSII complexes and oxygen evolution capacity as well as reduced light-harvesting efficiencies relative to wild-type cells. In contrast, the D1-H118Q mutant was capable of near wild-type rates of oxygen evolution at saturating light intensities. The D1-H118Q mutant also was substantially more resistant to photo-inhibition than wild type. This reduced sensitivity to photo-inhibition is presumably associated with a reduced light-harvesting efficiency in this mutant. Finally, it is noted that the PSII peripheral accessory Chls have similarities to a to a pair of Chls also present in the PSI reaction center complex

Neutron-deuteron elastic scattering from 6 to 12.5 GeV/c

The differential cross section for neutron-deuteron elastic scattering was measured for four-momentum transfers 0.3 t 2 with incident neutron momenta between 6 and 12.5 GeV/c. The measurement was made with spark chambers at the Argonne ZGS. Results are compared with proton-deuteron elastic scattering at comparable energies as a test of isospin invariance in strong interactions and with the predictions of the Glauber multiple scattering theory. Very good agreement is found.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21813/1/0000213.pd

Search for anomalous multiphoton production at 100-300 GeV

We have carried out a search for anomalous multiphoton production in neutron-Ch2 collisions at Fermilab. Both anomalous [gamma] events as might be produced in the annihilation of a magnetic monopole pair, as well as events with smaller opening angles, such as those observed in cosmic ray emulsions by Schein et al. and others were sought. No evidence for either type of event was found. An upper limit ~2.7 [mu]b is placed on the production cross section for "Schein" events or ~10-2 that deduced from the cosmic ray data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21926/1/0000333.pd

Advanced LIGO Laser Systems for O3 and Future Observation Runs

The advanced LIGO gravitational wave detectors need high power laser sources with excellent beam quality and low-noise behavior. We present a pre-stabilized laser system with 70 W of output power that was used in the third observing run of the advanced LIGO detectors. Furthermore, the prototype of a 140 W pre-stabilized laser system for future use in the LIGO observatories is described and characterized