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

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

Predicting death over 8 years in a prospective cohort of HIV-infected women: the Women's Interagency HIV Study.

ObjectivesPredicting mortality in middle-aged HIV-infected (HIV+) women on antiretroviral therapies (ART) is important for understanding the impact of HIV infection. Several health indices have been used to predict mortality in women with HIV infection. We evaluated: (1) an HIV biological index, Veterans Aging Cohort Study (VACS); (2) a physical index, Fried Frailty Index (FFI); and (3) a mental health index, Center for Epidemiologic Studies-Depression (CES-D). Proportional hazards regression analyses were used to predict death and included relevant covariates.DesignProspective, observational cohort.SettingMulticentre, across six sites in the USA.Participants1385 multirace/ethnic ART-experienced HIV+ women in 2005.Primary and secondary outcomesAll deaths, AIDS deaths and non-AIDS deaths up to ~8 years from baseline.ResultsIncluded together in one model, VACS Index was the dominant, significant independent predictor of all deaths within 3 years (HR=2.20, 95% CI 1.83, 2.65, χ2=69.04, p<0.0001), and later than 3 years (HR=1.55, 95% CI 1.30, 1.84, χ2=23.88, p<0.0001); followed by FFI within 3 years (HR=2.06, 95% CI 1.19, 3.57, χ2=6.73, p=0.01) and later than 3 years (HR=2.43, 95% CI 1.58, 3.75, χ2=16.18, p=0.0001). CES-D score was not independently associated with mortality.Conclusions and relevanceThis is the first simultaneous evaluation of three common health indices in HIV+ adults. Indices reflecting physical and biological ageing were associated with death

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

A prompt neutrino measurement

A test has been made to explore the possibility of beam dump neutrino experiments with short target‐detector separations and modest detectors. Results have given a positive neutrino signal which is interpreted in the context of various charmed‐meson production models. A limit to the lifetime and mass of the axion is also a byproduct of this test.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87326/2/246_1.pd

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

Neutron total cross sections on nuclei at Fermilab energies

We have measured total cross sections for neutrons on protons, deuteriom, beryllium, carbon, aluminium, iron, copper, cadmium, tungsten, lead, and uranium for momenta between 30 and 300 GeV/c. The measurements were carried out in a small-angle neutral beam at Fermilab. Typical accuracy of the data is 0.5 to 1%. The cross sections are consistent with an A0.77+/-0.01 dependence over the entire momentum range. The cross sections are compared with theoretical predictions. Agreement is found only if inelastic screening is included. Nuclear radii obtained from our data are in good agreement with previous determinations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22036/1/0000454.pd