Ultracold collisions in tight harmonic traps: Quantum defect model and application to metastable helium atoms

We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (GP) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schr\"{o}dinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with those computed self-consistently using the generalized self-consistent method.Comment: 11 pages,REVTEX, text substantially revised, title modifie

Modeling the adiabatic connection in H₂

Full configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing the ground state potential energy curve of H2, within spin-restricted density functional theory (DFT). For each internuclear separation R, accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchange-correlation energy expressed entirely in terms of FCI-derived quantities. This is combined with other FCI-derived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a [1/1]-Padé-based form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate R, the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the strong-interaction limit; none provide an accurate potential energy curve for all R, although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated ab initio calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required

Solar Carbon Monoxide, Thermal Profiling, and the Abundances of C, O, and their Isotopes

A solar photospheric "thermal profiling" analysis is presented, exploiting the infrared rovibrational bands of carbon monoxide (CO) as observed with the McMath-Pierce Fourier transform spectrometer (FTS) at Kitt Peak, and from above the Earth's atmosphere by the Shuttle-borne ATMOS experiment. Visible continuum intensities and center-limb behavior constrained the temperature profile of the deep photosphere, while CO center-limb behavior defined the thermal structure at higher altitudes. The oxygen abundance was self consistently determined from weak CO absorptions. Our analysis was meant to complement recent studies based on 3-D convection models which, among other things, have revised the historical solar oxygen (and carbon) abundance downward by a factor of nearly two; although in fact our conclusions do not support such a revision. Based on various considerations, an oxygen abundance of 700+/-100 ppm (parts per million relative to hydrogen) is recommended; the large uncertainty reflects the model sensitivity of CO. New solar isotopic ratios also are reported for 13C, 17O, and 18O.Comment: 90 pages, 19 figures (some with parts "a", "b", etc.); to be published in the Astrophysical Journal Supplement

Quantum-mechanical calculation of Stark widths of Ne VII n=3, Δn=0\Delta n=0 transitions

The Stark widths of the Ne VII 2s3s-2s3p singlet and triplet lines are calculated in the impact approximation using quantum-mechanical Convergent Close-Coupling and Coulomb-Born-Exchange approximations. It is shown that the contribution from inelastic collisions to the line widths exceeds the elastic width contribution by about an order of magnitude. Comparison with the line widths measured in a hot dense plasma of a gas-liner pinch indicates a significant difference which may be naturally explained by non-thermal Doppler effects from persistent implosion velocities or turbulence developed during the pinch implosion. Contributions to the line width from different partial waves and types of interactions are discussed as well.Comment: 8 pages, 3 figures; accepted by Phys. Rev.

Vortex Dynamics in Dissipative Systems

We derive the exact equation of motion for a vortex in two- and three- dimensional non-relativistic systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is given in terms of local gradients of the magnitude and phase of the complex field and is exact also for arbitrarily small inter-vortex distances. The results for vortices in a superfluid or a superconductor are recovered.Comment: revtex, 5 pages, 1 encapsulated postscript figure (included), uses aps.sty, epsf.te

Improving Predictions for Helium Emission Lines

We have combined the detailed He I recombination model of Smits with the collisional transitions of Sawey & Berrington in order to produce new accurate helium emissivities that include the effects of collisional excitation from both the 2 (3)S and 2 (1) S levels. We present a grid of emissivities for a range of temperature and densities along with analytical fits and error estimates. Fits accurate to within 1% are given for the emissivities of the brightest lines over a restricted range for estimates of primordial helium abundance. We characterize the analysis uncertainties associated with uncertainties in temperature, density, fitting functions, and input atomic data. We estimate that atomic data uncertainties alone may limit abundance estimates to an accuracy of 1.5%; systematic errors may be greater than this. This analysis uncertainty must be incorporated when attempting to make high accuracy estimates of the helium abundance. For example, in recent determinations of the primordial helium abundance, uncertainties in the input atomic data have been neglected.Comment: ApJ, accepte

J-resolved He I emission predictions in the low-density limit

Determinations of the primordial helium abundance are used in precision cosmological tests. These require highly accurate He I recombination rate coefficients. Here we reconsider the formation of He I recombination lines in the low-density limit. This is the simplest case and it forms the basis for the more complex situation where collisions are important. The formation of a recombination line is a two-step process, beginning with the capture of a continuum electron into a bound state and followed by radiative cascade to ground. The rate coefficient for capture from the continuum is obtained from photoionization cross sections and detailed balancing, while radiative transition probabilities determine the cascades. We have made every effort to use today's best atomic data. Radiative decay rates are from Drake's variational calculations, which include QED, fine structure, and singlet-triplet mixing. Certain high-$L$ fine-structure levels do not have a singlet-triplet distinction and the singlets and triplets are free to mix in dipole-allowed radiative decays. We use quantum defect or hydrogenic approximations to include levels higher than those treated in the variational calculations. [Abstract clipped]Comment: 31 pages, 2 figures, accepted by ApJ, tentatively scheduled for 20 July 2005, v628

Hadron therapy information sharing prototype

The European PARTNER project developed a prototypical system for sharing hadron therapy data. This system allows doctors and patients to record and report treatment-related events during and after hadron therapy. It presents doctors and statisticians with an integrated view of adverse events across institutions, using open-source components for data federation, semantics, and analysis. There is a particular emphasis upon semantic consistency, achieved through intelligent, annotated form designs. The system as presented is ready for use in a clinical setting, and amenable to further customization. The essential contribution of the work reported here lies in the novel data integration and reporting methods, as well as the approach to software sustainability achieved through the use of community-supported open-source components

Diagnosis and Management of Iliac Artery Endofibrosis: Results of a Delphi Consensus Study

Objective Iliac endofibrosis is a rare condition that may result in a reduction of blood flow to the lower extremity in young, otherwise healthy individuals. The data to inform everyday clinical management are weak and therefore a Delphi consensus methodology was used to explore areas of consensus and disagreement concerning the diagnosis and management of patients with suspected iliac endofibrosis. Methods A three-round Delphi questionnaire approach was used among vascular surgeons, sports physicians, sports scientists, radiologists, and clinical vascular scientists with experience of treating this condition to explore diagnosis and clinical management issues for patients with suspected iliac artery endofibrosis. Analysis is based on 18 responses to round 2 and 14 responses to round 3, with agreement reported when 70% of respondents were in agreement. Results Initially there was agreement on the typical symptoms at presentation and the need for an exercise test in the diagnosis. Round 3 clarified that duplex ultrasound was a useful tool in the diagnosis of endofibrosis. There was consensus on the most appropriate type of surgery (endarterectomy and vein patch) and that endovascular interventions were inadvisable. The final round helped to inform aspects of the natural history and post-operative surveillance. Progression of the disease was likely with continued exercise but cessation may prevent progression. Surveillance after surgery is generally recommended yearly with at least a clinical assessment. Conclusions There is broad agreement about the presenting symptoms and the investigations required to confirm (or exclude) the diagnosis of iliac endofibrosis. There was consensus on the surgical approach to repair. Disagreement existed about the specific diagnostic criteria that should be applied during non-invasive testing and about post-operative care and resumption of exercise