Predicting scattering properties of ultracold atoms: adiabatic accumulated phase method and mass scaling

Ultracold atoms are increasingly used for high precision experiments that can be utilized to extract accurate scattering properties. This calls for a stronger need to improve on the accuracy of interatomic potentials, and in particular the usually rather inaccurate inner-range potentials. A boundary condition for this inner range can be conveniently given via the accumulated phase method. However, in this approach one should satisfy two conditions, which are in principle conflicting, and the validity of these approximations comes under stress when higher precision is required. We show that a better compromise between the two is possible by allowing for an adiabatic change of the hyperfine mixing of singlet and triplet states for interatomic distances smaller than the separation radius. A mass scaling approach to relate accumulated phase parameters in a combined analysis of isotopically related atom pairs is described in detail and its accuracy is estimated, taking into account both Born-Oppenheimer and WKB breakdown. We demonstrate how numbers of singlet and triplet bound states follow from the mass scaling.Comment: 14 pages, 9 figure

Metastable neon collisions: anisotropy and scattering length

In this paper we investigate the effective scattering length $a$ of spin-polarized Ne*. Due to its anisotropic electrostatic interaction, its scattering length is determined by five interaction potentials instead of one, even in the spin-polarized case, a unique property among the Bose condensed species and candidates. Because the interaction potentials of Ne* are not known accurately enough to predict the value of the scattering length, we investigate the behavior of $a$ as a function of the five phase integrals corresponding to the five interaction potentials. We find that the scattering length has five resonances instead of only one and cannot be described by a simple gas-kinetic approach or the DIS approximation. However, the probability for finding a positive or large value of the scattering length is not enhanced compared to the single potential case. The complex behavior of $a$ is studied by comparing a quantum mechanical five-channel numerical calculation to simpler two-channel models. We find that the induced dipole-dipole interaction is responsible for coupling between the different |\Omega> states, resulting in an inhomogeneous shift of the resonance positions and widths in the quantum mechanical calculation as compared to the DIS approach. The dependence of the resonance positions and widths on the input potentials turns out to be rather straightforward. The existence of two bosonic isotopes of Ne* enables us to choose the isotope with the most favorable scattering length for efficient evaporative cooling towards the Bose-Einstein Condensation transition, greatly enhancing the feasibility to reach this transition.Comment: 13pages, 8 eps figures, analytical model in section V has been remove

Analytic structure and power-series expansion of the Jost function for the two-dimensional problem

For a two-dimensional quantum mechanical problem, we obtain a generalized power-series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similarly to the standard effective range expansion. In order to do this, we consider the Jost-function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power-series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost-function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model simlar to those used in the theory of quantum dots.Comment: 42 pages, 9 figures, submitted to J.Phys.

Radio-Frequency Spectroscopy of Ultracold Fermions

Radio-frequency techniques were used to study ultracold fermions. We observed the absence of mean-field "clock" shifts, the dominant source of systematic error in current atomic clocks based on bosonic atoms. This is a direct consequence of fermionic antisymmetry. Resonance shifts proportional to interaction strengths were observed in a three-level system. However, in the strongly interacting regime, these shifts became very small, reflecting the quantum unitarity limit and many-body effects. This insight into an interacting Fermi gas is relevant for the quest to observe superfluidity in this system.Comment: 6 pages, 6 figure

Techniques for measuring weight bearing during standing and walking

OBJECTIVE: To classify and assess techniques for measuring the amount of weight bearing during standing and walking.BACKGROUND: A large variety of weight bearing measuring techniques exists. This review describes their advantages and limitations to assist clinicians and researchers in selecting a technique for their specific application in measuring weight bearing.METHODS: A literature search was performed in Pubmed-Medline, CINAHL, and EMBASE. Measurement techniques were classified in 'clinical examination', 'scales', 'biofeedback systems', 'ambulatory devices' and 'platforms', and assessed on aspects of methodological quality, application, and feasibility.RESULTS: A total of 68 related articles was evaluated. The clinical examination technique is a crude method to estimate the amount of weight bearing. Scales are useful for static measurements to evaluate symmetry in weight bearing. Biofeedback systems give more reliable, accurate and objective data on weight bearing compared to clinical examination and scales, but the high costs could limit their use in physical therapy departments. The ambulatory devices can measure weight bearing with good accuracy and reliability in the hospital and at home. Platforms have the best methodological quality, but are mostly restricted to a gait laboratory, need trained personnel, and are expensive.CONCLUSIONS: The choice of a technique largely depends upon the criteria discussed in this review; however the clinical utilisation, the research question posed, and the available budget also play a role. The new developments seen in the field of 'ambulatory devices' are aimed at extending measuring time, and improved practicality in data collection and data analysis. For these latter devices, however, mainly preliminary studies have been published about devices that are not (yet) commercially available.</p

Optical excitations in a non-ideal Bose gas

Optical excitations in a Bose gas are demonstrated to be very sensitive to many-body effects. At low temperature the momentum relaxation is provided by momentum exchange collisions, rather than by elastic collisions. A collective excitation mode forms, which in a Boltzmann gas is manifest in a collision shift and dramatic narrowing of spectral lines. In the BEC state, each spectral line splits into two components. The doubling of the optical excitations results from the physics analogous to that of the second sound. We present a theory of the line doubling, and calculate the oscillator strengths and linewidth.Comment: 5 pages, 3 eps figure

A 5-year follow-up study of Alfredson's heel-drop exercise programme in chronic midportion Achilles tendinopathy

Background: Eccentric exercises have the most evidence in conservative treatment of midportion Achilles tendinopathy. Although short-term studies show significant improvement, little is known of the long-term (>3 years) results. Aim: To evaluate the 5-year outcome of patients with chronic midportion Achilles tendinopathy treated with the classical Alfredson's heel-drop exercise programme. Study design: Part of a 5-year follow-up of a previously conducted randomised controlled trial. Methods: 58 patients (70 tendons) were approached 5 years after the start of the heel-drop exercise programme according to Alfredson. At baseline and at 5-year follow-up, the validated Victorian Institute of Sports Assessment-Achilles (VISA-A) questionnaire score, pain status, alternative treatments received and ultrasonographic neovascularisation score were recorded. Results: In 46 patients (58 tendons), the VISA-A score significantly increased from 49.2 at baseline to 83.6 after 5 years (p<0.001) and from the 1-year to 5-year follow-up from 75.0 to 83.4 (p<0.01). 39.7% of the patients were completely pain-free at follow-up and 48.3% had received one or more alternative treatments. The sagittal tendon thickness decreased from 8.05 mm (SD 2.1) at baseline to 7.50 mm (SD 1.6) at the 5-year follow-up (p=0.051). Conclusion: At 5-year follow-up, a significant increase of VISA-A score can be expected. After the 3-month Alfredson's heel-drop exercise programme, almost half of the patients had received other therapies. Although improvement of symptoms can be expected at long term, mild pain may remain

Structure and stability of bosonic clouds: alkali atoms with negative scattering length

We investigate the form and stability of a cloud of atoms confined in a harmonic trap when the scattering length is negative. We find that, besides the known low density metastable solution, a new branch of Bose condensate appears at higher density when non locality effects in the attractive part are taken into account. The transition between the two classes of solutions as a function of the number $N$ of atoms can be either sharp or smooth according to the strength and range of the attractive interaction. Use of tight traps is favorable for investigating the evolution of the system as the strength of the effective interaction increases with $N$.Comment: 11 pages, Latex, 2 figures, to be published in Phys. Rev.