82 research outputs found
Glory Oscillations in the Index of Refraction for Matter-Waves
We have measured the index of refraction for sodium de Broglie waves in gases
of Ar, Kr, Xe, and nitrogen over a wide range of sodium velocities. We observe
glory oscillations -- a velocity-dependent oscillation in the forward
scattering amplitude. An atom interferometer was used to observe glory
oscillations in the phase shift caused by the collision, which are larger than
glory oscillations observed in the cross section. The glory oscillations depend
sensitively on the shape of the interatomic potential, allowing us to
discriminate among various predictions for these potentials, none of which
completely agrees with our measurements
Quasiclassical double photoionization from the 2^{1,3}S excited states of helium including shakeoff
We account for the different symmetries of the 2^{1,3}S helium excited states
in a quasiclassical description of the knockout mechanism augmented by a
quantum shakeoff contribution. We are thus able to formulate the separate
contribution of the knockout and shakeoff mechanisms for double photoionization
for any excess energy from the 2^{1,3}S states. Photoionization ratios and
singly differential cross sections calculated for the 2^{1,3}S excited states
of helium are found to be in very good agreement with recent theoretical
results.Comment: 9 pages, 5 figure
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 ,
and for two rubidium atoms in the same excited level , and find
that they scale like , and , 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
Acceleration of generalized hypergeometric functions through precise remainder asymptotics
We express the asymptotics of the remainders of the partial sums {s_n} of the
generalized hypergeometric function q+1_F_q through an inverse power series z^n
n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k}
may be recursively computed to any desired order from the hypergeometric
parameters and argument. From this we derive a new series acceleration
technique that can be applied to any such function, even with complex
parameters and at the branch point z=1. For moderate parameters (up to
approximately ten) a C implementation at fixed precision is very effective at
computing these functions; for larger parameters an implementation in higher
than machine precision would be needed. Even for larger parameters, however,
our C implementation is able to correctly determine whether or not it has
converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added
several references, added comparison to other methods, and added discussion
of recursion stabilit
From Majorana theory of atomic autoionization to Feshbach resonances in high temperature superconductors
The Ettore Majorana paper - Theory of incomplete P triplets- published in
1931, focuses on the role of selection rules for the non-radiative decay of two
electron excitations in atomic spectra, involving the configuration interaction
between discrete and continuum channels. This work is a key step for
understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two
electron excitations and the 1958 Herman Feshbach paper on the shape resonances
in nuclear scattering arising from configuration interaction between many
different scattering channels. The Feshbach resonances are today of high
scientific interest in many different fields and in particular for ultracold
gases and high Tc superconductivity.Comment: 13 pages, 7 figures. Journal of Superconductivity and Novel Magnetism
to be publishe
Protonation States of Remote Residues Affect Binding-Release Dynamics of the Ligand but not the Conformation of apo Ferric Binding Protein
We have studied the apo (Fe3+ free) form of periplasmic ferric binding
protein (FbpA) under different conditions and we have monitored the changes in
the binding and release dynamics of H2PO4- that acts as a synergistic anion in
the presence of Fe3+. Our simulations predict a dissociation constant of
2.20.2 mM which is in remarkable agreement with the experimentally
measured value of 2.30.3 mM under the same ionization strength and pH
conditions. We apply perturbations relevant for changes in environmental
conditions as (i) different values of ionic strength (IS), and (ii) protonation
of a group of residues to mimic a different pH environment. Local perturbations
are also studied by protonation or mutation of a site distal to the binding
region that is known to mechanically manipulate the hinge-like motions of FbpA.
We find that while the average conformation of the protein is intact in all
simulations, the H2PO4- dynamics may be substantially altered by the changing
conditions. In particular, the bound fraction which is 20 for the wild type
system is increased to 50 with a D52A mutation/protonation and further to
over 90 at the protonation conditions mimicking those at pH 5.5. The change
in the dynamics is traced to the altered electrostatic distribution on the
surface of the protein which in turn affects hydrogen bonding patterns at the
active site. The observations are quantified by rigorous free energy
calculations. Our results lend clues as to how the environment versus single
residue perturbations may be utilized for regulation of binding modes in hFbpA
systems in the absence of conformational changes.Comment: 26 pages, 4 figure
The PhenX Toolkit: Get the Most From Your Measures
The potential for genome-wide association studies to relate phenotypes to specific genetic variation is greatly increased when data can be combined or compared across multiple studies. To facilitate replication and validation across studies, RTI International (Research Triangle Park, North Carolina) and the National Human Genome Research Institute (Bethesda, Maryland) are collaborating on the consensus measures for Phenotypes and eXposures (PhenX) project. The goal of PhenX is to identify 15 high-priority, well-established, and broadly applicable measures for each of 21 research domains. PhenX measures are selected by working groups of domain experts using a consensus process that includes input from the scientific community. The selected measures are then made freely available to the scientific community via the PhenX Toolkit. Thus, the PhenX Toolkit provides the research community with a core set of high-quality, well-established, low-burden measures intended for use in large-scale genomic studies. PhenX measures will have the most impact when included at the experimental design stage. The PhenX Toolkit also includes links to standards and resources in an effort to facilitate data harmonization to legacy data. Broad acceptance and use of PhenX measures will promote cross-study comparisons to increase statistical power for identifying and replicating variants associated with complex diseases and with gene-gene and gene-environment interactions
Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
The Gauss hypergeometric functions 2F1 with arbitrary values of parameters
are reduced to two functions with fixed values of parameters, which differ from
the original ones by integers. It is shown that in the case of integer and/or
half-integer values of parameters there are only three types of algebraically
independent Gauss hypergeometric functions. The epsilon-expansion of functions
of one of this type (type F in our classification) demands the introduction of
new functions related to generalizations of elliptic functions. For the five
other types of functions the higher-order epsilon-expansion up to functions of
weight 4 are constructed. The result of the expansion is expressible in terms
of Nielsen polylogarithms only. The reductions and epsilon-expansion of q-loop
off-shell propagator diagrams with one massive line and q massless lines and
q-loop bubble with two-massive lines and q-1 massless lines are considered. The
code (Mathematica/FORM) is available via the www at this URL
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 19 pages, LaTeX, 1-eps figure; v5: The code (Mathematica/FORM) is
available via the www http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htm
Numerical methods for the computation of the confluent and Gauss hypergeometric functions
The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric functions in different parameter and variable regimes. The methods that we investigate include Taylor and asymptotic series computations, Gauss-Jacobi quadrature, numerical solution of differential equations, recurrence relations, and others. We discuss the results of numerical experiments used to determine the best methods, in practice, for each parameter and variable regime considered. We provide 'roadmaps' with our recommendation for which methods should be used in each situation
Basic Methods for Computing Special Functions
This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are
frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website
- …