119446389
Pseudopotential approximation in a harmonic trap
The pseudopotential method @1,2# is an important tool for the study of interacting particles. The key idea is to replace the actual, possibly complicated interaction potential by a much simpler pseudopotential operator, such that the exact energy eigenvalues of the interacting system are reproduced at least to the lowest few orders in a suitable expansion parameter. This approach now is of central importance for the theoretical description of Bose-Einstein condensates @3‐5#, where the approximate pseudopotential mimics the real twobody interaction solely through its s-wave scattering length. However, the condensates are subjected to a trapping potential, and one expects some influence of this external potential on the pseudopotential at least with tight traps, i.e., when the distance over which the trapping potential varies significantly becomes comparable to the scattering length. In this paper we investigate the influence of the trap in detail for a hard-sphere interaction potential, and quantify the accuracy of the standard pseudopotential approximation in an isotropic harmonic trap. Let us briefly recapitulate the essence of the pseudopotential approach @2# for two identical particles of mass m which interact, in the absence of an additional external trapping potential, via a finite-range potential V(uru) without twobody bound states, so that the Hamiltonian is given by
9426399
Implications from analyticity constraints used in a Landshoff-Donnachie fit
Landshoff and Donnachie[hep/ph 0509240, (2005)] parametrize the energy behavior of pp and pp̄ scattering cross sections with five parameters, using: σ = 56.08s + 21.70s for pp, (1) σ = 98.39s + 21.70s for pp̄. (2) Using the 4 analyticity constraints of Block and Halzen[M. M. Block and F. Halzen, Phys. Rev. D 72, 036006 (2005)], we simultaneously fit the Landshoff-Donnachie form to the same “sieved” set of pp and pp̄ cross section and ρ data that Block and Halzen used for a very good fit to a ln s parametrization. We show that the satisfaction of the analyticity constraints will require complicated modifications of the LandshoffDonnachie parametrization for lower energies, greatly altering its inherent appeal of simplicity and universality. Landshoff and Donnachie[1, 2, 3] parameterize the scattering cross section with five parameters, using: σ = 56.08s + 21.70s for pp, (3) σ = 98.39s + 21.70s for pp̄, (4) where s is in GeV. Using the high energy limit s → 2mν, where ν is the laboratory energy and m is the proton mass, we rewrite these equations, as well as ρ, the ratio of the real part to the imaginary part of the forward scattering amplitude, more generally as σ = A ( ν m )α−1 + B ( ν m )β−1 ± D ( ν m )α−1 , (5) dσ d(ν/m) = A(α − 1) ( ν m )α−2 + B(β − 1) ( ν m )β−2 ± D(α − 1) ( ν m )α−2 , (6)
120614937
Elastic scattering in nucleon-nucleon collisions
Recently, E811 has measured[1] the total cross section for pp scattering at √s = 1800 GeV. In this paper, we refit the experimental data for σtot, ϱ and B for both pp and pp to a QCD-inspired eikonal model, including the new σtot measurement.
119733346
A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function
We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function $F_{2}^{\gamma p}(x,Q^{2})$. We numerically inverted the function g(s), s being the variable in Laplace space, to G(v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g(s)→0 less rapidly than 1/s as s→∞, e.g., as 1/sβ for 0<β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G(v) is given by the product of a power vβ−1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10−6 obtaining numerical results that imitate the Dirac delta function δ(v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q2=5 GeV2 down to the lower virtuality Q2=1.69 GeV2. For devolution, β is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.
121023736
PHASE-SPACE INTEGRALS FOR MULTIPARTICLE SYSTEMS
The total phase-space integrals, occurring in the Fermi statistical theory of meson production, for 2-, 3-, 4-, and 5-body final states are reduced to forms suitable for numerical evaluation by hand computation. In addition, the momentum spectrum of any one particle, as derived from the statistical factor, is evaluated. For the 3- and 4-body systems, the $Q$ distribution for any two of the particles (effective mass minus the rest masses of the 2-particle subsystem) is derived. Numerical results are presented for nucleon-nucleon collisions at 0.8-, 1.5-, and 2.7-Bev bombarding kinetic energies.
13499391
New evidence for the saturation of the Froissart bound
Fits to high energy data alone cannot cleanly discriminate between asymptotic lns and ln{sup 2}s behavior of total hadronic cross sections. We demonstrate that this is no longer true when we require that these amplitudes also describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to high energy measurements of: (i) the {pi}{sup +}p and {pi}{sup -}p total cross sections and {rho}-values (ratio of the real to the imaginary portion of the forward scattering amplitude), for {radical}(s){>=}6 GeV, while requiring that the asymptotic fits smoothly join the {sigma}{sub {pi}{sup +}}{sub p} and {sigma}{sub {pi}{sup -}}{sub p} total cross sections at {radical}(s)=2.6 GeV--both in magnitude and slope, and (ii) separately simultaneously fit the pp and pp total cross sections and {rho}-values for {radical}(s){>=}6 GeV, while requiring that their asymptotic fits smoothly join the the {sigma}{sub pp} and {sigma}{sub pp} total cross sections at {radical}(s)=4.0 GeV--again both in magnitude and slope. In both cases, we have used all of the extensive data of the Particle Data Group [K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 010001 (2002).]. However, we then subject these data to a screening process, the Sieve algorithm [M. M. Block,more » physics/0506010.], in order to eliminate outliers that can skew a {chi}{sup 2} fit. With the Sieve algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high {delta}{chi}{sub i}{sup 2}, the individual ith point's contribution to the total {chi}{sup 2}. The {chi}{sup 2} fits are then made to the sieved data. Both the {pi}p and nucleon-nucleon systems strongly favor a high energy ln{sup 2}s fit of the form: {sigma}{sup {+-}}=c{sub 0}+c{sub 1}ln(({nu}/m))+c{sub 2}ln{sup 2}(({nu}/m))+{beta}{sub P{sup '}}(({nu}/m)){sup {mu}}{sup =} -{sup 1}{+-}{delta}(({nu}/m)){sup {alpha}}{sup -1}, basically excluding a lns fit of the form: {sigma}{sup {+-}}=c{sub 0}+c{sub 1}ln(({nu}/m))+{beta}{sub P{sup '}}(({nu}/m)){sup {mu}}{sup -1}{+-}{delta}(({nu}/m)){sup {alpha}}{sup -1}. The upper sign is for {pi}{sup +}p (pp) and the lower sign is for {pi}{sup -}p (pp) scattering, where {nu} is the laboratory pion (proton) energy, and m is the pion (proton) mass.« less
35775070
Surveying the Agents of Galaxy Evolution in the Tidally Stripped, Low Metallicity Small Magellanic Cloud (SAGE-SMC). I. Overview
The Small Magellanic Cloud (SMC) provides a unique laboratory for the study of the lifecycle of dust given its low metallicity (~1/5 solar) and relative proximity (~60 kpc). This motivated the SAGE-SMC (Surveying the Agents of Galaxy Evolution in the Tidally Stripped, Low Metallicity Small Magellanic Cloud) Spitzer Legacy program with the specific goals of studying the amount and type of dust in the present interstellar medium, the sources of dust in the winds of evolved stars, and how much dust is consumed in star formation. This program mapped the full SMC (30 deg^2) including the body, wing, and tail in seven bands from 3.6 to 160 μm using IRAC and MIPS on the Spitzer Space Telescope. The data were reduced and mosaicked, and the point sources were measured using customized routines specific for large surveys. We have made the resulting mosaics and point-source catalogs available to the community. The infrared colors of the SMC are compared to those of other nearby galaxies and the 8 μm/24 μm ratio is somewhat lower than the average and the 70 μm/160 μm ratio is somewhat higher than the average. The global infrared spectral energy distribution (SED) shows that the SMC has approximately 1/3 the aromatic emission/polycyclic aromatic hydrocarbon abundance of most nearby galaxies. Infrared color-magnitude diagrams are given illustrating the distribution of different asymptotic giant branch stars and the locations of young stellar objects. Finally, the average SED of H II/star formation regions is compared to the equivalent Large Magellanic Cloud average H II/star formation region SED. These preliminary results will be expanded in detail in subsequent papers.
29749856
SPATIAL VARIATIONS OF DUST ABUNDANCES ACROSS THE LARGE MAGELLANIC CLOUD
Using the data obtained with the Spitzer Space Telescope as part of the Surveying the Agents of a Galaxy's Evolution (SAGE) legacy survey, we have studied the variations of the dust composition and abundance across the Large Magellanic Cloud (LMC). Such variations are expected, as the explosive events which have lead to the formation of the many H I shells observed should have affected the dust properties. Using a model and comparing with a reference spectral energy distribution from our Galaxy, we deduce the relative abundance variations of small dust grains across the LMC. We examined the infrared color ratios as well as the relative abundances of very small grains (VSGs) and polycyclic aromatic hydrocarbons (PAHs) relative to the big grain abundance. Results show that each dust component could have different origins or evolution in the interstellar medium (ISM). The VSG abundance traces the star formation activity and could result from shattering of larger grains, whereas the PAH abundance increases around molecular clouds as well as in the stellar bar, where they could have been injected into the ISM during mass loss from old stars.
8901792
LABOCA observations of giant molecular clouds in the southwest region of the Small Magellanic Cloud
Context. The amount of molecular gas is a key for understanding the future star formation in a galaxy. Because H2 is diffi cult to observe directly in dense and cold clouds, tracers like the CO molecule are used. However, at low metallicities especially, CO only traces the shielded interiors of the clouds. In this context , millimeter dust emission can be used as a tracer to unveil the total dense gas masses. However, the comparison of masses deduced from the continuum SIMBA 1.2 mm emission and virial masses (thought to trace the whole potential of the clouds) in a sample of giant molecular clouds in the Small Magellanic Cloud (SMC) by Rubio et al. (2004) and Bot et al. (2007) showed a discrepancy between these two quantities that is in need of an explanation. Aims. This study aims at better assessing possible uncertainties on the dust emission observed in the sample of giant molecular clouds from the SMC. It focuses on the mass comparison in the densest parts of the giant molecular clouds where CO is detected in order to confirm the mass discrepancy observed. Methods. New observations of the south-west region of the SMC were obtained with the LABOCA camera on the APEX telescope. All the giant molecular clouds previously observed in CO are detected and their emission at 870� m is compared to ancillary data. The different contributions to the sub-millimeter emission are est imated, as well as dust properties (temperatures, emissivi ties), in order to deduce molecular cloud masses precisely. Results. The (sub-)millimeter emission observed in the giant molecular clouds in the south west region of the SMC is dominated by dust emission and masses are deduced for the part of each cloud where CO is detected and compared to the virial masses. The mass discrepancy between both methods is confirmed at 870� m with the LABOCA observations: the virial masses are on average 4 times smaller than the masses of dense gas deduced from dust emission, contrary to what is observed for equivalent clouds in our Galaxy. Conclusions. At present, the origin of this mass discrepancy in the SMC remains unkown. The direct interpretation of this effect is that the CO linewidth used to compute virial masses do not measure the full velocity distribution of the gas. Geometrical effects and uncertainties on the dust properties are also discussed.
10030510
DUST PRODUCTION AND MASS LOSS IN THE GALACTIC GLOBULAR CLUSTER NGC 362
We investigate dust production and stellar mass loss in the Galactic globular cluster NGC 362. Due to its close proximity to the Small Magellanic Cloud (SMC), NGC 362 was imaged with the Infrared Array Camera and Multiband Imaging Photometer cameras onboard the Spitzer Space Telescope as part of the Surveying the Agents of Galaxy Evolution (SAGE-SMC) Spitzer Legacy program. We detect several cluster members near the tip of the red giant branch (RGB) that exhibit infrared excesses indicative of circumstellar dust and find that dust is not present in measurable quantities in stars below the tip of the RGB. We modeled the spectral energy distribution (SED) of the stars with the strongest IR excess and find a total cluster dust mass-loss rate of 3.0{sup +2.0}{sub -1.2} x 10{sup -9} M{sub sun} yr{sup -1}, corresponding to a gas mass-loss rate of 8.6{sup +5.6}{sub -3.4} x 10{sup -6} M{sub sun} yr{sup -1}, assuming [Fe/H] =-1.16. This mass loss is in addition to any dustless mass loss that is certainly occurring within the cluster. The two most extreme stars, variables V2 and V16, contribute up to 45% of the total cluster dust-traced mass loss. The SEDs of the more moderate stars indicate themore » presence of silicate dust, as expected for low-mass, low-metallicity stars. Surprisingly, the SED shapes of the stars with the strongest mass-loss rates appear to require the presence of amorphous carbon dust, possibly in combination with silicate dust, despite their oxygen-rich nature. These results corroborate our previous findings in omega Centauri.« less