Bulletin of the American Physical Society
APS April Meeting 2010
Volume 55, Number 1
Saturday–Tuesday, February 13–16, 2010; Washington, DC
Session X7: Few-Body Theory |
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Sponsoring Units: GFB DNP Chair: Ionel Stetcu, University of Washington Room: Delaware A |
Tuesday, February 16, 2010 10:45AM - 10:57AM |
X7.00001: Higher Fock-State Effect to the Bound-State in Light-Front Dynamics Yukihisa Tokunaga Solving the relativistic bound-state problem is an important task in nuclear physics. Even the two-body bound-state problem has been solved only under a certain approximation due to the nonperturbative nature. The two-body Bethe-Salpeter equation in the Wick-Cutkosky model was often solved in the ladder approximation without including the cross-ladder contribution, although many different and more accurate treatments of the numerical method to solve the bound-state problem have been developed nowadays. In this presentation, we use the light-front dynamics (LFD) to solve the two-body bound-state problem and extend the light-front ladder approximation to include the cross-ladder contribution. In particular, we include the particle and antiparticle effect to the cross-ladder contribution and show the attractive nature of this effect. To find the bound-state system where this effect is significant, we discuss the case with different masses of two scalar particles and also with the exchange particle of non-zero mass to compare the effect in the Coulomb potential vs. the Yukawa potential. [Preview Abstract] |
Tuesday, February 16, 2010 10:57AM - 11:09AM |
X7.00002: The Pseudospectral Method: A Numerically Exact Partial Differential Equation Solver Applied to the Two-Electron Atom Paul Grabowski, David Chernoff The pseudosprectral method can produce solutions to partial differential equations which converge exponentially fast towards the exact solution. We present how to use this method to solve the non-relativistic Schr\"{o}dinger equation for helium and the negative hydrogen ion. We show how to properly treat the two-particle coalescence cusps and examine the effect of logarithmic terms in the exact solution. The only evidence of non-exponential convergence was for derivatives taken near the triple coalescence point. As developed and applied here the PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wavefunction near cusps or at large distances, the local energy (${\cal{H}}\psi/\psi$) is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. As the number of collocation points grows, the method achieves exponential convergence up to the resolution tested. [Preview Abstract] |
Tuesday, February 16, 2010 11:09AM - 11:21AM |
X7.00003: Parity-violating three-body forces in effective field theory Matthias R. Schindler Hadronic parity violation in the two-nucleon system has been studied using a pionless effective field theory (EFT). The advantage of an EFT over a model-dependent description is that it allows for the consistent description of three- and few-body systems. I will present the extension of the parity-violating EFT program to the three-body system, discussing the leading parity-violating three-body forces and whether these are required to consistently describe $nd$ scattering. These results can then be used in the description of the reaction $nd \to t\gamma$, for which a new experimental measurement might be performed in the future. [Preview Abstract] |
Tuesday, February 16, 2010 11:21AM - 11:33AM |
X7.00004: Ab initio no core results for light nuclei with a Woods-Saxon basis Gianina Alina Negoita, James Vary, Peter Maris, Andrey Shirokov We perform no-core (NCFC) calculations for a set of light nuclei with the realistic NN interaction, JISP16. We perform our calculations both in a harmonic oscillator and Woods-Saxon basis and compare convergence rates for the ground state energies, energies of selected excited states, rms radii and other observables. Initial results for the binding energies and rms radii of $^{4}$He and $^{12}$C will be presented. The differences in the convergence rates of these results with increasing basis space size reflects the infra-red properties of the basis states. We will discuss factorization of the center-of-mass motion and show how insuring factorization affects the results in the Woods-Saxon basis spaces. [Preview Abstract] |
Tuesday, February 16, 2010 11:33AM - 11:45AM |
X7.00005: The Similarity Renormalization Group with Spurious Deep Bound States K.A. Wendt, R.J. Furnstahl, R.J. Perry Similarity Renormalization Group (SRG) transformations decouple low- and high-energy degrees of freedom. The simplest examples are unitary and fixed by relatively simple flow equations that govern how the effective hamiltonian transforms. We study how decoupling emerges in cases where deeply bound states appear (e.g., spurious bound states in some effective field theories with large cutoff). We show that with the appropriate choice of SRG generator, deeply bound states decouple from low energy physics once the cutoff is lowered below the deep scale. Qualitatively, the high-energy region of the hamiltonian is diagonalized (the analog of integrating out these states) and a universal low-energy effective hamiltonian emerges. [Preview Abstract] |
Tuesday, February 16, 2010 11:45AM - 11:57AM |
X7.00006: Effective theory approach to few-fermion systems in a trap Jimmy Rotureau, Ionel Stetcu, Bruce Barrett, Mike Birse, Ubirajara Van Kolck The properties of strongly interacting Fermi gases have been the object of great interest in recent years. When the scattering length $a_2$ is much larger than the effective range of the interaction $r_0$, few-atom systems serve as a testing ground for techniques developed for the ab-initio solution of few-nucleon systems. We have applied the principles of Effective Field Theory to describe few-fermions systems in a harmonic trap. The interaction is written as a controllable expansion of contact interactions with derivatives. The no-core shell model is used to solve the many-body Schr\"odinger equation at leading order and corrections beyond LO are treated in perturbation theory. We have also adressed the relationship between the two-body and many-body cutoffs needed for a consistent model space. Results for the energies of the 3-fermions system at unitarity will be presented and shown to agree with known results. Results for systems with 3, 4 fermions for different values of $a_{2}/b$ (b being the trap length) and $r_{0}/b$ will also be presented. [Preview Abstract] |
Tuesday, February 16, 2010 11:57AM - 12:09PM |
X7.00007: Phase-fluctuating regime of a ring-shaped Bose-Einstein condensate Ludwig Mathey, Anand Ramanathan, Kevin Wright, William Phillips, Charles Clark We study the phase-fluctuating condensate regime of ultra-cold atoms trapped in a ring-shaped geometry. We first consider a simplified box geometry, in which we identify the conditions to create a state that is dominated by thermal phase fluctuations, and then explore the actual experimental geometry. We also address possible ways of detecting this regime. [Preview Abstract] |
Tuesday, February 16, 2010 12:09PM - 12:21PM |
X7.00008: Dissipative hydrodynamics (DHD) of rigid spherical particles Albert Kim, Yong Shi Phenomena of many spherical particles in aqueous phase are ubiquitous in a plethora of natural and engineered processes. Brownian dynamics (BD), as originated from molecular dynamics (MD), is inherently limited to point-particles governed by the Oseen diffusion tensor. Stokesian dynamics (SD) incorporates accurate multi-pole expansions and lubrication for accurate far- and near-field hydrodynamic interactions, respectively. Dissipative particle dynamics (DPD) overcame the relaxation-time restriction of BD and SD by developing Fokker-Planck equations including the Wiener process, but allowed pair-wise superposition of approximate hydrodynamic interactions. We unified DPD and SD and developed dissipative hydrodynamics (DHD) of rigid spherical particles, which incorporates many-body hydrodynamics of SD formalism and satisfies the fluctuation-dissipation theorem. DHD is more rigorous than SD and BD, and its accuracy is controllable with the choice of time step. Translations and rotations, influenced by both deterministic and random forces exerted on all the particles, can be accurately mimicked in a given uniform or shear flow within a range of the mean free path of a particle. [Preview Abstract] |
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