Bulletin of the American Physical Society
2007 APS April Meeting
Volume 52, Number 3
Saturday–Tuesday, April 14–17, 2007; Jacksonville, Florida
Session E8: Dynamic Few-Body Effects |
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Sponsoring Units: GFB Chair: Chris Greene, University of Colorado, JILA Room: Hyatt Regency Jacksonville Riverfront City Terrace 4 |
Saturday, April 14, 2007 3:30PM - 3:42PM |
E8.00001: Dissociative recombination of H$_{3}^{+}$ Samantha Santos, Viatcheslav Kokoouline, Chris Greene The process of dissociative recombination (DR) of the H$_{3}^{+}$ ion has been studied over the past years and it was found that the coupling of vibrational and electronic degrees of freedom plays a crucial role in the mechanism: when the Janh-Teller coupling effect was incorporated into the theoretical treatmnet it yielded DR rates in much better agreement with experiments. The previous work on H$_{3}^{+}$ was performed using hyperspherical coordinates and Siegert states for the vibrational wave functions. SVD technique employed in this study provides more accurate vibrational energies than the Siegert state approach for it takes into account the non-adiabatic coupling between different adiabatic channels. Another improvement towards theory-experiment agreement was to take into account the conditions and parameters of the experiments performed. The present approach uses SVD vibrational states in the calculatiion of H$_{3}^{+}$ DR rates and accounts for experimental conditions. Incorporating averaging procedures that describe better the experimental conditions improves the agreement between theory and experiment. Results for vibrationally-excited initial states of H$_{3}^{+}$ are also presented in this work. [Preview Abstract] |
Saturday, April 14, 2007 3:42PM - 3:54PM |
E8.00002: Numerical Solutions to the Time-Dependent, Coupled Dirac Equation Athanasios Petridis, Khinlay Win The time-dependent Dirac equation for interacting spinors is solved using the numerical staggered leap-frog algorithm. This method is very stable, fast and easily implemented on standard desk-top computers without any loss of accuracy. The relativistic decay of spinors initially set in potential wells that are constant in time is studied and found to exhibit strong non-exponential features as well as non-monotonic dependence on the potential strength. The problem of two spinors coupled by means of their electromagnetic potentials is addressed in one spatial dimension in free space and in external spatially periodic potentials. This system may represent a decaying meson. [Preview Abstract] |
Saturday, April 14, 2007 3:54PM - 4:06PM |
E8.00003: Chiral Symmetry Breaking and Effective Interactions in Nodal Fermion Systems William Shively, Dmitri Khveshchenko In strongly correlated electron systems such as graphene, low-energy quasiparticle excitations behave as Dirac (pseudo-relativistic) particles with two effective fermion ``flavors'' and with the speed of light replaced by the Fermi velocity. Recent results have revealed that such kinematics may have significant repercussions in a variety of many-body phenomena, such as in recent observations of the quantum Hall effect. Such condensed matter systems also provide formal analogues for a variety of phenomena in particle physics. We discuss excitonic pairing in nodal fermion systems and associated quantum phase transitions, and what these results might reveal about chiral symmetry breaking, Higgs-Yukawa interactions, and (2+1)-D QED. [Preview Abstract] |
Saturday, April 14, 2007 4:06PM - 4:18PM |
E8.00004: Accurate numerical solutions of the time-dependent Schr\"odinger equation W. van Dijk, F.M. Toyama We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schr\"odinger equation. The generalization yields numerical solutions accurate to order $(\Delta x)^{2r-1}$ in space and $(\Delta t)^{2M}$ in time for any positive integers $r$ and $M$, while CN employ $r=M=1$. We note dramatic improvement in the attainable precision (circa 10 or greater orders of magnitude) along with several orders of magnitude reduction of computational time. We show that the cumulative error and the CPU time of the numerical calculations scale as functions of $r$ and $M$. The method can be generalized further to obtain solutions of nonhomogeneous Schr\"odinger-type equations such as those arising when perturbation theory is applied to coupled-channel systems. The improved method is shown to lead to feasible studies of coherent-state oscillations with additional short-range interactions, wavepacket scattering, and long-time studies of decaying systems. Examples of solutions of nonhomogeneous equations will also be presented. [Preview Abstract] |
Saturday, April 14, 2007 4:18PM - 4:30PM |
E8.00005: Nucleon-Nucleon Scattering as a Stochastic Process in Phase Space Sarah John Nucleon-nucleon scattering is presented in the Wigner representation of the quantum Liouville equation. The antisymmetrized Wigner function, derived from minimum wave packets, is evolved in four-dimensional phase space representing spatial one-dimensional scattering. In the quasiclassical approximation, phase space points are evolved in a one-pion exchange potential in deterministic classical and stochastic quantum momentum jumps. Wave packet spreading inherent to linear dynamics is offset by intrinsic harmonic oscillation, resulting in phase space spin that perhaps lends meaning to the nucleon spin. Computed cross sections show good agreement with experiments in medium to high energy range. [Preview Abstract] |
Saturday, April 14, 2007 4:30PM - 4:42PM |
E8.00006: Nucleon-deuteron scattering in configuration space Vladimir Suslov, Mikhail Braun, Igor Filikhin, Branislav Vlahovic A new computational method for solving the configuration-space Faddeev equations for the breakup scattering problem [1] has been applied to consider the elastic \textit{pd} scattering. To perform numeric calculations for arbitrary nuclear potential and with arbitrary number of partial waves retained, we use approach proposed in [2]. The calculations of the inelasticity and phase-shift for various lab energies were performed with the charge independent AV14 potential. The results are compared with those of the Pisa group [3]. 1. V.M. Suslov and B. Vlahovic, Phys. Rev. C\textbf{69}, 044003 (2004). 2. S.P. Merkuriev, C. Gignoux and A. Laverne, Ann. Phys. \textbf{99}, 30 (1976). 3. A.Kievsky, M. Viviani, S. Rosati, Nucl. Phys. A\textbf{577}, 511 (1994). [Preview Abstract] |
Saturday, April 14, 2007 4:42PM - 4:54PM |
E8.00007: Numerical solution of the differential Yakubovsky equations for a system including three non-identical particles Branislav Vlahovic, Igor Filikhin, Vladimir Suslov The four-body system $\alpha \Lambda \Lambda \Xi$, having three non-identical particles, is considered. The OBE-simulating potential of the NSC97 model for the $\Lambda\Xi$ and $\Lambda\Lambda$ interactions is used [1]. Different phenomenological potentials of the $\Xi\alpha$ ($\Lambda\alpha $) interaction are applied. The differential Faddeev-Yakubovsky equations for the $\alpha \Lambda \Lambda \Xi$ system and its subsystems are numerically solved by the cluster reduction method [2] in $s$-wave approach. We have evaluated the binding energy of the hypothetical multi- strangeness nucleus $^7_{\Lambda \Lambda \Xi^0}$He. It was found that the existence of the ground state of this nucleus drastically depends on form of $\Xi\alpha$ potential. 1. I.N. Filikhin and A. Gal, Phys. Rev. {\bf C65}, 047001 (2002). 2. S.L. Yakovlev, I.N. Filikhin, Few-Body Systems Suppl. {\bf 10}, 36 (1999). [Preview Abstract] |
Saturday, April 14, 2007 4:54PM - 5:06PM |
E8.00008: Calculation of three-body resonances using slow-variable discretization coupled with complex absorbing potential Juan Blandon, Viatcheslav Kokoouline, Francoise Masnou-Seeuws We developed a method to calculate positions and widths of three-body resonances. The method combines the hyperspherical adiabatic approach, slow variable discretization method (Tolstikhin et al., J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996)), and a complex absorbing potential. The method can be used to obtain resonances having short-range or long-range wave functions. In particular, we applied the method to obtain very shallow three-body Efimov resonances for a model system (Nielsen et al., Phys. Rev. A 66, 012705 (2002)). [Preview Abstract] |
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