Bulletin of the American Physical Society
2011 Fall Meeting of the APS Division of Nuclear Physics
Volume 56, Number 12
Wednesday–Saturday, October 26–29, 2011; East Lansing, Michigan
Session ND: Nuclear Theory IV: For Theorists |
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Chair: Richard Furnstahl, The Ohio State University Room: Heritage |
Saturday, October 29, 2011 10:30AM - 10:42AM |
ND.00001: Renormalization and Power Counting of Chiral Nuclear Forces Bingwei Long, Chieh-Jen Yang We study renormalization of chiral nuclear forces by examining the cutoff dependence of the solution to the Lippmann-Schwinger equation for nucleon-nucleon scattering. In particular, we are interested in the interplay between renormalization and power counting of nucleon-nucleon contact interactions, leading to necessary modifications to Weinberg's original power counting scheme. We also discuss the difference between the conclusions of the previous investigations and ours. [Preview Abstract] |
Saturday, October 29, 2011 10:42AM - 10:54AM |
ND.00002: Two nucleons in a harmonic-oscillator trap with chiral potential Chiehjen Yang, Jimmy Rotureau, U. Van Kolck, Bruce Barrett We establish the connection between the bound-state energy spectrum for two nucleons in a harmonic-oscillator trap and their scattering phase shifts in the continuum with potentials derived from chiral effective field theory (EFT). We compare our results for the $^1S_0$ and $^3S_1-^3D_1$ channels to those obtained with pionless EFT. Our results extend the EFT approach to the no-core shell model to a higher-energy region. [Preview Abstract] |
Saturday, October 29, 2011 10:54AM - 11:06AM |
ND.00003: Understanding the Evolution of Three-Body Forces via Similarity Renormalization Group Kyle Wendt, Richard Furnstahl, Robert Perry The Similarity Renormalization Group (SRG) is a continuous series of unitary transformations. When the relative kinetic energy ($T_{\rm rel}$) is used in the SRG generator, high- and low- momentum scales are decoupled, but at a cost of induced many-body forces. For few-body nuclei or when including only short-range initial three-body forces, the four-body (and possibly higher) forces have been kept small. However, recent evolutions with long-range initial three-body forces, indicate that induced many- body forces gain significant strength for larger nuclei. We present some novel methods for examining the SRG evolution as well as results from model calculations where we have attempted to control these induced forces. [Preview Abstract] |
Saturday, October 29, 2011 11:06AM - 11:18AM |
ND.00004: Behavior of SRG evolved interactions into the p-shell Eric Jurgenson, Pieter Maris, Richard Furnstahl, Petr Navratil, Erich Ormand, James Vary The Similarity Renormalization Group has provided a powerful and versatile means to soften interactions for ab initio nuclear calculations. The large contribution of three-body forces to the nuclear interaction has required the consistent evolution of free-space Hamiltonians in the three-particle space. Fully evolved NN+3N calculations at A=6 show very minor contributions due to induced four-body forces, signalling a controlled hierarchy of renormalization effects. However, questions have arisen whether this situation persists for larger systems. We will present investigations into this question and discuss efforts at further many-body calculations with evolved interactions. [Preview Abstract] |
Saturday, October 29, 2011 11:18AM - 11:30AM |
ND.00005: Euclidean relativistic quantum mechanics I Wayne Polyzou, Philip Kopp We introduce a formulation of relativistic quantum mechanics where the dynamical input is Euclidean generating functionals or Green functions. We discuss how dynamical calculations can be performed in this framework without analytic continuation. We discuss the structure of model generating functionals, the construction of the Hilbert space, the Poincar\'e Lie Algebra, one particle eigenstates, and representations of finite Poincar\'e transformations. [Preview Abstract] |
Saturday, October 29, 2011 11:30AM - 11:42AM |
ND.00006: Euclidean relativistic quantum mechanics II Philip Kopp, Wayne Polyzou We discuss the calculation of scattering amplitudes in relativistic Euclidean quantum mechanics. We discuss the general formulation of the scattering problem, in terms of the existence of wave operators and formal methods for computing scattering amplitudes without analytic continuation. Two models are discussed to illustrate the method and the accuracy of the computations. [Preview Abstract] |
Saturday, October 29, 2011 11:42AM - 11:54AM |
ND.00007: Effective field theory for the Helium-6 halo nucleus Chen Ji, Charlotte Elster, Daniel Phillips The ground-state of Helium-6 can be treated as a two-neutron halo with an alpha-particle core. This bound state is generated by the resonant $nn$ and $n\alpha$ interactions. The latter is dominated by a shallow p-wave resonance, where both the scattering length and effective range appear at leading order [1]. Here we first study a separable-potential model which fits the $nn$ and $n\alpha$ scattering parameters (c.f., e.g. [2]). This reproduces known properties of He-6 moderately well for a specific choice of interaction ranges. We then show that the He-6 binding energy diverges in the limit that the range of the $n \alpha$ and $nn$ forces goes to zero. This indicates that within Halo EFT this three-body system needs an $nn \alpha$ contact interaction to be properly renormalized at leading order. We adjust the coefficient of this $nn \alpha$ force to reproduce the Helium-6 ground-state energy, and present its running as a function of the cutoff. The correlations amongst Helium-6 properties that result from this successful renormalization of the leading-order three-body problem in halo EFT with p-wave resonant interactions will be discussed. \\[4pt] [1] C.~A.~Bertulani, {\it et al.}, Nucl.\ Phys.\ {\bf A712}, 37 (2002). \newline [2] A.~Ghovanlou, D.~R.~Lehman, Phys.\ Rev.\ {\bf C9}, 1730 (1974). [Preview Abstract] |
Saturday, October 29, 2011 11:54AM - 12:06PM |
ND.00008: Vector variable solution of the N-N scattering problem using the momentum-space Argonne V18 interaction Saravanan Veerasamy, Elster Charlotte, Wayne Polyzou We discuss the formulation and solution of the nucleon-nucleon scattering problem using a vector-variable approach in momentum space. We take the Argonne V18 potential as input potential. The operator form of this potential is represented by the sum of a complete set of spin-isospin operators multiplied by functions of the momentum transfer, which are accurately approximated using Chebyshev polynomials. This representation makes it easy to compute Wolfenstein parameters directly from the solution of the Lippmann-Schwinger equation. The Wolfenstein parameters are then used to calculate the experimental observables. This approach overcomes some of the difficulties in using partial wave expansions to represent smooth scattering amplitudes at medium energies. Wolfenstein parameters and a representative set of observables will be presented and compared to calculations based on partial waves. [Preview Abstract] |
Saturday, October 29, 2011 12:06PM - 12:18PM |
ND.00009: Low Density Matter and Bose Einstein Condensates in Nuclei Katarzyna Schmidt The ability to isolate low density matter in near Fermi Energy collisions and the high degree of alpha clustering at such low densities suggest that we search for evidence of Bose Condensates which are predicted to occur in the density and temperature range which we are exploring [1-3]. A natural way to pursue this question experimentally appears to be to apply our techniques of low density gas investigation to collisions of ``alpha-conjugate'' nuclei expected to have significant initial alpha cluster character. Such nuclei might show a more natural predilection to evolve into a Bose Condensate. We have initiated a search for evidence of Bose Condensates using the NIMROD array. Our first experiments, carried out at the end of 2008 employed 10, 25, 35 MeV/u beams of $^{40}$Ca and $^{28}$Si incident on $^{40}$Ca, $^{28}$Si, $^{12}$C and $^{180}$Ta targets. The data are currently being analyzed. It is our expectation that a Bose Condensate would manifest itself as an assemblage of alpha conjugate products with particular kinematic correlations. References: [1] Y. Funakiet al., Phys. Rev. C 80, 064326 (2009). [2] G. Roepke et al., Phys. Rev. Lett. 80, 3177(1998). [3] T. Sogo et al., Phys. Rev. C 81, 064310 (2010). [Preview Abstract] |
Saturday, October 29, 2011 12:18PM - 12:30PM |
ND.00010: Neutron Matter as a Composite Bose-Fermi Superfluid Goran Arbanas, Arthur Kerman, Hai Ah Nam, Jirina Stone We model infinite neutron matter as an interacting Bose-Fermi superfluid consisting of superconducting neutrons and a Bose-Einstein condensate of a six-quark Feshbach state. The interaction term in the many-body grand canonical Hamiltonian is defined by a coupling form-factor and a coupling strength that are determined by fitting an expression for neutron-neutron scattering (via the same Feshbach state) to the $^{1}$S$_{0}$ phase shift. Extremization of the expectation value of the grand canonical Hamiltonian in the ground state yields an equation of state for infinite neutron matter that we numerically solve for particle-number densities between 10$^{-7}$ and 0.5 fm$^{-3}$. In the unitary limit (i.e., infinite scattering length and a zero effective range), we find the energy per particle to be 0.6 that of a free Fermi gas. The effect of random-phase-approximation corrections to our equation of state is addressed. [Preview Abstract] |
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