Bulletin of the American Physical Society
2007 Annual Meeting of the Division of Nuclear Physics
Volume 52, Number 10
Wednesday–Saturday, October 10–13, 2007; Newport News, Virginia
Session CH: Few-Body Systems |
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Chair: Ch. Elster, Ohio University Room: Newport News Marriott at City Center Blue Point I |
Friday, October 12, 2007 9:00AM - 9:12AM |
CH.00001: $\pi N$ scattering in the $\Delta(1232)$ region Bingwei Long, Ubirajara van Kolck We develop a chiral effective field theory based on the rest-frame heavy-baryon formalism to describe $\pi N$ scattering in the $\Delta$(1232) resonance region. The phase shift in the $P_{33}$ elastic channel is calculated up to next-to-next-to-leading order. A comparison is made with phenomenological phase-shift analyses. [Preview Abstract] |
Friday, October 12, 2007 9:12AM - 9:24AM |
CH.00002: Search for collective enhancement of the nuclear Schiff moment Alexander Volya, Naftali Auerbach, Vladimir Zelevinsky The non-zero expectation value of the nuclear Schiff moment violates invariance under spatial inversion and time reversal and produces the electrostatic potential that induces the electric dipole moment (EDM) of the atom. The experimental discovery of the atomic EDM pursued by several experimental groups would mark a significant progress in understanding fundamental symmetries of nature; the best limits on P,T-violating forces come from the EDM measurements in Hg and Xe nuclei. Strong interactions in the nucleus influence the value of the Schiff moment. The static octupole deformation was shown [1] to produce large enhancement of the Schiff moment in deformed nuclei through the mixing of parity doublets. We study the idea [2] of the possible enhancement in spherical nuclei with soft quadrupole and octupole collective modes. The existence of the effect was confirmed [3] in the limit of very small collective frequencies in the framework of the RPA. We show the results of the exact diagonalization in the model with pairing and multipole-multipole forces that demonstrate the presence of the enhancement as a result of the mixing in the odd nucleus of states with the same angular momentum and opposite parity having large phonon components. \newline [1] V. Spevak, N. Auerbach and V.V. Flambaum, Phys. Rev. C 56 (1997) 1357. [2] V.V. Flambaum and V.G. Zelevinsky, Phys. Rev. C 68 (2003) 035502. [3] N. Auerbach, et.al., Phys. Rev. C 74 (2006) 025502. [Preview Abstract] |
Friday, October 12, 2007 9:24AM - 9:36AM |
CH.00003: Poincar\'e Invariant Three-body Scattering T. Lin, Ch. Elster, W. Polyzou, W. Gloeckle The Poincar\'e invariant Faddeev equation for three-body scattering is directly formulated in momentum space without employing a partial wave decomposition. The scattering amplitude is obtained as functions of vector momenta by solving the Faddeev equation in three dimensions through Pad\'e iteration. Based on a Malfliet-Tjon type potential, differential cross sections for elastic and break-up scattering (inclusive and exclusive) are calculated at selected energies up to the GeV scale. The reaction mechanisms at higher energies associated with different kinematic configurations such as quasi-free (QFS) and final state interaction (FSI) are investigated and compared to the corresponding non-relativistic cross sections. Especially, multiple rescattering contributions beyond the leading order of the two-body t matrix are analyzed as function of energy and kinematic configuration. [Preview Abstract] |
Friday, October 12, 2007 9:36AM - 9:48AM |
CH.00004: Decoupling via the Similarity Renormalization Group for Nucleon-Nucleon Forces E.D. Jurgenson, R.J. Furnstahl, S.K. Bogner The Similarity Renormalization Group (SRG) provides a compelling new method for decoupling low-energy nuclear physics from high-energy details. While observables are unchanged by the SRG's unitary transformations, the dependence of matrix elements on high-momentum contributions is modified by the running transformation. The SRG has the effect of partially diagonalizing the potential to a width of order the evolution parameter lambda. Because of this diagonalization, one expects a simple decoupling of the low-energy observables for these high-energy degrees of freedom. In a previous work,\footnote{S.K. Bogner, R.J. Furnstahl, R.J. Perry and A. Schwenk, Phys. Lett. B 649 (2007) 488.} evidence for decoupling in phase shifts and the deuteron was shown for the Argonne V18 potential. Here we extend the demonstration of decoupling to other NN potentials and up to A=6 nuclei to verify its universal nature and to show quantitatively that the residual coupling is perturbative above the energy corresponding to the SRG evolution parameter. [Preview Abstract] |
Friday, October 12, 2007 9:48AM - 10:00AM |
CH.00005: Chiral NN potentials and renormalization Ruprecht Machleidt, David Entem In recent years, quantitative nucleon-nucleon (NN) potentials based upon chiral perturbation theory (ChPT) have been developed. All these potentials apply what is known as ``Weinberg power counting''. However, this renormalization scheme has been the subject of varying forms of criticism for more than a decade. Systematic investigations of the issue conducted to date have been restricted to only the leading order (LO) of ChPT. Since quantitative chiral NN potentials are constructed at next-to-next-to-next-to-leading (N3LO), it is necessary to investigate the power counting issue beyond LO, and ultimately at N3LO. We have launched such a program and will report the current status of our findings. [Preview Abstract] |
Friday, October 12, 2007 10:00AM - 10:12AM |
CH.00006: Loop Corrections and Naturalness in a Chiral Effective Field Theory Brian Serot, Jeff McIntire The loop expansion is applied to a chiral effective hadronic lagrangian; with the techniques of Infrared Regularization, it is possible to separate out the short-range contributions and to write them as local products of fields that are already present in our lagrangian. (The appropriate field variables must be re-defined at each order in loops.) The corresponding parameters implicitly include short-range effects to all orders in the interaction, so these effects need not be calculated explicitly. The remaining (long-range) contributions that must be calculated are nonlocal and resemble those in conventional nuclear-structure calculations. Nonlinear isoscalar scalar $(\sigma)$ and vector $(\omega)$ meson interactions are included, which incorporate many-nucleon forces and nucleon substructure. Calculations are carried out at the two-loop level to illustrate these techniques at finite nuclear densities and to verify that the coupling parameters remain natural when fitted to the empirical properties of equilibrium nuclear matter. Contributions from the $\omega N$ tensor coupling are also discussed. [Preview Abstract] |
Friday, October 12, 2007 10:12AM - 10:24AM |
CH.00007: Operator Evolution via the Similarity Renormalization Group E.R. Anderson, S.K. Bogner, R.J. Furnstahl, R.J. Perry The Similarity Renormalization Group (SRG) uses unitary transformations to suppress off-diagonal matrix elements, forcing the Hamiltonian towards a band-diagonal form. An SRG transformation applied to nucleon-nucleon interactions leads to greatly improved convergence properties while preserving observables, and provides a method to consistently evolve many-body potentials and other operators.\footnote{S.K. Bogner, R.J. Furnstahl, and R.J. Perry, Phys. Rev. C 75 (2007) 061001.} Here the nature of operator evolution is explored, taking as an example the operator for the bare momentum distribution. The equivalence of a direct evolution via SRG equations and a construction from evolved eigenstates is shown. The flow of the operator and its matrix elements in the deuteron is exhibited and analyzed on the basis of the SRG flow equations for the operator. Conjectures\footnote{S.K. Bogner \textit{et al.}, Phys. Lett. B 649 (2007) 488.} on the factorization of the unitary operator $U({\bf k},{\bf q})$ into $K_\lambda({\bf k})Q({\bf q})$ for $k<\lambda$ and $q \gg \lambda$ are explored pictorially and analytically. [Preview Abstract] |
Friday, October 12, 2007 10:24AM - 10:36AM |
CH.00008: No-core shell model as effective theory: applications to light nuclei and cold atoms in harmonic traps Ionel Stetcu Systems with large two-body scattering lengths are of particular interest because they exhibit universal behavior. While such systems have become popular in atomic physics only in the last decade, in nuclear physics they have been investigated since its beginning. Hence, it is not surprising that techniques developed for solving the nuclear few-body problem are immediately applicable to such systems in atomic physics. In this talk, I will present an effective-field theory approach to constructing two- and three-body effective interactions in no-core shell model finite spaces, with applications to the description of light nuclei and cold atom gases in harmonic traps, and I will argue how the same renormalization techniques can be applied to both kinds of systems. [Preview Abstract] |
Friday, October 12, 2007 10:36AM - 10:48AM |
CH.00009: Magnetic Monopole Atom Edwin Norbeck A N-S monopole pair should form an atom, an analog of positronium. Such atoms might be created by colliding Pb beams at the LHC for which the available energy is 1144 TeV. The difficulty in understanding such systems can be seen by using the textbook positronium formula and Dirac's observation that the effective ``charge'' of a monopole (to use in Coulomb's law) is 67.5 n times the electron charge. Even with the integer n = 1, the energy radiated by a pair of poles as the atom cascades to the ground state is 147 times the rest energy of the pair, in violation of energy conservation. Relativistic corrections increase this value. Vacuum polarization effects give a large correction in the right direction, but the usual QED can not be used because the magnetic fine structure constant is huge, 137/4. Even without detailed calculations it can be assumed that the mass of the atom is much smaller than the mass of two free poles. As a newly produced pair begins to separate, one could expect additional poles to be produced from the vacuum resulting in two atoms moving away from each other. These atoms would self annihilate resulting in back to back jets. [Preview Abstract] |
Friday, October 12, 2007 10:48AM - 11:00AM |
CH.00010: Quantum bound state of three protons in high magnetic field Sh. M. Tsiklauri, R. Ya. Kezerashvili, L.L. Margolin This paper consider possibility that three proton may bind uniform magnetic field. The purpose of this article is to use of the hyperspherical function method for investigation confined three protons. It is apparent that one requires magnetic fields order 10$^{12}$ T for the Coulomb repulsion to be modest enough to be treated as a correction. Such magnetic fields are believed to be found in nature -- on the surface of magnetars. This novel class of quantum bound states is the focus of the present paper. [Preview Abstract] |
Friday, October 12, 2007 11:00AM - 11:12AM |
CH.00011: A Cluster Model of $^{6}$He and $^{6}$Li Jeremy Armstrong, Alexander Sakharuk, Vladimir Zelevinsky Small nuclei provide an ideal testing ground of few-body theories. $^{6}$He is particularly interesting in that it shows an extended particle distribution similar to a halo nucleus, is loosely bound, and is a Borromean system. We apply the Brink Formalism in secondary quantization to study the structure of $^{6}$He. This formalism allows for the proper treatment of Fermi statistics and correct projection into eigenstates of angular momentum. The alpha plus dineutron configuration and ``cigar'' (neutron, alpha, neutron chain) configuration were studied to obtain binding energies, charge radii, matter radii, and B(E2) for $^{6}$He. The same configurations were used to obtain the same observables for $^{6}$Li. We were then able to calculate the log ft value for the beta decay of $^{6}$He. We now examine the effects of different nucleon-nucleon interactions on our systems. [Preview Abstract] |
Friday, October 12, 2007 11:12AM - 11:24AM |
CH.00012: Transition energy correlations in the three-body continuum of Borromean Halo Nuclei Boris Danilin, Jan Vaagen, Torbjoern Rogde, Sergey Ershov, Ian Thompson, Mikhail Zhukov Energy correlations in transitions from the bound state to the three-body continuum of Borromean halo nuclei are considered. A core+n+n three-body cluster model which reproduces experimentally known properties of $^6$He and $^{11}$Li has been used to study low-lying resonances and soft modes. The analysis of the correlated responses in $^6$He shows that in the case of the narrow three-body $2^+_1$ resonance the transition energy correlations are the same as in the intrinsic correlated structure in $3\rightarrow 3$ scattering. They differ significantly for wide $2^+_2$, $1^+_1$ resonances, and also for the soft dipole and monopole modes, where, due to the transition operators, the intertwining of the ground state and the three-body continuum plays a significant role. [Preview Abstract] |
Friday, October 12, 2007 11:24AM - 11:36AM |
CH.00013: How to Classify Three-Body Forces -- and Why Harald W. Griesshammer To add 3-body forces when theory and data disagree is untenable when predictions are required. For the ``pion-less'' Effective Field Theory at momenta below the pion-mass, I provide a recipe to systematically estimate the typical size of 3-body forces in all partial waves and orders, including external currents~[1]. It is based on the superficial degree of divergence of the 3-body diagrams which contain only two-body forces and the renormalisation-group argument that low-energy observables must be insensitive to details of short-distance dynamics. Na\"ive dimensional analysis must be amended as the asymptotic solution to the leading-order problem depends for large off-shell momenta crucially on the partial wave and spin-combination considered. The typical strength of most 3-body forces turns out weaker than expected, demoting many to high orders. As application, the thermal cross section of $nd\to t\gamma$ bears no new 3-body force~[2], besides those fixed by the triton binding energy and $nd$ scattering length in the triton channel: $0.485(\mathrm{LO})+0.011(\mathrm{NLO})+0.007(\mathrm{NNLO}) ];\mathrm{mb}=[0.503\pm0.003]\;\mathrm{mb}$, converges and compares well with data, $[0.509\pm0.015]\;\mathrm{mb}$. Potential models list $[0.49\dots0.66]\;\mathrm{mb}$, depending on the 2-nucleon potential and inclusion of the $\Delta(1232)$. [1] H.W.~Grie{\ss}hammer: Nucl.~Phys.~\textbf{A760} (2005) 110 [2] H.~Sadeghi, S.~Bayegan and H.W.~Grie{\ss}hammer: Phys.~Lett.\textbf{B643} (2006), 263. [Preview Abstract] |
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