Bulletin of the American Physical Society
APS April Meeting 2010
Volume 55, Number 1
Saturday–Tuesday, February 13–16, 2010; Washington, DC
Session Q8: The Nucleus as a Theorists' Laboratory |
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Sponsoring Units: DNP Chair: Dean Halderson, Western Michigan University Room: Delaware B |
Monday, February 15, 2010 1:30PM - 1:42PM |
Q8.00001: Tamm-Dancoff as the contraction limit of the Richardson-Gaudin equations for pairing Stijn De Baerdemacker The pairing interaction, resulting from the $J=0$ component of the short-range nucleon-nucleon interaction, plays a dominant role in the structure of atomic nuclei. The BCS treatment of the pairing Hamiltonian has provided considerable insight in the problem, however there is need for a canonical (number of particle conserving) technique, due to the finite number of particles in the system. One way around is to approximate a pair of nucleons as a single boson-like entity, however violating the underlying Pauli principle. Eventually it can be shown that, relying on the early studies of Richardson \& Gaudin, the reduced pairing Hamiltonian is exactly diagonalisable by means of a canonical Bethe Ansatz eigenstate, provided the set of non-linear Richardson-Gaudin equations are solved. In the present contribution it will be shown how one can regain the Tamm-Dancoff dispersion relation from the Richardson-Gaudin equations by deforming the $su(2)$ quasi-spin algebra towards the Heisenberg-Weil algebra in the contraction limit, leaving the Hamiltonian exactly solvable along the deformation path. [Preview Abstract] |
Monday, February 15, 2010 1:42PM - 1:54PM |
Q8.00002: Projected Hartree-Fock in a shell-model basis Joshua Staker, Calvin Johnson We implement projected Hartree-Fock in a shell-model basis and compare against exact numerical results from full space diagonalization. We consider the accuracy of projected Hartree-Fock for the excited state spectrum, the moment of inertia, and also odd-even staggering. [Preview Abstract] |
Monday, February 15, 2010 1:54PM - 2:06PM |
Q8.00003: A Performant Algorithm to Calculate Spin- and Parity-Dependent Nuclear Level Densities Roman Senkov, Mihai Horoi A new algorithm for calculating the spin- and parity-dependent shell model nuclear level densities using the moments method in the proton-neutron formalism will be presented. A new, parallelized code based on this algorithm was developed and tested using up to 4,000 cores on FRANKLIN/NERSC, for a set of nuclei from the $sd$-, $pf$-, and $pf+g9/2$- model spaces. By comparing the low excitation energy nuclear level densities for a given nucleus calculated in two model spaces, such as $pf$ and $pf+g9/2$, we could estimated its ground state energy in the larger model space, which is not accessible to direct shell model calculations because of the unmanageable dimension. Examples for the ground state energies of for ${}^{64}$Ge and ${}^{68}$Se in the $pf+g9/2$ model space will be presented. [Preview Abstract] |
Monday, February 15, 2010 2:06PM - 2:18PM |
Q8.00004: Sensitivity analysis of random shell-model interactions Plamen Krastev, Calvin Johnson The input to the configuration-interaction shell model includes many dozens or even hundreds of independent two-body matrix elements. Previous studies have shown that when fitting to experimental low-lying spectra, the greatest sensitivity is to only a few linear combinations of matrix elements. Following Brown and Richter [1], here we consider general two-body interactions in the 1s-0d shell and find that the low-lying spectra are also only sensitive to a few linear combinations of two-body matrix elements. We find out in particular the ground state energies for both the random and non-random (here given by the USDB) interaction are dominated by similar matrix elements, which we try to interpret in terms of monopole and contact interactions, while the excitation energies have completely different character. \\[4pt] [1] B. Alex Brown and W. A. Richter, Phys. Rev. C 74, 034315 (2006) [Preview Abstract] |
Monday, February 15, 2010 2:18PM - 2:30PM |
Q8.00005: Probing time-odd and tensor terms of the Skyrme functional in rotating nuclei V. Hellemans, P.-H. Heenen, M. Bender The parametrisation of the two-body part of a Skyrme energy density functional (EDF) can be determined by considering that it is generated by a two-body Skyrme interaction. This relation between the parameters of the functional and an interaction has often been used in single-reference EDF approaches (traditionally called self-consistent mean-field approaches).In general, the parameters of the effective interactions or EDF are adjusted to reproduce the properties of nuclear matter and the bulk properties of doubly magic nuclei. In this case, one assumes time reversal invariance, hence the so-called ``time-odd'' terms in the EDF, which is bilinear in densities and currents that are either even or odd under a time reversal operation, do not contribute and only the ``time-even'' terms are constrained by physical observables. One therefore has to investigate the role and the effect of these ``time-odd'' terms. In the same way, the role of a zero-range tensor interaction to the description of odd and of rotating nuclei requires to be investigated. Results on the role of both the time-odd terms and the tensor terms in the Skyrme EDF in rotating nuclei will be discussed. Supported by the US DOE under grant DE-FG02-95ER-40934. [Preview Abstract] |
Monday, February 15, 2010 2:30PM - 2:42PM |
Q8.00006: Dirac Oscillators and the Relativistic R-matrix Janina Grineviciute, Dean Halderson The R matrix formalism has been constructed for coupled channel reactions in which binary breakup channels satisfy relative Dirac equations. The basis for the expansion of the internal wave function is Dirac oscillators. An example of the calculations is calculating observables for proton scattering using the relativistic Love - Franey amplitudes of Horowitz.\footnote{C. J. Horowitz, Phys. Rev. C 31, 1340 (1985)} The R matrix formalism allows the nonlocal exchange terms to be calculated exactly. Exact and approximate treatments of the exchange term give different results, which can be traced to matrix elements of negative energy states. Another advantage of the R matrix approach is ability to make scattering states orthogonal to bound states which is important at low energies. [Preview Abstract] |
Monday, February 15, 2010 2:42PM - 2:54PM |
Q8.00007: Nonlinear Features of Nuclear Collective Vibrations Sarah Buchhorn, Vladimir Zelevinsky Atomic nuclei reveal rich diversity of collective modes of vibrational and rotational type. We analyze the experimental data for low-lying collective excitations in many medium-mass even-even nuclei and find convincing manifestations of systematic nonlinear effects that cannot be reduced to weak anharmonicity. Here we discuss two empirical trends. (i) The assumption that the main part of the restoring potential for the most collective quadrupole vibrations of spherical nuclei is quartic, $\propto \beta^{4}$, where $\beta$ is the quadrupole deformation coordinate, leads to the spin dependence of the yrast vibrational states $E\propto J^{4/3}$, in agreement with data for many isotopes of Cr, Ni, Zn, Ge, Se, Kr, Sr, Mo, Ru, Pd, Cd. (ii) The second effect is the systematic coupling between quadrupole ($2^{+}$) and octupole ($3^{-}$) modes that leads to the correlation of their energies, E(3)=A-B/E(2) in agreement with many isotopic chains; this is important for the search of (PT)-violating electric dipole moments. We present theoretic arguments explaining these trends. [Preview Abstract] |
Monday, February 15, 2010 2:54PM - 3:06PM |
Q8.00008: Is Deuterium Nuclear Fusion Catalyzed by Antineutrinos? Isaac Shomer The hypothesis of Fischbach and Jenkins that neutrinos emitted from the sun accelerate radioactive decay is noted. It is thought that neutrinos accelerate beta decay by reacting with neutron-rich nuclides to form a beta particle and a daughter product, with no antineutrino emitted. Conversely, it is proposed that antineutrinos can react with proton-rich nuclides to cause positron decay, with no neutrino emitted. It is also proposed that the nuclear fusion of the hydrogen bomb is triggered not only by the energy of the igniting fission bomb, but by the antineutrinos created by the rapid beta decay of the daughter products in the fission process. The contemplated mechanism for antineutrino initiated fusion is the following: 1. The antineutrinos from the fission daughter products cause positron decay of deuterium by the process outlined above. 2. In a later fusion step, these positrons subsequently react with neutrons in deuterium to create antineutrinos. Electrons are unavailable to annihilate positrons in the plasma of the hydrogen bomb. 3. These antineutrinos thereafter react with more deuterium to form positrons, thereby propagating a chain reaction. [Preview Abstract] |
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