Bulletin of the American Physical Society
2008 Annual Meeting of the Division of Nuclear Physics
Volume 53, Number 12
Thursday–Sunday, October 23–26, 2008; Oakland, California
Session HD: Nuclear Theory: Structure of Nuclei |
Hide Abstracts |
Chair: Petr Navratil, Lawrence Livermore National Laboratory Room: Jewett Ballroom G-H |
Saturday, October 25, 2008 2:00PM - 2:12PM |
HD.00001: Effective Field Theory and Pseudospin Symmetry Joseph Ginocchio Recently effective field theories have been developed which derive effective nucleon-nucleon interactions which involve the spin. We may ask why don't these expansions naturally involve the pseudospin [1] as well? First we found that the spin-spin interaction between nucleons is equivalent to the pseudospin-pseudospin interaction between nucleons. Second we showed that the tensor interaction is a spin-pseudospin interaction. This is an interesting insight and implies that the tensor interaction violates both spin and pseudospin equally. However, the two body spin-orbit and the two body pseudospin-pseudo-orbit interactions are not equivalent and imply different physics. The two body pseudospin-pseudo-orbit interaction can be written in terms of a linear combination of the two body spin-orbit interaction and the tensor interaction. Although the tensor interaction conserves neither spin or pseudospin, the two body spin-orbit interaction conserves spin but not pseudospin and, vice-versa, the two body pseudospin-pseudo-orbit interaction conserves pseudospin but not spin. This suggests that, instead of writing the effective nucleon-nucleon interaction in terms of the tensor interaction, a more revealing exposition would to be to write the effective nucleon-nucleon interaction as a linear combination of the two body spin-orbit interaction and two body pseudospin-pseudo-orbit interaction. \newline [1] Joseph N. Ginocchio, Physics Reports 414, 165 (2005). [Preview Abstract] |
Saturday, October 25, 2008 2:12PM - 2:24PM |
HD.00002: The Nuclear Born Oppenheimer Method and Nuclear Rotations Nouredine Zettili In this presentation, we want to discuss how to apply the Nuclear Born Oppenheimer (NBO) formalism to the description of nuclear rotations. This application will be illustrated on nuclei that are axially-symmetric and even (but non-closed shell). We will focus, in particular, on the derivation of expressions for the energy and for the moment of inertia. In addition, we will examine the connection of the NBO method with the self-consistent cranking model. We will compare the moment of inertia generated by the NBO method with the Thouless-Valantin formula and hence establish a connection between the NBO method and the large body of experimental data. [Preview Abstract] |
Saturday, October 25, 2008 2:24PM - 2:36PM |
HD.00003: Nuclear structure with the algebraic collective model M.A. Caprio, D.J. Rowe, T.A. Welsh A tractable scheme for numerical diagonalization of the Bohr Hamiltonian, based on $\mathrm{SU}(1,1)\times\mathrm{SO}(5)$ algebraic methods, has recently been proposed. The direct product basis obtained from an optimally chosen set of $\mathrm{SU}(1,1)$ $\beta$ wave functions and the $\mathrm{SO}(5)$ spherical harmonics $\Psi_{v\alpha L M}(\gamma,\Omega)$ provides an exceedingly efficient basis for numerical solution, as compared to conventional diagonalization in a five-dimensional oscillator basis. In this talk, the status of the $\mathrm{SU}(1,1)\times\mathrm{SO}(5)$ algebraic collective model will be summarized and applications will be presented. In particular, the transition from axially symmetric to triaxial structures will be explored. Supported by the US DOE under grant DE-FG02-95ER-40934. [Preview Abstract] |
Saturday, October 25, 2008 2:36PM - 2:48PM |
HD.00004: Light nuclei without a core Pieter Maris, Andrey Shirokov, James Vary We report on recent progress in ab initio no-core full configuration basis calculations. We present results for the ground state energy and spectrum for the low-lying states of nuclei up to A = 14 using a realistic NN interaction, JISP16. Our spectra are in reasonable agreement with available experimental data. In addition to the energies, we also calculate selected observables such as rms radii and quadrupole moments. [Preview Abstract] |
Saturday, October 25, 2008 2:48PM - 3:00PM |
HD.00005: Pairing in Small, 2D Fermi Systems Jeremy Armstrong, Massimo Rontani, Sven Aberg, Vladimir Zelevinsky, Stephanie Reimann In recent years, trapped, ultra-cold atomic gasses have provided a rich testing ground for quantum theories. We apply a pairing model from nuclear physics to a 2D harmonically confined, two-component atomic gas containing 2-9 particles. Our Hamiltonian consists of the oscillator mean field and a contact pairing interaction. We calculate excitation spectra, yrast spectra, the BCS pairing gap, and addition energies for various values of the pairing strength. As expected, when the interaction is weak, the oscillator mean field is dominant, and as the interaction strength is increased, pairing effects become quite clear. Results are compared with \textit{ab initio} calculations. [Preview Abstract] |
Saturday, October 25, 2008 3:00PM - 3:12PM |
HD.00006: An Isospin Revival for 2008 Aram Mekjian, Larry Zamick We can make an association of isospin and angular momentum in a single j shell.For 2 particles the interaction in isospin a +b t(1).t(2) is equivlant to c +d(-1)$^J$ where J is the angular momentum of the 2 particles. Considering a system of one proton and 2 neutrons we are able to get a formula that counts the number of states of 3 identical particles in a j shell with J=j. This is at first surprising because for identical partices the above isospin interaction is a constant a+b/4. How can a constant tell us something useful? Using the above isospin interaction we can get a relation invoving the number of isospin T=0 and T=2 states for a system of 2 protons and 2 neutrons.If in the even -even Ti isotopes we constrain the angular momental of the 2 protons and 2 neutrons to be either zero or two. then we find there is no freedom in how much each of these angular momenta is present. This is because of the constraint that the T=0 and T=2 states must be orthogonal. Despite this one gets reasonable results for 46Ti and 48Ti. Isospin consideratios can simplify experessions for the number of pairs of particles of a particular angular momentum. [Preview Abstract] |
Saturday, October 25, 2008 3:12PM - 3:24PM |
HD.00007: Effective Shell-Model Interactions from the Valence Cluster Expansion A.F. Lisetskiy, M.K.G. Kruse, B.R. Barrett, P. Navratil, I. Stetcu, J.P. Vary The {\em ab initio} No-Core Shell Model (NCSM) has had considerable success in describing the binding energies, excitation spectra and other physical properties of light nuclei, $A\le12$ {\it e.g.} [1]. However, it becomes rather challenging to produce converged results for nuclei with $A>12$. Following the idea of Ref. [2], we develop a valence cluster expansion to construct effective 2- and 3-body Hamiltonians for the $0p$-shell by performing $12\hbar\Omega$ NCSM calculations for $A=6$ and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the $0\hbar\Omega$ space. We separate these effective Hamiltonians into 0-, 1- and 2-body contributions (also 3-body for $A=7$) and analyze the systematic behavior of these different parts as a function of the mass number $A$ and size of the NCSM basis space. The role of effective 3- and higher-body interactions for $A>6$ will be discussed. [1] P. Navratil, J.P.Vary, B.R.Barrett, {\it Phys. Rev. C.} {\bf 62}, 054311 (2000). [2] P. Navratil, M. Thoresen, and B. R. Barrett, Phys. Rev. C. {\bf 55}, R573 (1997). [Preview Abstract] |
Saturday, October 25, 2008 3:24PM - 3:36PM |
HD.00008: Properties of States in the g9/2 Shell that are Eigenstates of all Interactions Larry Zamick, Pieter Van Isacker In the (g9/2)$^4$ configuration there are special states with angular momenta I=4 and I=6 which have seniority v=4 and which are eigenstates of all interactions, seniority conserving or not. The energy of, say, the I=4 special state can be expressed as Sum X(J) E(J) where E(J) are the 2 particle matrix elements. The quantity X(J) can be interpreted as the number of pairs with angular momentum J in the I=4 v=4 special state. A striking property is that X(4) is one. We attempt to prove this and find that in order for this to be true a coefficient of fractional parentage [(j$^4$)I=4 v=4|)(j$^5$)j v=5] has to vanish. It does indeed vanish but a proof of why is lacking. (A similar story holds for I=6). There are strong E2 transition matrix elements between the I=6 v=4 and I=4 v=4 special states. For states of the (f7/2)$^4$ configuration with I=2 v=4 X(2) is also equal to one and this can be proved (likewise X(4)=1 for I=4 v=4). The energy of these states can be derived i.e. all the X(J) can be determined from solvable interactions and the condition that X(I)=1 for the v=4 states. [Preview Abstract] |
Saturday, October 25, 2008 3:36PM - 3:48PM |
HD.00009: Parameters of the Heaviest Element Albert Khazan The theory of equilateral hyperbola, which looks for the heaviest element of the Periodical Table of Elements, manifests the fact that, according to the boundary conditions, the arc along the ordinate axis is limited by the line Y=1, while the arc can be continued up to any value of X along the abscissa axis. Calculation shows: to draw the hyperbolae in the same scale the value X=600 is necessary and sufficient. The top of each hyperbola, found through Lagrange's theorem, should be located in the real axis. Beryllium: the ratio Y=K/X gives the coordinates X=60.9097, Y=0.14796. On the other hand, the formal properties of equilateral hyperbolae give Xo=Yo=3.00203 (these are the sq. root of the atomic mass of the element, 9.0122). This shows that there is the reciprocal law for coming from one reference in the case to another: X/Xo=Yo/Y=20.2895. We call this number the scaling coefficient. As seen the tangent of the angle of the real axis is Y/X=0.00242917, while this line intersects the line Y=1 in the point where K=X=411.663243. Assuming this X into our equation we deduced, we arrive at the number 155. These two values are attributed to the heaviest element of the Table (Progr. Phys., 2007, 1, 38; 2, 83; 2, 104; 2008, 3, 56). [Preview Abstract] |
Saturday, October 25, 2008 3:48PM - 4:00PM |
HD.00010: The Upper Limit in the Periodic Table Albert Khazan Many scientists believe in the idea that the Periodic Table of Elements may be expanded to the period 8, 9, and so forth. Offered atomic nucleuses on 114, 126, 164 protons and 184, 258 neutrons. However no one claim was made yet on the upper limit of the Table. The standard methods of nucleosynthesis of super-heavy elements include recognition of the products came from nuclear reactions, where new elements may be discovered as well. This fact however gives no information about a possible limit in the up of the Table (a last element). To fill this gap a new theoretical approach is proposed, an essence of which is the idea that on any chemical composition of a molecular mass X the content Y of the recognized element K which should be related to one gram-atom, for unification. In such a case, meaning K the atomic mass, the equation Y=K/X manifests an equal-side hyperbola which lies in the 1st quadrant (K$>$0), while the top of the hyperbola should be located in a real axis directed with 45 deg to the positive direction of the abscissa axis with the boundary conditions Y$\le $ 1, K$\le $ X. The equation allows calculation for the content of any element in any chemical composition (Progr. Phys., 2007, 1, 38; 2, 83; 2, 104; 2008, 3, 56). [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700