HITES 2012: 'Horizons of Innovative Theories, Experiments, and Supercomputing in Nuclear Physics'

This volume contains the contributions of the speakers of an international conference in honor of Jerry Draayer's 70th birthday, entitled 'Horizons of Innovative Theories, Experiments and Supercomputing in Nuclear Physics'. The list of contributors includes not only international experts in these fields, but also many former collaborators, former graduate students, and former postdoctoral fellows of Jerry Draayer, stressing innovative theories such as special symmetries and supercomputing, both of particular interest to Jerry. The organizers of the conference intended to honor Jerry Draayer not only for his seminal contributions in these fields, but also for his administrative skills at departmental, university, national and international level. Signed: Ted Hecht University of Michigan ##IMG## [http://ej.iop.org/images/1742-6596/403/1/011001/confphoto.jpg] {Conference photograph ----- -- Scientific Advisory Committee ----- -- Ani Aprahamian -- University of Notre Dame ----- -- Baha Balantekin -- University of Wisconsin ----- -- Bruce Barrett -- University of Arizona ----- -- Umit Catalyurek -- Ohio State Unversity ----- -- David Dean -- Oak Ridge National Laboratory ----- -- Jutta Escher (Chair) -- Lawrence Livermore National Laboratory ----- -- Jorge Hirsch -- UNAM, Mexico ----- -- David Rowe -- University of Toronto ----- -- Brad Sherill & Michigan State University ----- -- Joel Tohline -- Louisiana State University ----- -- Edward Zganjar -- Lousiana State University ----- -- Organizing Committee ----- -- Jeff Blackmon -- Louisiana State University ----- -- Mark Caprio -- University of Notre Dame ----- -- Tomas Dytrych -- Louisiana State University ----- -- Ana Georgieva -- INRNE, Bulgaria ----- -- Kristina Launey (Co-chair) -- Louisiana State University ----- -- Gabriella Popa -- Ohio University Zanesville ----- -- James Vary (Co-chair) -- Iowa State University ----- -- Local Organizing Committee ----- -- Laura Linhardt -- Louisiana State University ----- -- Charlie Rasco -- Louisiana State University ----- -- Karen Richard (Coordinator) -- Louisiana State University -----Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98638/1/1742-6596_403_1_011001.pd

Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,

A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of n(n-1)/2 commuting variables and depending on n-1 complex representation parameters r_i, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q - difference equations, i.e., these are kernels of invariant q - difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally the states in all subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files

Occupation probability of harmonic-oscillator quanta for microscopic cluster-model wave functions

We present a new and simple method of calculating the occupation probability of the number of total harmonic-oscillator quanta for a microscopic cluster-model wave function. Examples of applications are given to the recent calculations including $\alpha+n+n$-model for $^6$He, $\alpha+t+n+n$-model for $^9$Li, and $\alpha+\alpha+n$-model for $^9$Be as well as the classical calculations of $\alpha+p+n$-model for $^6$Li and $\alpha+\alpha+\alpha$-model for $^{12}$C. The analysis is found to be useful for quantifying the amount of excitations across the major shell as well as the degree of clustering. The origin of the antistretching effect is discussed.Comment: 9 page

Observing the Profile of an Atom Laser Beam

We report on an investigation of the beam profile of an atom laser extracted from a magnetically trapped $^{87}$Rb Bose-Einstein condensate. The transverse momentum distribution is magnified by a curved mirror for matter waves and a momentum resolution of 1/60 of a photon recoil is obtained. We find the transverse momentum distribution to be determined by the mean-field potential of the residing condensate, which leads to a non-smooth transverse density distribution. Our experimental data are compared with a full 3D simulation of the output coupling process and we find good agreement.Comment: 4 pages, 4 figure

Phenomenology of the Baryon Resonance 70-plet at Large N_c

We examine the multiplet structure and decay channels of baryon resonances in the large N_c QCD generalization of the N_c = 3 SU(6) spin-flavor 70. We show that this ``70'', while a construct of large N_c quark models, actually consists of five model-independent irreducible spin-flavor multiplets in the large N_c limit. The preferred decay modes for these resonances fundamentally depend upon which of the five multiplets to which the resonance belongs. For example, there exists an SU(3) ``8'' of resonances that is eta-philic and pi-phobic, and an ``8'' that is the reverse. Moreover, resonances with a strong SU(3) ``1'' component prefer to decay via a K-bar rather than via a pi. Remarkably, available data appears to bear out these conclusions.Comment: 26 pages, ReVTe

Observation of Brewster's effect for transverse-electric electromagnetic waves in metamaterials: Experiment and theory

We have experimentally realized Brewster's effect for transverse-electric waves with metamaterials. In dielectric media, Brewster's no-reflection effect arises only for transverse-magnetic waves. However, it has been theoretically predicted that Brewster's effect arises for TE waves under the condition that the relative permeability r is not equal to unity. We have designed an array of split-ring resonators as a metamaterial with mu_r 1 using a finite-difference time-domain method. The reflection measurements were carried out in a 3-GHz region and the disappearance of reflected waves at a particular incident angle was confirmed.Comment: 4 pages, 5 figure

Phase operators, phase states and vector phase states for SU(3) and SU(2,1)

This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases

Neutron-Proton Correlations in an Exactly Solvable Model

We examine isovector and isoscalar neutron-proton correlations in an exactly solvable model based on the algebra SO(8). We look particularly closely at Gamow-Teller strength and double beta decay, both to isolate the effects of the two kinds of pairing and to test two approximation schemes: the renormalized neutron-proton QRPA (RQRPA) and generalized BCS theory. When isoscalar pairing correlations become strong enough a phase transition occurs and the dependence of the Gamow-Teller beta+ strength on isospin changes in a dramatic and unfamiliar way, actually increasing as neutrons are added to an N=Z core. Renormalization eliminates the well-known instabilities that plague the QRPA as the phase transition is approached, but only by unnaturally suppressing the isoscalar correlations. Generalized BCS theory, on the other hand, reproduces the Gamow-Teller strength more accurately in the isoscalar phase than in the usual isovector phase, even though its predictions for energies are equally good everywhere. It also mixes T=0 and T=1 pairing, but only on the isoscalar side of the phase transition.Comment: 13 pages + 11 postscript figures, in RevTe

Vector coherent state theory of the generic representations of so(5) in an so(3) basis

For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. The algorithm has been implemented in MAPLE, and some tables of results are presented.Comment: 20 pages, uses multirow.sty, submitted to J. Math. Phy

Construction of SU(3) irreps in canonical SO(3)-coupled bases

Alternative canonical methods for defining canonical SO(3)-coupled bases for SU(3) irreps are considered and compared. It is shown that a basis that diagonalizes a particular linear combination of SO(3) invariants in the SU(3) universal enveloping algebra gives basis states that have good $K$ quantum numbers in the asymptotic rotor-model limit.Comment: no figure