Cluster sum rules for three-body systems with angular-momentum dependent interactions

We derive general expressions for non-energy weighted and energy-weighted cluster sum rules for systems of three charged particles. The interferences between pairs of particles are found to play a substantial role. The energy-weighted sum rule is usually determined by the kinetic energy operator, but we demonstrate that it has similar additional contributions from the angular momentum and parity dependence of two- and three-body potentials frequently used in three-body calculations. The importance of the different contributions is illustrated with the dipole excitations in $^6$He. The results are compared with the available experimental data.Comment: 11 pages, 3 figures, 2 table

Further search for a neutral boson with a mass around 9 MeV/c2

Two dedicated experiments on internal pair conversion (IPC) of isoscalar M1 transitions were carried out in order to test a 9 MeV/c2 X-boson scenario. In the 7Li(p,e+e-)8Be reaction at 1.1 MeV proton energy to the predominantly T=0 level at 18.15 MeV, a significant deviation from IPC was observed at large pair correlation angles. In the 11B(d,n e+e-)12C reaction at 1.6 MeV, leading to the 12.71 MeV 1+ level with pure T=0 character, an anomaly was observed at 9 MeV/c2. The compatibility of the results with the scenario is discussed.Comment: 12 pages, 5 figures, 2 table

Collaboration between Mathematics and Mathematics Education

Abstract Our chapter is in four sections. Michèle Artigue tells the story of her transition from mathematical logic to mathematics education and of collaborations at a wide variety of institutional levels. Günter Törner gives a history of collaboration between mathematics and mathematics education in Germany along with a list of recommendations to foster collaboration. Ehud de Shalit shares lessons learned from personal experiences collaborating in the production of a math fair and in the design of a mathematics education major. Pat Thompson tells of several collaborative efforts at his home institution and examines ways that mathematics education contributed mathematically to them. A concluding section provides a reflection on our charge -structural and cultural issues involved in collaborations between mathematics and mathematics education

Isoscalar g Factors of Even-Even and Odd-Odd Nuclei

We consider T=0 states in even-even and odd-odd N=Z nuclei. The g factors that emerge are isoscalar. We find that the single j shell model gives simple expressions for these g factors which for even-even nuclei are suprisingly close to the collective values for K=0 bands. The g factors of many 2+ in even-even nuclei and 1+ and 3+ states in odd-odd nuclei have g factors close to 0.5

``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States

Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.Comment: LaTex, 4 pages, including 4 .eps-figures, to be appear in pr

Random Matrices and Chaos in Nuclear Physics

The authors review the evidence for the applicability of random--matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random--matrix predictions are fulfilled. An introduction into the basic concepts of random--matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random--matrix ensembles patterned after the shell model such as the embedded two--body ensemble, the two--body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground--state regions of strongly deformed nuclei.Comment: 54 pages, 28 figure

Direct detection of supersymmetric dark matter- Theoretical rates for transitions to excited states

The recent WMAP data have confirmed that exotic dark matter together with the vacuum energy (cosmological constant) dominate in the flat Universe. Supersymmetry provides a natural dark matter candidate, the lightest supersymmetric particle (LSP). Thus the direct dark matter detection is central to particle physics and cosmology. Most of the research on this issue has hitherto focused on the detection of the recoiling nucleus. In this paper we study transitions to the excited states, focusing on the first excited state at 50 keV of Iodine A=127. We find that the transition rate to this excited state is about 10 percent of the transition to the ground state. So, in principle, the extra signature of the gammai ray following its de-excitation can be exploited experimentally.Comment: LaTex, 13 pages, 3 postscript figures, 1 table, to appear in IJMP

Iwasawa theory and p-adic L-functions over Zp2-extensions

We construct a two-variable analogue of Perrin-Riou’s p-adic regulator map for the Iwasawa cohomology of a crystalline representation of the absolute Galois group of Q p , over a Galois extension whose Galois group is an abelian p-adic Lie group of dimension 2. We use this regulator map to study p-adic representations of global Galois groups over certain abelian extensions of number fields whose localisation at the primes above p is an extension of the above type. In the example of the restriction to an imaginary quadratic field of the representation attached to a modular form, we formulate a conjecture on the existence of a “zeta element”, whose image under the regulator map is a p-adic L-function. We show that this conjecture implies the known properties of the 2-variable p-adic L-functions constructed by Perrin-Riou and Kim

Cluster Transformation Coefficients for Structure and Dynamics Calculations in n-Particle Systems: Atoms, Nuclei, and Quarks

The structure and dynamics of an n-particle system are described with coupled nonlinear Heisenberg's commutator equations where the nonlinear terms are generated by the two-body interaction that excites the reference vacuum via particle-particle and particle-hole excitations. Nonperturbative solutions of the system are obtained with the use of dynamic linearization approximation and cluster transformation coefficients. The dynamic linearization approximation converts the commutator chain into an eigenvalue problem. The cluster coefficients factorize the matrix elements of the (n)-particles or particle-hole systems in terms of the matrix elements of the (n-1)-systems coupled to a particle-particle, particle-hole, and hole-hole boson. Group properties of the particle-particle, particle-hole, and hole-hole permutation groups simplify the calculation of these coefficients. The particle-particle vacuum-excitations generate superconductive diagrams in the dynamics of 3-quarks systems. Applications of the model to fermionic and bosonic systems are discussed.Comment: 13 pages, 5 figures, Wigner Proceedings for Conference Wigner Centenial Pecs, July 8-12, 200

Implications of Pseudospin Symmetry on Relativistic Magnetic Properties and Gamow - Teller Transitions in Nuclei

Recently it has been shown that pseudospin symmetry has its origins in a relativistic symmetry of the Dirac Hamiltonian. Using this symmetry we relate single - nucleon relativistic magnetic moments of states in a pseudospin doublet to the relativistic magnetic dipole transitions between the states in the doublet, and we relate single - nucleon relativistic Gamow - Teller transitions within states in the doublet. We apply these relationships to the Gamow - Teller transitions from $^{39}Ca$ to its mirror nucleus $^{39}K$.Comment: 17 pages, 2 figures, to be published in PRC. Slightly revised text with one reference adde