Estimating the strength of chaos from the power spectrum

It is rigorously proved that for nonlinear dynamical systems whose time dependence is described by one dimensional, everywhere expanding maps, the width of broadband noise in the power spectrum is bounded by the generalized entropiesK ₂ andK ₃, which measure the strength of chaos in this system asK ₂2K ₃.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Critical dynamics of φ2n with random fields in the tree approximation

In the tree approximation, the critical relaxational dynamics of ²ⁿ with quenched random fields is calculated by renormalization near the upper critical dimensiond _u=4+2/(n–1). Although the relation between the characteristic frequency _c q and the wave-numberq is as usual,unusual results are obtained for the asymptotic decay of the order-parameter correlation functionS(q,t).Dedicated to Prof. Dr. W. Döring on the occasion of his 75th birthday     

Cluster model study of lightp-shell Λ-hypernuclei with OBE-based effective ΛN interaction

The structures of the lightp-shell hypernuclei \({}_\Lambda ^6 He,{}_\Lambda ^7 Li,{}_\Lambda ^9 Liand{}_\Lambda ^9 Be\) are studied by using a realistic effectiveΛN interaction (YNG), and compared to those with the use of the simple one-range Gaussian (ORG) interaction. The YNG interaction, which simulates theΛNG-matrix for the Nijmegen OBE modelD, is characterized by the inner repulsive core and the density-dependence along with the space-exchange and spin-spin components. The framework we adopt is the microscopic α +x + Λ (x=n, d, t or α) three-cluster model, where nucleon antisymmetrization is exactly treated. The characteristic behaviors ofΛ?x andΛ?(αx) interactions derived from the YNG are displayed and discussed. In spite of the remarkable characteristic of YNG, the calculated energy levels of the four hypernuclei are very similar to those previous obtained by using the simple ORG interaction. The stabilization and contraction of the hypernuclear system due to the glue-like role ofΛ-particle persists in the present calculation, though the repulsive core of theΛN interaction tends to prevent from too much contraction.     

Hyperfine structure and isotope shift investigations in202–222Rn for the study of nuclear structure beyond Z=82

The hyperfine structure (hfs) and isotope shift (IS) in the isotopic chain of the radioactive element radon have been studied for the first time. The measurements were carried out by collinear fast-beam laser spectroscopy at the mass separator facility ISOLDE at CERN. The IS between 16 isotopes in the mass range 202A222 and the hfs of 7 odd-A isotopes were determined in the transitions 7s [3/2]₂-7p [5/2]₃ (745 nm) of Rn I. The nuclear spins and moments, as well as the observed inversion of the odd-even staggering for^218–222Rn, can be associated with the effects of octupole instability around N=134.This work was supported by the Bundesministerium für Forschung und Technologie and the Deutsche Forschungsgemeinschaft.     

Parity violation in the 17/2−–17/2+ doublet in93Tc

The parity-violating mixing of the 17/2^– and 17/2⁺ levels in⁹³Tc nuclei, polarized by the tilted multifoil interaction, was measured by the observation of the forward-backward-ray asymmetry. The nuclear polarization, induced by the tilted multifoils, was measured directly for the neighboring^88,90Zr isomers. The forward to backward asymmetry was determined to be A=(2.5±2.1) 10^–3 which implies a parity violating matrix element ¦H _PV )¦=(4.0±3.7)meV.     

Measurement of local moment on Ce in CeRh3B2

We have employed the TDPAC technique to measure the paramagnetic enhancement factor of¹⁴⁰Ce in CeRh₃B₂ in the temperature range 300 K down to 115 K. Our measurements show that above T_c=115 K, the trend for(T) closely follows that for trivalent cerium.     

Experimental tests for detecting spin polarization pick-up of single-electron19F-ions on emergence from magnetized iron

A new method to detect polarization pick-up by ions emerging from thin polarized ferromagnetic layers has been tested. The applied technique consists in the observation of attenuated-angular correlations and atomic spin precessions for single-electron ions recoiling through vacuum in weak transverse magnetic fields. The Coulomb-excited¹⁹F(5/2⁺) state at 197 keV was used as probe. The experimental concept is described and the expected effects are discussed using the perturbed angular correlation formalism for polarized hyperfine interactions.     

Lattice instability in Hf1-x Ta x V2 compounds

The temperature dependence of the electric quadrupole interaction frequency _l ^o , experienced by the¹⁸¹Ta probe occupying Hf site in the compounds Hf_1-xTa_xV₂ has been measured for x=0.06, 0.10 and 0.20 in the temperature region between 8.5 K to 296 K. The measurements show lattice transformation in all the three compounds below 120 K.     

Spanning tree formulas and chebyshev polynomials

The Kirchhoff Matrix Tree Theorem provides an efficient algorithm for determiningt(G), the number of spanning trees of any graphG, in terms of a determinant. However for many special classes of graphs, one can avoid the evaluation of a determinant, as there are simple, explicit formulas that give the value oft(G). In this work we show that many of these formulas can be simply derived from known properties of Chebyshev polynomials. This is demonstrated for wheels, fans, ladders, Moebius ladders, and squares of cycles. The method is then used to derive a new spanning tree formula for the complete prismR _n (m) =K _m ×C _n . It is shown that $$2^{\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)\left( {1 - \frac{1}{{r - 1}} + o\left( 1 \right)} \right)} $$ whereT _n (x) is then ^th order Chebyshev polynomial of the first kind.