Loss of collectivity in 79Rb

High-spin states in ⁷⁹Rb were populated in the reaction at E(beam) = 60 MeV. The lifetimes of the excited states of the positive-parity yrast band and of the negative-parity band in ⁷⁹Rb were measured by the Doppler Shift Attenuation Method. The deduced transition quadrupole moments Q_t are found to have a decreasing trend with rotational frequency for both the bands, consistent with those found experimentally in neighbouring nuclei. An erratum to this article is available at .     

Masses ofq 2 \bar q 2 states in a Bethe-Salpeter model

Ground-state masses ofq ^{2 –2} states (true and mock baryonium) are investigated in the framework of a Bethe-Salpeter formalism motivated from QCD. The four-particle system is described by pairwise interactions betweenqq orq pairs with a spectator approximation for the non-interacting pair. The quark-quark interactions are Coulomb plus harmonic interactions; the harmonic terms have been modified to produce linear confinement for heavier quarks, in agreement with experimental spectra. The confining interaction is proportional to the strong coupling constant _s. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant ₀; (ii) a constantC ₀/ ₀ ² , which defines the vacuum structure; (iii) a constantA ₀, which provides a smooth transition from quadratic to linear confinement as one goes from light to heavy quark systems. These three constants [ ₀ = 0.158 GeV;C ₀=0.296;A ₀=0.0283] have been shown to produce excellent fits to all quarkonia states [q ,q ,Q ] as well as baryon spectra (qqq); thus our predictions forq ^{2 2} states contain no free parameters. In this model, theL=0 ground states occur in the range 1.8–2 GeV, 2.15–2.3 GeV and 6.72–6.75 GeV foru ^{2 2},s ^{2 2} andc ^{2 2} states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of thes ^{2 2} state, this is likely to have a rather narrow width, and may correspond to theX(2.22 GeV) meson observed in radiative decays of theJ/ meson. Thec ^{2 2} state might also be visible as a resonance with an appreciable width.Research supported in part by the National Science Foundation under grant NSF-PHY 86-06364Research supported in part by the U.S. Department of Energy     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Gauge-invariant on-shellZ 2 in QED,QCD and the effective field theory of a static quark

We calculate theon-shell fermion wave-function renormalization constantZ ₂ of a general gauge theory, to two loops, inD dimensions and in an arbitrary covariant gauge, and find it to be gauge-invariant. In QED this is consistent with the dimensionally regularized version of the Johnson-Zumino relation: d logZ ₂/da ₀=i(2)^–D e ₀ ² d ^D k/k ⁴=0. In QCD it is, we believe, a new result, strongly suggestive of the cancellation of the gauge-dependent parts of non-abelian UV and IR anomalous dimensions to all orders. At the two-loop level, we find that the anomalous dimension _F of the fermion field in minimally subtracted QCD, withN _L light-quark flavours, differs from the corresponding anomalous dimension of the effective field theory of a static quark by the gauge-invariant amount

On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator onL 2(ℝ)+

We consider a random Schrödinger operator onL ²(^v) of the form , {C _i} being a covering of ^v with unit cubes around the sites of ^v and {q _i} i.i.d. random variables with values in [0, 1]. We assume that theq _i's are continuously distributed with bounded densityf(q) and that 0<P(q ₀<1/2)=<1. Then we show that an ergodic mean of the quantity dx|x|²|(exp(itH ))(x)|²t ^–1 vanishes provided =g _E(H ), where is well-localized around the origin andg _E is a positiveC -function with support in (0,E),EE*(, |f|). Our estimate ofE*(, |f|) is such that the set {x ^v |V (x) E*(, |f|)} may contain with probability one an infinite cluster of cubes {C _i} which are nearest neighbours. The proof is based on the technique introduced by Fröhlich and Spencer for the analysis of the Anderson model.Work supported in part by C.N.R. (Italy) and NAVF (Norway)On leave of absence from Instituto di Fisica Università di Roma, Italia     

Feynman path integrals and the trace formula for the Schrödinger operators

We study Schrödinger operators of the form on ^d , whereA ² is a strictly positive symmetricd×d matrix andV(x) is a continuous real function which is the Fourier transform of a bounded measure. If _n are the eigenvalues ofH we show that the theta function is explicitly expressible in terms of infinite dimensional oscillatory integrals (Feynman path integrals) over the Hilbert space of closed trajectories. We use these explicit expressions to give the asymptotic behaviour of (t) for smallh in terms of classical periodic orbits, thus obtaining a trace formula for the Schrödinger operators. This then yields an asymptotic expansion of the spectrum ofH in terms of the periodic orbits of the corresponding classical mechanical system. These results extend to the physical case the recent work on Poisson and trace formulae for compact manifolds.Partially supported by the USP-Mathematisierung, University of Bielefeld (Forschungsprojekt Unendlich dimensionale Analysis)     

The droplet in the tube: A case of phase transition in the canonical ensemble

We consider the 2-dimensional Ising model with ferromagnetic nearest neighbour interaction at inverse temperature. LetS _N = _t be the total magnetization inside anN×N square box, ^per be the Gibbs state in with periodic b.c., andm() be the spontaneous magnetization. We show the existence of the limit

Diffusion in a periodic potential with a local perturbation

We consider the diffusion of a particle at X_t in a drift field derived from a smooth potential of the formV+B, whereV is periodic andB is a bump of compact support. With no bump,B=0, the mean squared displacementE(t) E |X _t – X₀|² =D(V)t +C +O(e ^–t ),>0, in any dimension. WhenB0, we establish in one dimension the asymptotic expansion , 0, ast. Our analysis relies on the Nash estimates developed in previous work for the transition density of the process and their consequences for the analytic structure,of the Laplace transform ofE(t).     

Equilibrium points of the tilted perfect fluid Bianchi VI<Subscript><Emphasis Type="Italic">h</Emphasis></Subscript> state space

We present the full set of evolution equations for the spatially homogeneous cosmologies of type VI_h filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > –1 a self-similar solution exists. In particular we show that for h > – there exists a self-similar equilibrium point provided that whereas for h < – the state parameter belongs to the interval (1, . This family of new exact self-similar solutions belongs to the subclass n = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying n = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model ( = ), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VI_h.     

TM-polarized nonlinear waves guided by asymmetric dielectric layered structures

We found the field structure, exact dispersion relations and power flow ofp-polarized nonlinear guided and surface waves travelling along a three-component layered structure consisting of a film of thicknessd with dielectric constant _b bounded at the negativez-side by a linear medium with dielectric constant _a and at the positivez-side by a nonlinear uniaxial substrate characterized by the diagonal dielectric tensor ₁₁ = ₂₂ = + (|E ₁|² + |E ₂|²), ₃₃ = , <0 (self-defocusing medium),E ₁ andE ₂ being the components of the electric field in thex andy-direction, respectively. It is shown that for sufficiently smalld/ (: wavelength) the nonlinear wave may exist only at power flows exceeding some certain minimum values. For sufficiently larged/ to some values of the power flow there correspond two distinct values of the propagation constant. In this case with increasing of the power flow the number of waveguide modes is decreasing and for higher-order modes the film-waveguide exhibits an optical-power limiter from the above behaviour.     

A Class of Generalized Gamma Functions

We study a family of holomorphic functions defined by infinite products of the form (a, r real, ar > 0) which generalize Eulers definition since . We obtain analogues of classical formulas (e.g. Gauss multiplication and complement formulas) for these functions _a,r(s)     

A new isomer in 136 Ba populated by deep inelastic collisions

Excited states in ¹³⁶Ba, populated in deep inelastic collisions by the interaction of 450 MeV ⁸²Se ions with a ¹³⁹La target, have been studied by means of in-beam -ray spectroscopy. A new isomer with has been identified at an excitation energy E_x = 3.357 MeV. The half-life was determined as ns. The extracted B(E2) value is much smaller than those in ¹³²Te and ¹³⁴Xe. This hindrance is investigated by a shell model calculation.Received: 22 September 2003, Revised: 11 November 2003, Published online: 6 April 2004PACS: 21.10.Tg Lifetimes - 23.20.Lv transitions and level energies - 27.60. + j      

q-Analogue of the Watanabe Unitary Transform Associated to the q-Continuous Gegenbauer Polynomials

We associate a family of Hilbert spaces H _q ^2;(D) of analytic functions on the unit disk D=z :|z|<1 the q-continuous Gegenbauer polynomials C _n (x;q) on the interval]–1;1[ and give a q-analogue of the unitary integral transform that Watanabe constructed from the Hilbert space L ²(]–1;1[;(1–x ²)^– dx onto the weighted Hilbert space H ^2;(D).     

Symmetry conservation and integrals over local charge densities in quantum field theory

For conserved local currents ^µ j ^µ (x)=0 in quantum field theory it is shown that anR-dependence of _R (x ₀) inj ₀(f _R(x)· _R (x ₀)) leads to nicer properties than a fixed (x ₀). The behaviour of j ₀(f _R(x)·_R(x ₀) is discussed under this aspect.     

The energy levels for simplified anharmonic oscillators

The energy levels for quantum mechanical oscillators with interaction imitatingx (for integer >2) are found by perturbative methods in finite number of dimensions. It is argued that in the limit of infinite dimensional space the coefficients in the expansion for the energy of theith level are growing with the perturbation ordern like . For the ground state (i=1) this reproduces estimates established for anharmonic oscillators.     

Analysis of Ωb? (bss) and Ωc0 (css) with QCD sum rules

We calculate the masses and the pole residues of the heavy baryons Ω _c ⁰(css) and Ω _b ⁻(bss) with the QCD sum rules. The numerical values  GeV (or  GeV) and  GeV (or  GeV) are in good agreement with the experimental data.     

From the deuteron to deusons,an analysis of deuteronlike meson-meson bound states

A systematic study of possible deuteronlike twomeson bound states,deusons, is presented. Previous arguments that many such bound states may exist are elaborated with detailed arguments and numerical calculations including, in particular, the tensor potential. This tensor potential which is crucial for the deuteron binding is shown to be very important also in the mesonic case. Especially, in the pseudoscalar³ P ₀ pseudoscalar-vector and vector-vector channels the important observation is made that the centrifugal barrier from theP-wave can be overcome by the 1/r ² and 1/r ³ terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteronlike and composites bound by approximately 50 MeV. Composites of and states bound by pion exchange alone are expected near the thresholds, while in the light meson sector one generally needs some additional short range attraction to form bound states. The quantum numbers of these states areI=0, andJ ^PC=0^–+, 1⁺⁺ for the states andI=0,J ^PC=0⁺⁺, O^–+, 1^+– and 2⁺⁺ for the composites. In the states: ^b (10545), _b1(10562) are predicted and in , one finds the states: ^b (10590), _bQ (10582),h _b(10608), _b2(10602). Near the threshold the states: ^c (3870), _c0(3870) are predicted, and near the threshold one finds the states: _b0(4015), ^c (4015),h _c(4015), _c2(4015). Within the light meson sector pion exchange gives strong attraction for and systems with quantum numbers where the best non- candidates exist, although pion exchange alone is not strong enough to support such bound states. Thus, although one cannot conclude with certainty it to be the case, this fact does favour the picture that the (1440) and thef ₁ (1420) are mainly composites and thef ₀(1710) mainly a bound state, while thef ₀(1515) andf ₂(1520) could be predominantly composites. If the predicted and states are found, these would support this interpretation of the light states. In channels with exotic flavour orCP quantum numbers pion exchange is generally repulsive or quite weak. Therefore one does not expect that such deuteronlike bound states exist, althoughB*B* may be an exception.     

Operators with singular continuous spectrum,VII. Examples with borderline time decay

We construct one-dimensional potentialsV(x) so that if onL ²(), thenH has purely singular spectrum; but for a dense setD, D implies that |,e ^-itH |C |t|^-1/2 ln(|t|) for t>2. This implies the spectral measures have Hausdorff dimension one and also, following an idea of Malozemov-Molchanov, provides counterexamples to the direct extension of the theorem of Simon-Spencer on one-dimensional infinity high barriers.This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.     

The Klein-Gordon equation with light-cone data

It is shown that the characteristic Cauchy problem ·u(x,t)=0,u(x,–|x|)=f(x),x ⁿ ,n1 has a unique finite energy weak solution for allf such that dx(|f|²+|f|²)< and all finite energy weak solutions of the equation are obtained in this way.