Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

Inductive limit automorphisms of the irrational rotation algebra

It is shown that the flip automorphismUU ^*,VV ^* of the irrational rotation algebra A is an inductive limit automorphism. Here, the algebra A is generated by unitariesU, V satisfyingVU=e²ⁱ UV, where is an irrational number. Recently, Elliott and Evans proved that A can be approximated by unital subalgebras isomorphic to a direct sum of two matrix algebras over , the algebra of continuous functions on the unit circle. This is the central result which they used to obtain their structure theorem on A; namely, that A is the inductive limit of an increasing sequence of subalgebras each isomorphic to a direct sum of two matrix algebras over . In their proof, they devised a subtle construction of two complementary towers of projections. In the present paper it is shown that the two towers can be chosen so that each summand of their approximating basic building blocks is invariant under the flip automorphism and, in particular, that the unit projection of the first summand is unitarily equivalent to the complement of the unit of the second by a unitary which is fixed under the flip. Also, an explicit computation of the flip on the approximating basic building blocks of A is given. Further, combining this result along with others, including a theorem of Su and a spectral argument of Bratteli, Evans, and Kishimoto, a two-tower proof is obtained of the fact established by Bratteli and Kishimoto that the fixed point subalgebra B (under the flip) is approximately finite dimensional. Also used here is the fact that B has the cancellation property and is gifted with four basic unbounded trace functionals. The question is raised whether other finite order automorphisms of A (arising from a matrix in SL(2,)) are inductive limit automorphisms - or evenalmost inductive limit automorphisms in the sense of Voiculescu.Research partly supported by NSERC grant OGP0169928     

Comparisons of vector analyzing-power data and calculations for neutron-deuteron elastic scattering from 10 to 14 MeV

High-accuracy analyzing-powerA _y() data forn-d elastic scattering at 12 MeV have been measured using the polarized-neutron facilities at the Triangle Universities Nuclear Laboratory (TUNL). The present data have been combined with our previousn-d measurements at 10, 12, and 14.1 MeV to form the highest-accuracyA _y() data set forn-d elastic scattering below 20 MeV. These data are compared to recent Faddeev-based neutron-deuteron (n-d) calculations which use the Paris and Bonn equivalent separable potentials PEST and BEST, as well as Doleschall's representation of theP- andD-wave nucleon-nucleon interactions. None of these models adequately describe the data in the angular region around the maximum ofA _y(). Possible reasons for the discrepancies are discussed. The sensitivity of the present Faddeev-based calculations to various angular momentum components of the nucleon-nucleon interaction are examined.     

Non-commutative spheres

LetA be the irrational rotation algebra, i.e. theC ^*-algebra generated by two unitariesU, V satisfyingVU=e ²ⁱ UV, with irrational, and consider the fixed point subalgebraB under the flip automorphismUU ^–1,VV ^–1. We prove thatB is an AF-algebra.Dedicated to Professor Huzihiro Araki on the occasion of his 60'th birthday     

Is the Cabibbo Angle a Function of the Weinberg Mixing Parameter?

The (u, c) quarks and (d, s) quarks arerequired to have mass matrices of a certainform. To achieve these mass matrices appropriate Lagrangians are assumed. Theu quark is coupled to the standard Higgs scalar _L. Thec quark has a ₅ couplingwith _L and _R, where _R is the Higgs scalar corresponding to theleft-rightmodel. The u quark has no ₅ coupling. Both u,c quarks have a Yukawa couplingwith a Higgs multiplet. Exactly similar Lagrangians are chosen for thed, s qurks.Using these mass matrices, the Cabibbo angle is found to be 13° 11. The ratiom _c/m _s is shown to be approximately 3.1 with the help of the Weinberg mixingparameter. The mixing angles ₂ and ₁ determine the Cabibbo angle. The ratiotan ₂/ tan ₁ is shown to be a function of the Weinberg mixing parameter.     

One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ¹ It is known that equilibrium (i.e., time-invariant attractive) states for this model are translationally invariant Gaussian ones, with the mean 0, which satisfy some linear relations involving the interaction quadratic form. The natural parameter characterizing equilibrium states is the spectral density matrix function (SDMF)F(), [– , ). Time evolution of a space profile of local equilibrium parameters is described by a space-time SDMFF(t;x, ) t, xR ¹. The hydrodynamic equation forF(t; x, ) which we derive in this paper means that the normal mode profiles indexed by are moving according to linear laws and are mutually independent. The procedure of deriving the hydrodynamic equation is the following: We fix an initial SDMF profileF(x, ) and a familyP ,>0 of mean 0 states which satisfy the two conditions imposed on the covariance of spins at various lattice points: (a) the covariance at points close to the value ^–1 x in the stateP is approximately described by the SDMFF(x, ); (b) The covariance (on large distances) decreases with distance quickly enough and uniformly in. Given nonzerotR ¹, we consider the states P _–1 ,>0, describing the system at the time moments ^–1 t during its harmonic time evolution. We check that the covariance at lattice points close to ^–1 x in the state P _–1 is approximately described by a SDMFF(t;x, ) and establish the connection betweenF(t; x, ) andF(x,).     

On the determination of elliptic differential and finite difference operators in vector bundles overS 1

For an elliptic differential operatorA overS ¹, , withA _k (x) in END(^r) and as a principal angle, the -regularized determinant Det A is computed in terms of the monodromy mapP _A , associated toA and some invariant expressed in terms ofA _n andA _n–1 . A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature ofA whenA is self adjoint and show that the determinant ofA is the limit of a sequence of computable expressions involving determinants of difference approximation ofA.Partially supported by an NSF grant     

Natural boundaries for area-preserving twist maps

We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value.     

The rate of growth of the magnetic energy density during a gravitational collapse

It is shown that during an isotropic gravitational collapse of a fluid with infinite electrical conductivity, the magnetic energy density cannot grow faster than ^4/3 no matter the equation of state, where is the total proper energy density. If the equation of state is=c ², where 01, then the rate of growth of the magnetic energy density in such a collapse is proportional to ^4/3(1+). If an isotropic collapse is also locally adiabatic, it is shown, independently of any equation of state, that the rate of increase of the magnetic energy density is proportional tor ^4/3, wherer is the proper material density. If the collapse is nonisotropic, shear can modify these results. Numerical estimates of the magnetic field strength at various stages in the collapse of a magnetic star are given.     

Opto-thermal study of the melting transition of benzophenone

We report a series of opto-thermal transient emission radiometry (OTTER) measurements on benzophenone over the temperature range 20–80°C, which includes the melting transition at 48°C. At temperatures sufficiently close, but below the melting point, the form of the opto-thermal decay curves was found to change, when the laser pulse energy was sufficient to cause transient melting near the surface. Such measurements could be useful in the study of re-crystallation dynamics in pulsed laser annealing and similar surface treatments. In addition, the experiment gives a direct measure of ₀, the initial jump in surface temperature, and a comparison of solid and liquid thermal diffusivities. The values found in the present study are ₀, andD(solid)/D(liquid)=2.2±0.2.     

Isotropic spherical coordinates

The method of using regularization to analyze singularities is applied to the Schwarzschild metric in isotropic spherical coordinates (3). It is found that there arises a singularity at the gravitational radius which does not satisfy the conditions of physical realizability (T =T ,T ₀ ⁰ =T =0). Consequently, this metric cannot be considered as corresponding to pure vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–87, April, 1987.     

Strict inequalities for some critical exponents in two-dimensional percolation

For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL():={(x, y):x=r cos, y=r sin for some r0, or} and():=limpp _c [log(p–p _c )]^–1 log P_cr {itO is connected to by an occupied path inL()}, then() is strictly decreasing in on [0, 2]. Similarly, lim_n [–logn]^–1 logP _cr {itO is connected by an occupied path inL()() to the exterior of [–n, n]×[–n, n] is strictly decreasing in on [0, 2].     

Cross-section asymmetry for the reactions γd →pn, γd → π0 d by linearly polarized photons in the energy rangeE γ = 0·4 – 0·8 GeV

The beam asymmetryB has been measured for the reactiond pn in the energy rangeE = 0·4 ÷ 0·8 GeV and angles _p ^cm = 45 ÷ 95° and ford ⁰d at energiesE =0·5, 0·6, 0·7 GeV and angle ^cm = 130°. The results obtained are compared to existing theoretical predictions which take into account the possible contribution of dibaryon resonances.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Third-order processes and their relation to structural symmetry

We have studied the various nonlinear optical processes that can be described by a fourth-rank ⁽³⁾-tensor: signals of frequency in degenerate four-wave mixing (DFWM), harmonics of frequency 2 and 3, and ⁽³⁾-type difference-frequency generation (DFG) with observation of anti-Stokes emission of a signal of frequency 2₁ — ₂. Structural information in terms of normalized anisotropies is derived in all frequency domains by analysis of the elements of the respective orientation-dependent susceptibility tensor. A novel laser-based technique for the remote orientation analysis of crystalline structures is introduced.     

A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants

We study ergodic Jacobi matrices onl ²(Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n–1)+ cos(2n+)u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: |_ac|=||=4 –2.Work partially supported by the US-Israel BSF     

Corrections to cluster-radius scaling for branched polymers and percolation

We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent . We find -0.640±0.004 and =0.87±0.07 for isotropic animals in 2d, and =0.64±0.06 in 3d. For directed lattice animals we argue that the leading correction has= or= ; we also estimate =0.82±0.01 and 0.69 ±0.01 ind=2, 3 respectively. For percolation clusters at and abovep _c, we find (p _c) =0.58±0.06 and (p>p _c)=0.84±0.09 in 2d, and (p _c)=0.42±0.11 and (p>p _c)=0.41 ±0.09 in 3d.     

Nuclear physics with ion traps at ISOLDE: present and future

Nuclear physics experiments with ion traps started at the on-line separator ISOLDE/CERN, Geneva, with the installation of the tandem Penning trap mass spectrometer ISOLTRAP. With this device the massM of a stored ion is determined by measuring its cyclotron frequency _c=(q/M)B in a magnetic fieldB. Mass measurements with a resolving powerR=_c/_c(FWHM)1×10⁶ and accuracies of M/M10^–7 were performed on more than sixty unstable isotopes of the elements Rb, Sr, Cs, Ba, Fr, and Ra.     

On the global behaviour of symmetric Skyrmions

It is shown that the chiral angle, (r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, (r) is strictly convex or concave. As r, (r) and (r) approach their limit values at the rate Or ^- for any (0,2).