π0-production in12C+12C at 800 and 1000 MeV/u

⁰-production in the system¹²C+¹²C was studied with the two-arm photon spectrometer TAPS at projectile energies of 800 and 1000 MeV/u. The experiments focus on the determination of the cross sections and the correspondingp _t -distributions. The results will extend the existing systematics of ⁰-production in heavy-ion collisions to a system with small mass.Presented at the International School-Workshop Relativistic Heavy-Ion Physics, Prague (Czech Republic), 19–23 September 1994.     

The existence of maximal slicings in asymptotically flat spacetimes

We consider Cauchy data (g, ) on IR³ that are asymptotically Euclidean and that satisfy the vacuum constraint equations of general relativity. Only those (g, ) are treated that can be joined by a curve of sufficiently bounded initial data to the trivial data (, 0). It is shown that in the Cauchy developments of such data, the maximal slicing condition tr =0 can always be satisfied. The proof uses the recently introduced weighted Sobolev spaces of Nirenberg, Walker, and Cantor.Research partially supported by National Science Foundation Grants GP-39060 and GP-15735Research partially supported by National Science Foundation Grant GP-43909 to the University of North Carolina     

D-Dimensional ideal gas in parastatistics: Thermodynamic properties

We consider a parastatistics ideal gas with energy spectrum ¦k¦ (>0) or even more generally in ad-dimensional box with volumeV (periodic boundary conditions), the numberN of the gas particles being well determined (real particles) or not (quasiparticles). We calculate the main thermodynamic quantities (chemical potential, internal energy, specific heatC, equation of state, latent heat, average numbers of particles) for arbitraryd, ,T (temperature), andp (maximal number of particles per state allowed in the parastatistics). The main asymptotic regimes are worked out explicitly. In particular, the Bose-Einstein condensation for fixed densityN/V appears as a nonuniform convergence in thep limit, in complete analogy with the standard critical phenomena that appear in interacting systems in theN limit. The system behaves essentially like a Fermi-Dirac one forall finite values ofp, and reveals a Bose-Einstein behavioronly in thep limit. For instance, at low temperaturesC T ifp< andC T ^d/ ifp. Finally, the Sommerfeld integral and its expansion are generalized to an arbitrary, finitep.     

Zero measure spectrum for the almost Mathieu operator

We study the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n-1)+ cos (2n+)u(n), onl ² (Z), and show that for all ,, and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely |4–2|. In particular, for ||=2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and ||=2) we show that the Hausdorff dimension of the spectrum is smaller than or equal to 1/2.Work partially supported by the GIF     

The translation-rotation paradox in the nucleation theory

The factor of 10¹⁷ proposed by Lothe and Pound in the theory of nucleation of droplets from the vapor phase is studied using classical statistical mechanics. The controversial factor is derived from partition functions for an isolatedn-mer and for ann-molecular cluster imbedded in the bulk liquid phase. The rotational degrees of freedom have no place in, in agreement with Reiss, Katz, and Cohen's treatment. It is proved that the surface free energy of a cluster is proportional to the surface area. The estimate of what Lothe and Pound called the replacement term is different from those of previous authors. It is concluded that is written as a ratio = _g/_l, where _g and _l , are the volumes per molecule in the gas phase and in the liquid phase, respectively. For water at 300K, is approximately equal to 10₄.     

Vibronic properties of 2-azaanthracene and its derivatives

We report an experimental and theoretical (PPP method) study of the UV absorption spectra of 2-azaanthracene and four of its methyl-substituted derivatives. We find that the p bands of these compounds consist of two different vibronic ^* bands. Our experimental and theoretical results suggest a rule for evaluating the effect of methyl groups on ^* transition energies as a function of the charge on the atoms. We interpret the reasons for the different effects of a polar solvent and hydrogen bonding on the ^* bands of these compounds.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 7–15, June, 1977.     

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     

π0 → γγ in the Spinor Strong Interaction Theory

An expression for the decay rate (⁰ ) has been derived in the frameworkof the spinor strong interaction theory, a first-principles strong interaction theoryproposed some years ago as an alternative to low-energy QCD. The startingpoint is the SO(3) gauge-invariant action for two quark mesons which has beensuccessful in accounting for confinement, ^{+ +} , e⁺, and ⁰ e⁺, nonexistenceof the Higgs boson, and other low-energy mesonic phenomena. The quasi-four-quarkmeson equations developed for the decay of a vector meson into twopseudoscalar mesons V PP has been taken over here to apply to P(⁰) VV(^{+ –}) (plus ⁺ and ^– which annihilate each other). This mechanismin principle agrees with that of the assumption of vector meson dominance inthe literature. It, together with the effect of form factors, arises naturally in theformalism and need not be assumed. Equations for the perturbed vector mesonwave functions cannot be simply solved and an assumption has been made toobtain an estimate of their magnitude. Together with a constant associated withthe strong coupling obtained earlier from V() PP(K⁺K^–), the estimated decayrate is 19.2 eV, in order-of-magnitude agreement with data (7.74 eV).     

On the massive sine-Gordon equation in all regions of collapse

The ultraviolet stability for the cosine interaction in two dimensions and finite volume is rederived for values ² [4, 32/5[ and proven for the remaining ² [4, 8[ by using renormalization group methods developed in [G, GN1] to portray renormalized effective potentials arising from a multiscale decomposition.Supported by the Studienstiftung des Deutschen VolkesSupported in part by the Schweizerischer Nationalfonds     

Polarization of the secondary nucleons in thepp → ppπ 0 andpp→npπ+ reactions at 1000 MeV

The calculation of the secondary nucleons polarization in thepppp⁰ andppnp⁺ reactions at 1000 MeV is effected in the framework of the one-pion exchange model. It is shown that polarization is due to the interference of the resonant amplitude with the non-resonant amplitudes of theN virtual scattering. The angular dependence of the polarization is sensitive to the behaivour of theN scattering amplitudes off the mass shell.Submitted to the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Cosmological Dynamics of the Tachyon with an Inverse Power-Law Potential

We investigate tachyon dynamics with an inverse power-law potential V () ^–. We find global attractors of the dynamics leading to a dust behavior for > 2 and to an accellerating universe for 0 < 2. We study linear cosmological perturbations and we show that metric fluctuations are constant on large scales in both cases. In the presence of an additional perfect fluid, the tachyon with this potential behaves as dust or dark energy.     

Particle polarizations in decays of5HeΛ and4HΛhypernuclei

Nucleon polarizations are examined in the hypernucleus decays⁵He, ⁴He + p + _–,⁴H, ³H + p + _–, and⁴H, ³He + n + _–. The effect of the strong interaction in the final state is taken into account. A significant role is predicted for the resonance interaction in the p-⁴He system in the formation of the proton polarization in the⁵He decay. It is also shown that in the⁴H, ³H + p + _– decay the proton-polarization components should attain significant magnitudes, while in the charge-exchange decay⁴H, ³He + n + _–, the neutron polarization is expected to be not too large.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 100–103, October, 1988.     

ПЛОТНОСТЬ ТОКА В АНОД НЫХ ПЯТНАХ ИСКРОВЫХ РАЗРЯДОВ В ВОЗДУХЕ ПР И АТМОСФЕРНОМ ДАВЛЕН ИИ

annapamyp, . .     

Comparison of (π− d→nn withdσ(π+ d→pp) to test charge symmetry in the Δ-region

First results on ^– d are reported. The measurements were made using 8 specially designed neutron counters, which were carefully calibratedin situ. The differential cross sections atT =142, 180, 217, and 254 MeV were obtained at four angles between 0° and 90°, they are compared to ⁺ d pp data measured at the same energies and angles with the same setup. At every beam energy, the shape of the angular distributions of ^– d nn and ⁺ d pp is the same to ±2%. The absolute cross sections differ by 1 to 10%. The error in this comparison is ±4% implying a small violation of charge symmetry.Dedicated to Prof. I. laus on the occasion of his 60th birthdayDeceased     

Five-dimensional null-cone structure of big bang singularity

Firedmann model of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five dimensional Minkowski spaceM ⁵ is globally rigid: if F() and F() are isometric imbeddings inM ⁵ there is a motion of M⁵ such that F= °f. The big bang singularity is the vertex of a null half-cone inM ⁵. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.     

A new approach to the problem of the anomalous magnetic moment of the electron

A heuristic model for deriving the anomalous magnetic moment of the electron is presented. A term /2 – 0.327(/)² is deduced, in better agreement with experiment than is the QED derivation of /2 – 0.328(/)². The result is strengthened by the recent non-QED account of the Lamb shift by Yu and Sachs.     

Temperature-dependent bandstructure of ferromagnetic metals with localized moments

We consider a theoretical model for ferromagnetic metals like Gd, which takes into account the exchange interaction and the hybridization between two electronic subsystems. The first is built up by quasi-localized electrons, which take care for the existence of permanent magnetic moments, and is described by an atomic limit multiband Hubbard-Hamiltonian. The second subsystem consists of relatively broad conduction bands with more or less free electrons. We investigate the influence of electron correlations on the conduction band states in dependence of temperatureT and bandfillingn. A sensitive reaction of the band states on the magnetic ordering of the moment system leads to strong band deformations. The main goal is the determination of a quasiparticle bandstructure, which we derive in analogy to the experiment (PES, IPE) directly from the spectral density. The new aspect is a splitting of the bare dispersion _m (k) into several quasiparticle dispersion curves with stronglyT-andn-dependent spectral weights. Even forT>T _c an exchange-caused splitting is found. — In this paper we use as input for the free band energies _m (k) a nondegenerate simple cubic-tight binding expression, and in addition seven dispersionlessf-levels, in order to stress mainly the influence of many body effects. It is discussed how the model can be coupled to a LDA bandstructure calculation, in order to get quantitative results for theT-dependent electronic structure of the ferromagnetic 4f-metal Gd, the presentation of which is intended in a forthcoming paper.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

, , . , . .

---

The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.