The quasilinear theory of two-stream cyclotron instability of electron beams

The paper is devoted to a study of cyclotron instability ( _e) of two opposite beams of electrons from the aspect of the quasilinear effects. For this case of instability the authors evolve the diffusion equation in the velocity space for an averaged distribution function. They estimate the relaxation times , _z of the spreading of the distribution function in the velocity space. At the end of the paper, they compare their results with an experiment described by M. Seidl and P. unka [Phys. Letters11 (1964), 31].     

Radioactive decay of Re188

The spectra of negatons, conversion electrons and photoelectrons were measured with the iron-yoke double focusing spectrometer. Two-groups with end-point energies 2128 and 1973 keV andlgf values 8.04 and 8.41 respectively were observed. TheK andL conversion coefficients of 155.0 keV transition were found to be in agreement with theoretical prediction within a few per cent. Three new-transitions, 635, 1175 and 1461 keV, were observed and some corrections of the decay scheme were made. The possible interpretations of the excited states are discussed.     

Effect of multiple reemission on the shape of the magnetic depolarization contour. II

The equations for the reflection and transmission functions of polarized resonant radiation are solved for the case of a layer of small optical thickness in the presence of a magnetic field H. Results of numerical calculations are presented. It is found that even at small the rotation of the polarization plane exceeds 45, as shown by the appearance of a negative value of the Stokes parameter Q as H rises. Finally, the passage of radiation through an optically thick layer is considered, and it is established that with an increase in the width of the depolarization contour decreases indefinitely.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 30–35, December, 1976.The author thanks V. L. Ginzburg for a discussion of the work.     

Time evolution automorphisms in generalized mean-field theories

A general class of time evolutions ^Q of infinite quantum systems is rigorously defined. It generalizes thermodynamic limits of polynomial mean-field evolution of quantum spin lattices, the simplest case of which is the strong coupling version of the quasi spin B.C.S.-model of superconductivity. A distinguished feature of the considered type of time evolution is the ^Q -non-invariance of the usually consideredC ^*-algebraA of quasilocal observables of the infinite system. A largerC ^*-algebraC containingA as a subalgebra is introduced in such a way that ^Q has a natural extension to a one parameter group^*-automorphisms ofC. The algebraC contains a commutative subalgebra of classical observables (consisting of the intensive observables of the large quantal system determined by a Lie groupG action(G) ^*-autA) denoted byN which is ^Q invariant and the restriction of ^Q toN reproduces the classical Hamiltonian flow ^Q corresponding to the chosen classical Hamiltonian functionQ on the classical phase space of the intensive observables. The evolution ^Q is determined uniquely by the classical Hamiltonian functionQ as well as by the action(G). Continuity properties of ^Q are considered and reviewed.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Measurements of long atomic lifetimes at an ion storage ring

Millisecond lifetimes of excited levels in multicharged ions may be measured at ion storage rings. At the Heidelberg ion storage ring TSR, particle detection after collisions between the circulating ions and electrons of the cooler has been used to obtain dielectronic recombination spectra as well as time curves of ionization and recombination for four-electron ions, with the aim of measuring transition probabilities for magnetic dipole and for electric dipole intercombination decays. The measurements on the 2s2p³P ₁ ^o level in the Be-like ions of N and O indicate lifetime values of =(1.6±0.2) ms for N³⁺ and of =(0.5±0.1) ms for O⁴⁺. Problems of these experiments are discussed as well as the prospects for improved measurements on other such ions of astrophysical interest, planning for state-specific optical detection.     

The peak constrained positive exponential sum method of inverting Laplace transform applied to correlation spectroscopy

As a contribution to the basic problem of correlation spectroscopy, a method has been developed for the Laplace transform inversion with a given number of maxima in the nonnegative inverted function() (i.e. in the distribution function of decay times recalculated as a density function on a logarithmic scale) by the least squares method. The resulting solution consists of the given number of-functions, each of which may be accompanied on one or both sides by one or several histogram bins decreasing away from the-function. When applied to simulated data for quasielastic light scattering (QELS), the method yields good agreement of the calculated distributions with the simulated ones, except that it yields sharp edges to the histogram bins and artefact-functions at the maxima of all the bands. An example shows the method to be a useful tool in interpreting QELS data.     

Kramers time in weakly nonpotential systems

We consider a bistable Fokker-Planck system with a known stationary distribution and a small nonpotential part in the drift force. We perform a perturbation calculation of its Kramers time, _K, and compare it with the corresponding time, _K ⁽⁰⁾ , for the potential system which has the same stationary distribution. We show that _K/ _K ⁽⁰⁾ depends only on the properties of the drift force close to the saddle-point.The authors would like to dedicate this work to their colleagues Y. Orlov, R. Nazarian, and V. Brailovski.     

Positive resonances and the limiting amplitude principle

We define the positive resonance points of self-adjoint operators without using the analytical continuation of corresponding resolvents and show that the limiting amplitude principle for the abstract wave equation does not take place in general, if ² = , where is the disturbing frequency and is the resonance point. The asymptotics of corresponding solutions as t are obtained, which imply the growth of the oscillation amplitude as t , 0<<1, or as ln t, t .     

Energy level crossings in quantum mechanics

From the eigenvalue equationH \ _n () =E _n ()\ _n () withH H ₀ +V one can derive an autonomous system of first order differential equations for the eigenvaluesE _n () and the matrix elementsV _mn () where is the independent variable. To solve the dynamical system we need the initial valuesE _n ( = 0) and \ _n ( = 0). Thus one finds the motion of the energy levelsE _n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H ₀ +V ₁ + ² V ₂ and give an application to a supersymmetric Hamiltonian.     

Muon lifetimes and weak interaction coupling constants

Improvements in determining muon lifetimes that are possible with the pulsed muon beam at the ISIS accelerator complex near Oxford, UK, are examined. The requirements of the standard model do not require an improvement in (µ⁺)[G_µ], which is fortunate as the low repetition rate of ISIS make such difficult. However, for stopping µ^± in liquid hydrogen the differences [(µ⁺) –(µ^–, observing decay e^–)] and [(µ^–, e^–) – (µ^–, observing capture n)] can be well improved to give the induced pseudo-scalar coupling constant,g _P, to ±2% and hence the first test of the chiral structure of the nucleon.On leave from Department of Physics, William & Mary, VA, USA.     

Cosmology with Curvature-Saturated Gravitational Lagrangian R/\sqrt {1 + l^4 R^2 }

We argue that the Lagrangian for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert Lagrangian _EH = R/16G and a pure cosmological constant for large R with the ansatz _cs = _EH/ , where l is a length parameter expected to be a few orders of magnitude above the Planck length. The curvature-dependent effective gravitational constant defined by d/dR = 1/16G _eff is G _eff = G , and tends to infinity for large R, in contrast to most other approaches where G _eff 0. The theory possesses neither ghosts nor tachyons, but it fails to be linearization stable. In a curvature saturated cosmology, the coordinates with ds ² = a ² [da ²/B(a) – dx ² – dy ² – dz ²] are most convenient since the curvature scalar becomes a linear function of B(a). Cosmological solutions with a singularity of type R ± are possible which have a bounded energy-momentum tensor everywhere; such a behaviour is excluded in Einstein's theory. In synchronized time, the metric is given by

Nonradiative excitation energy transport in one-component disordered systems

High-accuracy Monte Carlo simulations of the time-dependent excitation probabilityG ^s (t) and steady-state emission anisotropyr _M /r _0M for one-component three-dimensional systems were performed. It was found that the values ofr _M /r _0M obtained for the averaged orientation factor only slightly overrate those obtained for the real values of the orientation factor _ik ² . This result is essentially different from that previously reported. Simulation results were compared with the probability coursesG ^s (t) andR(t) obtained within the frameworks of diagrammatic and two-particle Huber models, respectively. The results turned out to be in good agreement withR(t) but deviated visibly fromG ^s (t) at long times and/or high concentrations. Emission anisotropy measurements on glycerolic solutions of Na-fluorescein and rhodamine 6G were carried out at different excitation wavelengths. Very good agreement between the experimental data and the theory was found, with _ex0-0 for concentrations not exceeding 3.5·10^–2 and 7.5·10^–3 M in the case of Na-fluorescein and rhodamine 6G, respectively. Up to these concentrations, the solutions investigated can be treated as one-component systems. The discrepancies observed at higher concentrations are caused by the presence of dimers. It was found that for _ex <_0-0 (Stokes excitation) the experimental emission anisotropies are lower than predicted by the theory. However, upon anti-Stokes excitation (_ex>_0-0), they lie higher than the respective theoretical values. Such a dispersive character of the energy migration can be explained qualitatively by the presence of fluorescent centers with 0-0 transitions differing from the mean at _0-0.     

Medium-spin excitations of the neutron-rich 84Se isotope: Possible decrease in energy of the N = 50 neutron-core excitation

The ⁸⁴Se nucleus has been produced as fission fragment in the fusion reaction ¹⁸O + ²⁰⁸Pb at 85MeV bombarding energy and studied with the Euroball IV array. Medium-spin states of this neutron-rich isotope have been identified for the first time. Its level scheme has been obtained up to 4.9MeV excitation energy and spin I 7. Its structure is interpreted by analogy with those of the stable heavier isotones. The evolution of the energy of the N = 50 neutron-core excitation is discussed as a function of the proton number.     

Energy of the 5− isomer and (πg 9/2⊗vg 9/2) states in82Rb

Excited states in the doubly-odd nucleus⁸²Rb have been investigated via the reactions⁷⁹Br(,n) and⁷⁸Se(⁷Li,3n) using in-beam-ray spectroscopy. The level energy of the longlived 5^– isomer has been determined to 68.3 keV which is below the energy of the 2^– state found at 88.9 keV with a lifetime of=2.4(2) ns. A sequence of positive-parity states beginning with a 6⁺ level at 191.3 keV (=20(3) ns) and extending to a (10⁺) level has been interpreted to contain the two-particle configuration (g ₉/2 _9/2) and collective excitations.     

Study of fermilab data for the reaction π−p → π0n

Fermilab data for the angular distribution measurements of the reaction ^–p ⁰n are investigated and it is shown that a good fit with experiment is obtained by using a simple Regge pole model with phenomenological residue functions. The energy dependence in this case is found to be different from that for the d/dt data obtained at Serpukhov.Work supported by the Pakistan Science Foundation under contract No. P-PU-PHY(11/1).     

Superintegrable chiral Potts model: Thermodynamic properties,an “inverse” model,and a simple associated Hamiltonian

The partition function of theN-state Superintegrable chiral Potts model is obtained exactly and explicitly (if not completely rigorously) for a finite lattice with particular boundary conditions. This yields the bulk and surface free energies, and horizontal and vertical correlation lengths and interfacial tensions. The critical exponents are =1–2/N, _hor=_hor=2/N, and _vert=_vert=1, and the finite-size corrections are obtained at criticality. The eigenvalue spectrum of the column-to-column transfer matrix is that of a direct product ofN byN matrices. Inverting this matrix gives a related solvable model which is a generalization of the free-fermion model. The associated Hamiltobian has a very simple form, suggesting there may be a more direct algebraic method (perhaps a generalized Clifford algebra) for obtaining its eigenvalues.     

An invariant solution of the Fokker-Planck equation and rheological equation of state of a macromolecular solution

The Fokker-Planck equation is solved for a soft dumbbell in a homogeneous hydrodynamic field invariantly with respect to rheonomous transformations. The equation of state for a soft dumbbell with relaxation time has the form:P ^ab + ^–1 P ^ab =1/2kTG ^ab .P ^ab is the convected derivative of the stress tensorP ^ab andG ^ab the metric tensor. For a more general model-network composed of Hookean springs with constant hydrodynamic interaction (e.g. a model of Gaussian sub-chains) we obtain the equation of state by combining the contributions of the above-mentioned type. Such an equation of state describes linear visco-elastic behaviour with general spectrum of the relaxation times. If convected derivation with respect to time is used in the calculation, the viscosity is Newtonian even if the calculation is performed in a coordinate system rotating with the molecule.     

Correlation tensors of the blackbody radiation in rectangular cavities

Electromagnetic equilibrium fluctuations in finite cavities filled with a dissipative medium (dielectric function ()=+i) and bounded by walls of infinite conductivity are considered. Expanding the fields in terms of a complete and orthonormal set of functions and solving the Maxwell equations the response of the EM field to external forces (polarization and magnetization) is obtained. With the aid of the fluctuation dissipation theorem and the linear response functions the 2nd order correlation tensors of the EM field are derived.For rectangular cavities explicit considerations are made. In the case of transparent media (=0) the spectral energy density of the EM radiation is calculated.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Low-energy elementary surface excitations of symmetric films of liquid4He atT=0 K

It is known that low-energy elementary excitations of symmetric films of liquid⁴He atT=0 K are characterized by a momentum q parallel to the surface and may be described by bound states. We have evaluated wave functions and energies of these states for both best short-ranged and optimal long-ranged correlations. Quantities of physical interest may be expressed in terms of these eigenstates and, in particular, for very small momenta (q<0.2 Å^–1) they are mainly determined by the contribution due to the lowest-lying one. We propose analytic expressions for the lowest-lying excitations and fluctuations in the long-wavelength limit. It is proved that in this limiting case, the excitation energy _LW(q) and the averaged static structure functionS _LW(q) should go linearly to zero asq0, whereas the averaged direct correlationX _LW ^Dg (q) should diverge at the origin as 1/q. It is shown that numerical solutions exhibit the expected long-wavelength behavior provided that optimal correlations are used. All these results are displayed in a series of figures and are discussed in detail.