Table of contents

The growth rate for the instability of Bernstein waves in perpendicular collisionless shocks is calculated including pressure gradient effects. For typical experimental conditions the growth rate can be as much as an order of magnitude greater than that predicted by previous calculations.

Experimental results are presented which show that a large-amplitude wave of one of the Bernstein modes, above a certain threshold power, can decay into another Bernstein mode plus a low frequency ion-sound wave. At larger incident amplitudes, a whole spectrum of low-frequency ion waves was observed, with frequencies extending up to the ion plasma frequency. These results are compared with a previous theory and reasonable agreement is achieved.

The first and the second N-photon factorial moments for the superposition of coherent and chaotic fields and the third N-photon factorial moment for the chaotic field are given for arbitrary spectrum and counting time intervals.

The new Durham Spectrograph, MARS, has been used to make a direct measurement of the mean rate of energy loss of cosmic ray muons in iron in the momentum range 5-40 GeV/c. Agreement is found with the predictions of Sternheimer, and Sternheimer and Peierls for ionization loss (together with values for the other losses) to within the statistical errors, which range from 2% at 6 GeV/c to 6% at 30 GeV/c.

The possibility of helium burning occurring through the reaction ¹²C( alpha , e^+or-)¹⁶O is examined for a temperature of 10⁸ K. As the isoscalar electric monopole sum rule does not rule this out, the results of an electron scattering experiment are reported which demonstrate the absence of electric monopole excitations in the continuum beyond the threshold for ¹²C+⁴He.

With Chiral Lagrangians in mind, the authors study Lagrangians whose Dyson index is non-negative, for which the problem is the removal of the ultraviolet divergences that remain after the usual resummation over the minor coupling constant. The authors have shown that for any rational interaction Lagrangian without derivatives and of Dyson index less than four, these divergences may be removed in all orders by local counter-terms. This is a special case of a more general result, namely that the method of local counter-terms works if L_int=L_p+L_np, where L_p is a polynomial of Dyson index less than four and L_np is a nonpolynomial for which the resummation leaves no divergences. They present the counter-terms explicitly after resummation over the minor coupling constant.

A recursive relation connecting the numbers of self-avoiding walks on an arbitrary network with the numbers of certain related topologies is given, and is used to obtain exact end-point distributions of self-avoiding walks on a variety of Bravais lattices in two and three dimensions. The growth (proportional to n gamma ) of the mean-square end-to-end distance of such walks of n steps is re-examined. The authors estimate (i) for the triangular lattice: gamma =1.488+or-0.002; (ii) for the face-centred cubic lattice: gamma =1.20+or-0.01. The first estimate is lower than gamma =1.5 conjectured by some workers in this field; however, there are differences in assumptions of how the mean-square end-to-end distance ought to depend on n.

Using the idea of a local hydrodynamical equilibrium in a two-component Coulomb gas, one can prove that the latter possesses a spatially periodic structure. The spatial period calculated is found to be in good agreement with the period experimentally measured for gas plasma.

A plasma mode of solids is proposed. It is shown that, in the presence of a local dynamic equilibrium in a steady-state electronic-ionic plasma, a spatially periodic selfconsistent potential can exist leading to a periodic structure in the solid-state plasma. Calculations for the period of the crystal structure of a number of metals with cubic (face-centered) and hexagonal symmetry are performed. The work function of some metals with cubic (face-centered) symmetry is also calculated. The results obtained are compared with the corresponding experimental data.

The integration method for many-particle van der Waals interactions of general order, which was found useful in Drude model calculations can be successfully used also in purely quantum mechanical investigations. The quantum mechanical perturbation series of the dispersion energy is shown not to contain any poles even if the unperturbed electron states are degenerate. It is factorized by means of a linear integral transformation, and subsequently integrated by combining concurrent interactions into effective matrix elements (Green's functions).

The stationary generalized Langevin equation is derived from the Liouville equation. The 'random force' involved in the obtained equation satisfies the equation of motion for a dynamical variable. The fluctuation-dissipation theorems are derived and written for the present equation. The relationship with Mori's generalized Langevin equation is given.

In the Hoyle-Narlikar particle theory of gravitation, the mass function at a point X due to particle a is defined asm^(a)(X)=- lambda integral G(X, A)da where G(X, A) is a Green's function which satisfies a simple wave equation. In this paper the coupling constant lambda is replaced by lambda _a where lambda _a can be positive or negative. Two possible subsequent generalizations of the action of the Hoyle-Narlikar theory are suggested and the two resultant particle theories developed. One special case of one of these theories is examined in some detail. This has particles which contribute negative inertia as well as those which contribute positive inertia and all the lambda _a such that mod lambda _a mod = lambda . In this theory the gravitational 'constant' G is a function of position and can be positive or negative.

Action principles using the Eulerian description are proposed for the elastic solid and perfect fluid in general relativity. By taking into account the constraints on the independent variables appearing in the Lagrangian density, it is shown that these action principles are equivalent to those using the Lagrangian description, which have been given previously.

The cooling behaviour of neutron stars, taking into account several models proposed by Tsuruta and Cameron, has been studied on the basis of neutrino emission according to the photon-neutrino weak coupling theory. It is shown that the internal energy storage is sufficient to interpret X-ray emission and other cosmic ray activities of neutron stars. Also it is found that only one supernova outburst in 100 years can explain the steady state cosmic ray flux in the galaxy. Finally, some remarks about the possible pulsation of neutron stars are made.

The authors investigate the statistical errors which arise in digital autocorrelation of photon counting fluctuations due to the finite duration of experiments. An expression for the accuracy with which individual points of the autocorrelation function of intensities can be measured is derived analytically and evaluated for Gaussian- Lorentzian light. The appropriate weighting for a 'least-squares' fitting procedure is determined and the error in spectral linewidth, obtained by this procedure from experiment, is calculated.

The effect of intensities of electromagnetic waves on their collisional mixing in an inert gas plasma has been investigated. For strong collisions the generated harmonic and combination frequencies in a helium plasma show a maximum (for an optimum value of wave intensity) while a continuous increase is found for weak collisions. In the presence of a static magnetic field the generation of odd harmonics is not possible with only one mode of the fundamental wave, though even harmonics can be generated if a dc electric field is present. Resonances appear at fundamental and harmonic frequencies.

From the study of non-steady-state separation in a hot-wire thermal diffusion column, it is shown that the experimental results for the magnitude H₀²/ mu (K_c+K_d) are proportional to the theoretical values predicted by the Furry-Jones-Onsager (FJO) formulation. This result, together with the earlier ones concerning the similar relations fulfilled by the logarithm of the maximum separation factor and the optimum pressure, ensures that the FJO theory is able to predict the experimental values of the three column constants H_0, K_c, and K_d, with the exception of a multiplicative temperature-independent constant, for Kr gas in the temperature range 300-1100 K.

The theory of diffuse transition is applied to study melting of short-chain hydrocarbons. An adjustable nucleation parameter reported earlier for polyethylene is used. Experimental data of Flory and Vrij are utilized.

Direct use of a generalized Laplace transform is proposed for applications in nonequilibrium quantum statistics. The method includes the equilibrium 'double-time' Green's function method as a special case. An example is given in optical theory in which non-Markoffian behaviour and Poincare recurrences have been explicitly found.

For pt. II see abstr. A35654 of 1971. A theory is developed to account for the intensity of ASE as a function of the length and diameter of the amplifying medium and of its inversion density. Detailed results are presented from a study of the 3.39 mu m transition in He-Ne which verify the theory. The theory is also shown to fit the experimental data obtained from the 0.337 mu m transition in N₂.

The net absorption coefficient allowing for stimulated emission in a nonrelativistic plasma is calculated using the cross sections found by Bunkin and Fedorov. The computations range over many values of their two parameters, which are determined by the initial electron velocity and the frequency and intensity of the electromagnetic field. The energy absorbed is found at strong enough flux to decrease with increasing flux and to be primarily determined by single photon processes for all parameter values considered.

On the basis of a calculation for the force and couple exerted on a moving point dipole given previously, a consistent description of classical spin for particles possessing charge and dipole moment is discussed.