Table of contents

The density field formalism of Sherrington is used to obtain diagrammatic expansions and thus complete expressions for the quantities evaluation of the density correlation function. It is shown how these diagrammatic expansions satisfy two important sum rules to all orders. The plasmon mode is obtained in a simple fashion from these expansions.

It is proved that the derivatives with respect to time of Boltzmann's H function alternate in sign for a gas whose behaviour may be described by the linearized Boltzmann equation.

The problem of the excluded volume in a polymer chain is studied with the aid of a function which approximates to the Heaviside step function. This step function excludes the inhibited configurations of the chain by not allowing the distance of the end points of its ith link and i+sth link (1<or=s<or=N-1, i,...,N-s) to be smaller than the chosen delta >0, 0< delta <a, where a²=²/₃(r_i²), (r_i²) is the mean square of link length. In a single-contact approximation, the limiting case delta to 0 leads to an asymptotic relation proportional to the relation from Fixman's perturbation theory of the first order. The cause of the disagreement lies in the approximate character of the step function used.

An elementary proof of the results of Wightman concerning the existence and non-existence of position observables for relativistic systems is presented. The method uses an explicitly described unitary transformation to relate the representations of the Euclidean group obtained by restricting the m not=0 representations of the Poincare group to representions having position observables. The position observables are displayed explicitly as differential operators in the cases in which they exist.

Gravitational and inertial field equations of a Maxwellian form are established which lead to a consistent theory of gravitation. The new approach to dynamics arising from the field theory is in agreement with the theory of special relativity, while producing a fresh insight into some of the relativistic phenomena.

Considers the most general cylindrically symmetric space-time from the point of view of Petrov classification. The Pirani matrix has been classified into six distinct cases. The Segre characteristics reveal that the cylindrically symmetric metric belongs to either Petrov type I or Petrov type II. It is also found that when the metric potentials are functions of time alone the space-time admits perfect fluid distribution.

In 1966 Bonnor and Rotenberg used the double-series approximation method, in conjunction with the Bondi metric, to study gravitational radiation from an isolated cohesive axisymmetric source vibrating smoothly during a finite interval u₁<or=u<or=u₂ (u=retarded time t-r). In part I of this paper a complete solution, clearly convergent for r>0 and all u, is given of the (24) approximation step of Bonnor and Rotenberg's work. The quadrupole-quadrupole interaction is shown to satisfy Huygens' principle, but the monopole-2⁴-pole interaction gives rise to 'wave tails'. In part II it is shown that, for u>u₂ (end of the source vibration), the 'wave tails' resulting from the monopole-2^s-pole contribution of the (2s) approximation (s>or=2) represent incoming 2^s-pole radiation, at any rate for s=2, 3, 4.

Particles comprising an extensive air shower do not originate from a point but are produced as secondaries to the products of interactions which take place along an axial core region. Their structure or arrival-time distribution should be related to their production depth and propagation properties. A detailed Monte Carlo calculation has been made on the delays arising in the development of the electron-photon component to form a basis for the interpretation of experimental observations. Results are presented for the estimated time-delay distributions in an extensive air shower of primary energy 9*10¹⁶ eV at radial core distances of 200, 400 and 600 m. Also considered are the energy spectra of photons at such distances, the lateral distribution of energy in the front and the relative muon and electron-photon contributions.

The mass difference for mirror nuclides is expressed in terms of the curvature 2C₂ of the corresponding isobaric mass parabola and the (fractional) 'atomic number' Z* corresponding to its minimum. With the Coulomb energy of a nucleus taken as gamma _AZ(Z-1)/A^1/3, it is shown that C₂(A-2Z*)= beta + gamma _A(A^2/3-A^-1/3) where beta represents the hydrogen-neutron mass difference. The relationship is valid for both odd and even values of A. The availability of empirical values of C₂ and Z* permits the evaluation of gamma _A and thence the 'Coulomb- energy radius' R_c=r_AA^1/3 where r_A identical to ³/₅e^/2 gamma _A. Consideration of a 'quantal' formula for the Coulomb energy of a nucleus shows that the 'quantal' values of r_A are slightly smaller than the 'classical' values but the difference becomes negligible for large values of A. Although there are significant variations in r_A, the general trend is to smaller values of r_A as A gets larger, e.g. r_A=1.47 fm for 16<or=A<or=74 whereas r_A=1.30 fm for 120<or=A<or=198. Values of r_A corresponding to almost all values of A from 16 to 249 are given graphically and estimates of the error are included.

The (p,n) reaction in ⁷Li at 94 MeV is studied in the impulse approximation. The differential cross sections for exciting the isobaric analogue state and the 0.431 MeV state in ⁷Be are obtained using LS-coupled shell-model wave functions. Fairly good shape agreement with the available experimental results is obtained. These results are discussed, together with the inelastic proton scattering to the 0.478 MeV state in ⁷Li, as a mode of investigating the model wave functions used; where the small-angle results as predicted by the theory appear to be in conflict with the experimental data. Need for more experimental data at small angles for these reactions is stressed.

Microwave transmission across a column of turbulent plasma is strongly influenced by the presence of small-scale plasma density inhomogeneities. In devices such as ZETA, fluctuations of 10-25% about mean densities of 10¹⁴ cm^-3 have been observed with correlation lengths of up to 5-10 cm and time scales of 10^-5 s. Scattering measurements have used microwaves with a free-space wavelength of 2 mm (corresponding to a critical density of 2.5*10¹⁴ cm^-3) and in ZETA multiple scattering processes are important. A numerical solution for the transport theory formulation of multiple scattering is used to interpret the measurements and good agreement with Langmuir probes is obtained.

Investigations at 0.633 mu m and 1.15 mu m in the He-Ne laser show that beat frequencies at about c/2l and 2c/2l between neighbouring axial modes are found to shift linearly with inserted cavity loss. These effects are explained using Lamb theory. Information is gained concerning the stability of mode distributions. The effect is also investigated in the argon ion laser at 0.488 mu m.

The Lamb theory of mode self-locking in gas lasers is approximated to provide criteria for self-locking to occur in practical systems. It is predicted that self-locking should be fairly easily attained in the He-Ne 1.15 mu m and 0.633 mu m lasers, and this is confirmed by experiment.

The single-mode intensity of a 0.6328 mu m He-Ne laser has been measured as a function e cavity Q. Significant deviations have been found from the predictions of the Lamb semi-classical theory, particularly near threshold. The results have been fully explained using the quantum theory of Scully and Lamb.

Breakdown of gases at a pressure of 15 mtorr under the action of a high-frequency uniform electric field is studied in tubes of length 5 cm, 7 cm and 15 cm and 3.5 cm diameter, as well as with a superimposed steady transverse magnetic field of 18 gauss to 45 gauss in the tube of length 5 cm. It is found that the breakdown voltage increases as the length is decrease The cut-off wavelength increases with the tube length. The breakdown is here due to secondary electron resonance. The phase angle phi and the maximum kinetic energy of the electron hitting the wall have been calculated and found to agree with earlier results. In the presence of a magnetic field the breakdown voltage, as well he cut-off wavelength, increases with rising magnetic field. The corresponding theory is developed and the effect of the angle on arrival at the end wall on the breakdown mechanism is considered. Comparisons of the observations with the theory yield values of the phase angle and of the electron's kinetic energy on arrival at the wall with a fair amount of accuracy, especially for magnetic fields smaller than 30 gauss. The probability of electrons colliding with the side walls is considered. Under the present experimental set-up the majority of electrons with energy sufficient to cause breakdown travel freely between the two ends of the tube. The validity of some of the simplifying assumptions made i the theory is discussed.

Discusses the statistical properties of the intensity fluctuations of light fields consisting of an incoherent Gaussian component heterodyned with a single-frequency coherent beam. The second moment of the intensity- fluctuation distribution is obtained in an analytic form for a Lorentzian incoherent spectrum for arbitrary values of the bandwidth and frequency displacement from the coherent mode. The analysis includes as special cases many of the exact results obtained in statistical optics over the last decade.

The spectrum of light scattered by particles suspended in a turbulent fluid is investigated theoretically.

It is shown that the equations for the probability of crystallization of supercooled aerosol obtained by Carte (see abstr. 9553, 1959) and Bigg (1953) are special cases of the more general equation.

In the course of investigating the Rainich equations of the 'already unified field theory' when the electromagnetic is non-static, Bera and Datta in 1968 obtained a metric which leads to empty flat space. It is shown that the said metric is Riemannian (non-flat) and satisfies the field equations of gravitation for empty space. Hence it is of great interest from the point of view of cosmology.

This letter finds lower bounds to the second-order correction to the eigenvalue of an observable for the ith excited state of a stationary quantum system.

A previous theory of the interaction of an ideal fluid with the gravitational field, as given by Rastall in 1968, is modified. It is now assumed that the natural internal energy per unit mass of the fluid is a function of the natural pressure and density.