Table of contents

The probability distribution of photon-counting relative to a Gaussian beam scattered by a Gaussian medium is evaluated.

Stangeby and Allen (1970) have demonstrated that the plasma-sheath boundary is a Mach surface in a collisionless plasma containing an anisotropic cold ion velocity distribution and no ionization. It is shown that the plasma-sheath boundary is still a Mach surface even when the effects of ionization, momentum-transferring collisions and a finite ion temperature are considered.

Bernstein waves which propagate in a direction opposite to the current flow in a perpendicular collisionless shock can have negative energy. These negative-energy waves can give rise to instability either by coming into resonance with the ion acoustic wave or by dissipating their energy through ion Landau damping. In the second case the instability can take place for T₁>or approximately=T_e.

The effects of finite sizes of source and detector on observed intensity fluctuations of Gaussian light are investigated both theoretically and experimentally. The theory allows a measurement of source size to be made using a single receiving aperture, rather than two as used in the Hanbury-Brown Twiss intensity interferometer.

The calculations of Schulman (1968) on the path integral formulation of the spherical top are generalized to the case of a free particle moving on the manifold of a simple Lie group. It is shown that the finite propagator takes on the same form as the short time one except for the phase factor exp (-¹/₁₂iRt) where R is the constant scalar curvature of the group manifold.

The subject of this paper is the solution of the convolution integral, which relates the observed line profile to the true profile which is obtained in the absence of instrumental resolution effects. In the case of perfectly accurate data this problem has (by assumption) a well-defined solution. This paper considers the practical problem that results when the experimental curve is subject to error. Estimates are given for the importance of the error and a criterion is developed for optimizing the deconvolution procedure. This leads to a deconvolution function which when convoluted with the experimental curve gives the true solution. Finally the method of solution by iteration is examined and the effect of error upon it studied.

An attempt is made to re-derive the radiation damping formula using Wheeler-Feynman formalism of the absorber theory of radiation. The point of departure is that the absorber response on the radiating charged particle is calculated by taking into account the principle of action and reaction.

The motion of a charged particle in a magnetic field composed of a uniform axial component and a spatially rotating transverse component is analysed. Solutions of the nonlinear equations of motion are obtained which describe an oscillatory transfer of kinetic energy between axial motion and rotational motion in the transverse plane. A simple physical description of the interaction in terms of impulsive Lorentz forces is given which has formal similarity to the Huygens' principle in physical optics.

The asymptotic form of the metric due to moving masses is calculated in terms of that due to a stationary mass. The work is modelled on the special-relativistic calculation of the electromagnetic field of moving charges from the Coulomb field of a stationary charge. The effects of acceleration and of terms not linear in the masses are neglected. The Lense-Thirring metric for a slowly-rotating spherically symmetric body is derived. It is shown that the precession of spinning satellites, the deflection of starlight by the Sun, and the Shapiro time-delay are all determined by the same parameter in the metric. The approximate metric due to an arbitrary moving mass distribution is shown to satisfy the linearized Einstein field equations.

The author presents a class of solutions of Einstein-Maxwell equations corresponding to stationary null electromagnetic fields in otherwise empty space.

This paper reports the investigation of two problems: (i) the possibility of bootstrapping boundstate scalar and vector mesons from scalar constituents, in an off-shell model, utilizing the direct interaction theory of Bakamjian and Thomas (1953), and then (ii) the effect of applying a linear perturbation procedure to the masses and coupling constants of these solutions. In (i) the Lippmann-Schwinger formalism and an approximate form of crossing symmetry are used to obtain expressions for the bound-state residues, giving solutions to both the scalar and vector cases with properties in excellent agreement with Bethe-Salpeter and N/D dispersion results of other excellent agreement with Bethe-Salpeter and N/D dispersion results of other workers. In (ii) the author calculates the relative contributions of the 'driving-term' and 'feedback' mechanisms. In the S-wave case he finds that the attractive perturbation increases the binding of the bound state, but in the P-wave case, treated with a cut-off, he obtains a 'sign-reversal' of the mass-shift arising from the 'feedback'.

In this paper the quasi-particle structure of the ground state of the pairing Hamiltonian is analysed for the Ni isotopes and ²⁰⁶Pb. The particle-number projected Bardeen-Cooper-Schrieffer states are used for describing the states under consideration. The quasi-particle amplitudes are evaluated in the saddle-point approximation. The amplitudes with the number of quasi-particles a multiple of four are shown to be comparable with the quasi-particle vacuum amplitude. The value of the other quasi-particle amplitudes depends essentially on the system considered. In particular, the two-quasi-particle component can sometimes be comparable with the four-quasi-particle one (²⁰⁶Pb). On the basis of the data obtained it is concluded that the random phase approximation ground-state wave function with small admixture of the quasi-particle components, the components with the odd number of quasi-particle pairs being neglected completely, is rather poor.

Rotational energy levels of the ground state band of a number of deformed even-even nuclei have been calculated using the models proposed by Krutov in 1968 and by Davydov and Filippov in 1958. The parameters, occurring in these models, have been evaluated by two different methods. The results are compared with the experimental values and the relative merits of the models discussed.

This paper reports some results obtained in an attempt to determine a nucleon-nuclear potential of the Morse function type that contains velocity-dependent, spin-orbit splitting, energy-dependent, centrifugal interaction, etc., terms. The single-particle energy formula for all nuclei in the Morse-type potential well has been shown as convenient as in the harmonic type and as reliable as perhaps Hartree-Fock calculations. In particular the neutron separation energies for ¹⁶O and ⁴⁰Ca have been calculated and compared with the recently published results obtained from similar calculations and compared with the recently published results obtained from similar calculations and also with the other theoretical and experimental works. The results are found to be in very good agreement with the data and are consistent with the other calculations except with those published recently.

The quantum theory of a laser developed by Scully and Lamb (1967) is reformulated to include the effects of atomic motion and detuning. The equations are solved to fourth order in the atom-field coupling constant. An approximate treatment of the mode structure is shown to reproduce the results of Lamb's semi-classical theory in the Doppler limit. In addition the photon distribution may be studied as a function of the detuning. The width of the photon distribution is found to increase monotonically with increasing detuning.

The generation of vlf waves as a result of nonlinear interaction of two microwaves with a plasma slab in the presence of a high dc field is investigated theoretically. The reflected and transmitted vlf power comes out to be very high compared with the case for high-frequency waves. The generated vlf power is found to be maximum for an optimum value of the nonlinearity parameter, which is a function of carrier mass, collision frequency and mass of the scatterer. The vlf power is also found to show maxima and minima at various slab thicknesses.

An investigation of the simultaneous occurrence of moving striations and backward disturbance waves in the helium positive column at low to medium pressure is described. The interaction between these nonlinear wave motions is discussed and an instability of the positive column for electrode separations greater than 14 cm is reported.

The effect of a change in volume on the chemical potential of an electron gas is investigated. It is found that an increase in volume generally gives rise to a decrease in chemical potential, the temperature coefficient of the chemical potential being of the same order of magnitude as the coefficient of volume expansion.

For pt. I see ibid. vol. 3, 427-41 (1970). A bonded fluid model on a plane triangular lattice is studied. Each molecule has three bonding directions at angles of 120 degrees to each other and two possible orientations in each of which its bonding directions point to three of the six nearest-neighbour sites. If the molecules of a nearest-neighbour pair have bonding directions pointing towards each other then a bond is formed and the pair has interaction energy -( epsilon +w), while an unbonded nearest-neighbour pair has interaction energy - epsilon ( epsilon >0, w>0). For epsilon /w<¹/₃ regions of open structure short- range order became important at low temperatures and pressures, with each molecule in such a region bonded to three others and one third of the sites vacant. At higher pressures the predominant low-temperature configuration is close-packed with all sites occupied. Calculations are performed, using a first-order approximation based on a triangle of sites, for epsilon /w=0 and epsilon /w=¹/₄. Critical points are deduced for separation into liquid and vapour phases, both without long-range order. The behaviour of the density as a function of pressure and temperature in the model resembles that found in fluid water, especially for epsilon /w=¹/₄. There is a supercritical region where curves of density against temperature at constant pressure show turning points, though at very high pressures the density decreases monotonically. For epsilon /w=¹/₄ these turning points are also found below the critical pressure in the liquid phase.