Table of contents

Measurements of the probability P(0) of detecting zero optical photons during a fixed counting time are used to verify an exact calculation of this quantity for the case of gaussian light with a Lorentz spectral line. The measurement of P(0) is of particular interest since it provides an explicit measurement of the 'generating function' Q( lambda ,t) mod _{lambda =1} used to generate all of the other probabilities P(n). The excellent agreement of the measurements with the exact calculation validates the use of this calculation in determining the corrections to the 'short time' approximation commonly used in photon counting experiments.

The effect of atomic excitation on the shape of the ³H beta spectrum near the end point is calculated and found to be small. However, depending on the type of spectrometer and the method of analysis of data, the effect could lead to a systematic error which is not negligible compared with the accuracies quoted in some recent determinations of the end point.

The counting rate of recoil electrons for the elastic scattering of electrons by solar neutrinos, considering that the CNO cycle is responsible for nuclear energy generation in the sun, is calculated according to the photon-neutrino weak coupling theory as well as the current-current coupling theory. It is suggested that this result can be used to decide which type of weak interaction exists in nature.

It is pointed out that, in the configuration of a perpendicular collisionless shock, a resonant interaction is possible between a negative Bernstein mode and two positive energy ion acoustic modes. An estimate is made of the growth rate of the resulting explosive instability.

Computer calculations have been performed to investigate the short range order near the freezing point, for fluids of particles interacting with an inverse twelfth power potential and with the Lennard-Jones potential. For these potentials, it is found that the onset of freezing is marked by the number of neighbours within a certain radius exceeding that of a close packed system of rigid spheres of a diameter determined by the free energy minimization procedure of Mansoori and Canfield.

Exact internal solutions for massive spheres with three different distributions of density have been found. The central core density is considered to be constant while the outer region has two types of varying densities: (i) varying inversely as the square of the radial distance; (ii) varying parabolically as rho varies as 1-r²/constant. The solutions are found to be continuous at different boundaries while the densities of different regions are not continuous but vary slightly. With proper choice of different parameters appearing in the solutions, the results can be applied to actual problems of stellar physics.

The first set of integrability conditions for the existence of a quadratic first integral of the geodesic equations in a general Riemannian space are obtained. A class of special quadratic first integrals is defined and their properties discussed.

Variational lower and upper bounds to energy levels of a quantum mechanical system with Hamiltonian H as well as to overlap integrals between approximate and exact wavefunctions, have been obtained by a unified treatment. This is based on Lagrange's method of undetermined multipliers, in which a number of calculated moments of H play the role of constraints. New lower and upper bounds to the energy of the first excited state of the system are derived.

The propagator for a harmonically bound charged particle in a constant uniform magnetic field is evaluated exactly from which the corresponding partition function and density of states are obtained. Then, the equilibrium response of an assembly of harmonically bound point charges is studied using both Boltzmann and Fermi-Dirac statistics. The results are considered in relation to the ionic lattice and to some extent to the charged nucleons.

The application of transfer theory to image formation in the electron microscope is discussed. The equivalence of the transfer theory and the diffraction integral formulation of image formation is established for a coherent monochromatic incident electron beam, and for elastic electron scattering. The transfer theory is extended to include partially coherent and nonmonochromatic radiation. The use of the results of the transfer theory leads to the diffraction integral formulation, which includes the effects of chromatic aberration (thermal energy effect) and the coherence of the incident electron beam. The modification to a criterion for optimum contrast in the final image when chromatic aberration is taken into account is discussed.

For pt.I see ibid. Vol.4, p782 (1971). The application of transfer theory to image formation by the inelastic component of the transmitted electron beam is discussed. The analysis includes the effects of chromatic aberration of the final image. In particular, it is shown that the chromatic aberration effect due to the inelastic component may be effectively cancelled by underfocus of the objective lens. In relation to the formation of image by the inelastically scattered electrons the coherence and the localization of the inelastically scattered wave is discussed.

A treatment of nonlinear optical phenomena beginning with a microscopically correct Hamiltonian containing the Bose operators of the light field and the Fermi operators for the optically active electrons in the medium is presented. Using techniques recently developed, a nonperturbative solution to the Schrodinger equation is possible. No linearization or semiclassical approximations are introduced. Two photon emission and absorption including both the degenerate and nondegenerate cases are considered. Parametric amplification and frequency conversion are investigated as examples of multiphoton processes. Atomic cooperation is shown to enhance the above phenomena. A formal treatment of a model illustrating super and subradiance is included.

Experimental confirmation is presented of recent theoretical results of Jakeman on the time ever aging of photon-counting fluctuations when utilizing clipping techniques for autocorrelation. The effects of finite electronic resolving time (dead-time correction) and finite receiving apertures (spatial-coherence correction) are included.

The quantization of Wheeler-Feynman direct interparticle action electrodynamics is refined and extended to the relativistic domain, using the S-matrix technique developed previously. The analysis is effected on the exact expression for S, rather than the perturbation expansion. Source particles are treated as indistinguishable fermions with antiparticles. The response of the universe is incorporated in a general way, without allusion to specific absorber mechanisms. All the results of conventional QED emerge, provided one makes certain cosmological assumptions.

A scheme developed by Scadron and Gault for calculating reggeized spin-averaged differential cross sections for boson exchange is extended, via s channel helicity vertices, to backward processes involving fermion Regge pole exchanges including those initiated by photons.

Parapositronium lifetime has been measured in toluene and fused quartz samples in a time distribution measurement experiment. The lifetime and intensity of the parapositronium components are tau ₀ (0.115+or-0.015) ns with I₀ (15+or-6)% for toluene and tau ₀ (0.126+or-0.010) ns with I₀ (14+or-6)% for fused quartz.

It is argued that the difference between the production cross section for T=0, abd T=1 hadronic final states is related to the U(3)(X)U(3) symmetry breaking. A simple sum rule is derived. Various symmetry breaking models are discussed. It is found that results from saturation of sum rule with vector mesons favour the previous obtained values b=c approximately=-1 for the U(3)(X)U(3) symmetry breaking parameters.

The arrival time spectra of hadrons of energy 5-40 GeV in extensive air showers of size 6.7*10⁴-1.8*10⁶ particles have been obtained and compared with the predictions from Monte Carlo calculations based on two different models, the 'fireball' and 'isobar-pionization' models, of high energy collisions. The 'fireball' modal predicts time spectra which are too steep compared to the observed ones. The 'isobar-pionization' model succeeds well in explaining the observed features of the arrival time spectra when increased NN production is taken into account. Thus it has been concluded that in high energy hadron collisions isobaric excitations of the interacting baryons play a very dominant role.

A simple theory id developed for the process pi K to pi K near threshold. It is similar to one recently proposed for pi pi to pi pi , and rests on an assumption of smoothness of the scattering amplitudes as functions of the energy-momentum invariants. The Adler PCAC consistency condition is imposed, but instead of current commutators, rho-meson dominance on the mass shell is used to fix overall normalization. The two approaches are connected by the KSRF relation, but because this model depends on two parameters (mass, width) more information is obtained. Thus the model contains P and D waves, and gives improved scattering-length predictions. Comparison with results from crossing-symmetric Regge models suggests that these need important additional terms.

When a large volume of data from cosmic ray emulsion reactions is analysed it is found that the variation of the mean dispersion s in the log tan theta plot of the charged secondaries, at each energy, follows a linear characteristic when plotted against the log energy of the incident particle. The slope of the characteristic is peculiar to the type of incident particle, and is higher for nucleon-nucleon collisions than for pion-nucleon events.

A large flash tube chamber has been constructed with the object of searching for relativistic e/3 quarks in extensive air showers at ground level. Experiments have been carried out to examine the applicability of the method; in particular, the response of the apparatus to muons of varying ionization has been investigated. It has been found that the logarithmic increase in ionization loss is reflected accurately in the variation of mean flash-tube efficiency with muon energy, which gives confidence in the method. The fluctuation in number of flashed tubes along a muon track is close to expectation. In a preliminary search no e/3 quarks have been detected amongst 439 carefully measured penetrating EAS particles.

Levels in ²¹Ne have been studied using the reaction ¹⁸O( alpha ,n) ²¹Ne. Lifetimes have been obtained for the states at 350, 1745, 2866, 3662, 4432, 5772 and 6548 keV by the Doppler shift attenuation method. The lifetimes are generally a factor of two to four smaller than previous measurements. The major part of these differences may be accounted for by discrepancies between the Warburton and Blaugrund approaches to the stopping theory when heavy stoppers are used. The lifetimes are compared with Nilsson model calculations and with predictions of the projected Hartree-Fock model.

The reaction ²⁷Al(d, alpha )²⁵Mg was used to study the decay of the ²⁵Mg levels at 2.738 and 2.801 MeV. A simple rotational model calculation without band mixing did not account for the measured branching ratios. The discussion of the existing experimental data suggests that band mixing plays an important role in this case.

The cross section for the process nu +Z to nu +Z+ lambda ⁺+ lambda ^-, where lambda ^+or- represents e^+or- or mu ^+or-, has been calculated form the point of view of the photon-neutrino weak coupling theory. The importance of this process to test the different theories of weak interactions has also been discussed.

Using a pure configuration shell model, differential and total cross sections have been evaluated for the photoproduction of positive pions from ¹⁶O leading to giant resonance states of various multipolarities in ¹⁶N. The two-particle-two-hole (2p-2h) ground state correlations in ¹⁶O are also taken into account. These 2p-2h correlations reduce the cross sections by about 30%. The total cross section for the 2⁺ giant quadrupole state is found to have a large peak near the first pion-nucleon resonance region, making it thereby possible to experimentally identify it from other multipole resonance states by varying the incident photon energy.

The equation of motion of the ions in an ion-rich plasma sheath as well as the appropriate initial conditions that hold for all frequencies well below the electron plasma frequency are obtained. The problem of ion motion in the case when a small amplitude rf voltage is applied to the sheath is solved. One thus obtains the sheath admittance as a function of the plasma parameters, the applied dc voltage and frequency. One reaches the conclusion that, besides the electron contribution, there also exists an ion contribution to the sheath conductance and that the sheath susceptance, although dominated by a capacitive term, cannot be wholly ascribed to this one alone. Simple equivalent circuits are proposed to represent the plasma sheath in the low and in the high frequency limits.

The heat conductivity of the nonpolar-polar gas mixtures, Ar-CH₃Cl and Xe-CH₃Cl has been measured as a function of composition at different temperatures. The conductivity-composition curves for both systems show minima and in some cases maxima also. Such minima and also points of inflexion have recently been observed by Gray et al. for some binary mixtures of inert gases with polar gases. The results indicate the limitations of the present theory for the heat conductivity of gas mixtures particularly for some specific systems. The need for a more sophisticated theory is stressed.

The mobilities of positive ions in liquid nitrogen have been determined from the transit times of the ions in a triode cell. Two mobilities could be defined from the plots of current against frequency: mu ₀ measured in the frame of reference of the cell, and mu _r in that of the liquid. The difference ( mu ₀- mu _r) was identified with mu _e, a mobility caused by an overall liquid motion induced by the viscous drag of the ions on the liquid. Both these results and earlier ones of Henson, Bruschi, Mazzi and Santini were similar and consistent, and could be explained by the liquid motion theory of Kopylov.