Table of contents

The probability densities of the time of arrival of photoelectrons and the time interval between consecutive photoelectrons are respectively proportional to the first and second time derivatives of the moment generating function. Expressions for these densities are given for several classes of optical fields.

The spatial coherence properties of quasi-stationary gaussian optical fields are discussed using a terminology that shows the importance of coherence functions of order N not=M. It is shown that this field is spatially less coherent than a thermal field.

Formally exact solutions to the quantum and semi-classical models of a single atom interacting with a single-field mode in the dipole approximation are compared. It is shown that the quantum results tend to the semi-classical ones in the limit n to infinity , in disagreement with the results of Chang and Stehle (1971).

A constructive method is given for obtaining all the symmetrized nth powers of an induced representation. These are the representations in one-one correspondence with the irreducible representations of the symmetric group S_n and they are obtained here as induced representations. This problem has only previously been solved in the case n=2 by Mackey (1951, 2 and 3), and Bradley and Davies (1970). Partial decomposition of the nth Kronecker power of an induced representation on subspaces labelled by double coset representatives is used. An action of the symmetric group is defined on these subspaces causing aggregates of them to form larger subspaces which may be symmetrized separately. This symmetrization is achieved by inducing through an intermediate subgroup so that a basis for the space is obtained which explicitly contains all permutations by elements of S_n.

The paper outlines the way in which the constructive method obtained for symmetrizing nth Kronecker powers of induced representations (see ibid., vol. 6, no. 12, 1807 (1973)) may be applied to space group representations. Also a step by step procedure is given for finding the symmetrized cubes of space group representations, with zinc-blende as an example, which may be used independently of the general theory.

A practical method is given for finding Clebsch-Gordan coefficients for space groups. It is immediately applicable since the formulae derived depend only on a knowledge of the vector and projective representations of point groups which are fully tabulated elsewhere.

The multiplier groups and factor systems of the 73 symmorphic space groups have been derived and the results are tabulated. It is possible that the results may be of significance in the analysis of the problem of the energy level degeneracy occurring when a crystal is subjected to a uniform external magnetic field, which has so far been the only area of application of similar results for the translation subgroups.

The cross section for free-free transitions-bremsstrahlung at non-relativistic velocities-can be reduced to simple formulae in various limiting cases. In two of these cases, the quantum-mechanical result is known to agree with Kramers' classical calculations (1928). The intermediate case does not seem to have been completely cleared up, and is investigated. The result found does not agree with the formula of Elwert (1939, 1948); it depends on a function of a single variable, and coincides with the classical result. This bridges the gap between the two low-frequency formulae. A short table of the function is given. A method is given for calculating the cross section in the more general conditions in which g is nearly equal to 1 (h nu not small compared with ¹/₂m nu ₁²). There is a region of overlap between the result so obtained and the preceding one, which provides a check on the correctness of both.

A general solution of the field equations of general relativity theory has been obtained for an elastic sphere of constant density. The equations have been solved under the condition that the pressure is zero at the boundary of the sphere and the density is constant inside this boundary. The present investigation represents an attempt to apply Rayner's theory of elasticity (1963) in general relativity for the construction of realistic models.

It is shown that an analogue of Birkhoff's theorem of general relativity (1927) exists in a scalar-tensor theory of gravitation proposed by Sen and Dunn (1971). Unlike in the Brans-Dicke scalar-tensor theory (1961), Birkhoff's theorem is valid in the present theory irrespective of the nature of the scalar field introduced.

The dimer problem on the covering lattice of the plane square lattice is shown to be isomorphic with an eight vertex model, and can be solved exactly when conjugate dimer activities are equal. Transitions in a more general dimer problem, in which the dimers interact, are investigated. The dimer problem on the 'bathroom tile' lattice is also shown to be isomorphic with an eight vertex model, but in this case the problem can be solved only when the free-fermion condition is satisfied.

Ising systems are approximated by a generalized mean-field approximation in which only some of the interactions are replaced by their expectation values. If all the interactions are positive then it is shown that a self-consistent solution exists for the magnetization in this model and that it gives an upper bound for the true magnetization. Using this mean-field approximation, a generalization of the random-phase approximation is obtained. This is shown to give an upper bound for two-spin correlation functions.

The results of a previous paper (see abstr. A72304 (1973)), which express the density of states for the Thorpe-Weaire model (1971) in terms of the number of returns to the origin, are generalized to the case of arbitrary coordination numbers, and the condition for the existence of a band gap obtained by studying the convergence of the series for the resolvent. The asymptotic form of the series is used to obtain the form of the density of states near the band edges for a topologically disordered lattice. It is found to be exactly the same as that for the periodic case.

The estimation of spectral parameters of optical fields by digital autocorrelation of photon counting fluctuations is investigated, taking into account the correlations that exist between readings of the autocorrelator channels. A general expression for the covariance of the normalized intensity autocorrelation estimators is derived for a gaussian field with general lineshape. Two estimation schemes are outlined, the maximum likelihood and the least-squares. Dependence of the estimation accuracy on the channel correlations and the system parameters is discussed.

The generating function is obtained for N photocounts for a gaussian optical field with a lorentzian profile without any restriction to the intervals during which the photodetectors are open. The method may be generalized to arbitrary spectral profiles using the method of Srinivasan and Sukavanam (1971 and 1972).

Formally exact continued fraction expressions for the eigenvectors and eigenvalues of the hamiltonian describing the interaction of a single atom with a single quantized field mode in the electric dipole approximation are presented. Explicit expressions for the eigen-solutions and the time-dependent properties are given in some special cases. Comparisons are made with the corresponding rotating wave solutions.

A massive spin-one field, interacting with external potentials, is described in terms of the Stuckelberg formalism (1938). Some points, concerning necessary and sufficient conditions for the classical theory to be causal, in the sense of Velo and Zwanziger (1969 and 1971) are clarified. It is then shown that with a simple restriction on the type of interaction considered, the classical theory is causal, in the above sense, if and only if the corresponding quantum theory is Lorentz invariant, in that the S operator in the interaction picture is normal independent. Incidental in this demonstration is the result that the characteristic and Lee-Yang determinants share the same form. It is indicated how this result generalized to interactions between Stuckelberg, Klein-Gordon and electromagnetic fields and the validity of the result, in the more usual vector formalism is established.

The determination of the optical-model potential for a high-energy charged particle using the diffraction model phase shifts is discussed. It is shown that the finiteness of the nuclear charge distribution hitherto neglected makes a non-negligible contribution to the real part of the calculated potential at small distances. It is further observed that the form of the calculated potentials is very much dependent on the model used for parameterizing the phase shifts.

The plasma mechanisms underlying a recent proposal for setting an upper limit on the mass of the photon are clarified by the study of a simplified model.

The role of turbulence on the radiation pattern of a radiating source (antenna) is discussed. A partial analysis of the radiation from an electric dipole in a turbulent plasma medium is made and an expression for the total energy flux of the dispersed field is obtained. The energy flux of the dispersed field is calculated for the plasma parameters in different situations.

Intensities of cosmic ray muons coming to rest in a 4441 liquid scintillator tank at depths 96, 417 and 985 hg cm^-2 (1 hg cm^-2=100 g cm^-2 of matter underground) have been measured. It is concluded that the observations can be accounted for in terms of muons produced in the atmosphere and penetrating to the respective depths, and muons generated locally by the decays of pions which are in turn produced in the hadronic cascades initiated by high energy muons via photomeson production by the virtual and real photons associated with muons. No new process for low energy muon production is required at the depths investigated.

The mechanism of particle production in nucleus-nucleus and nucleus-nucleon collisions produced by high-energy cosmic ray nuclei (6<or=Z<or=26) in nuclear emulsion has been studied. Theoretical formulae to estimate the lntan theta distributions of the individual groups of secondaries have been derived and used for the analysis. It is found that a large proportion of relativistic alpha particles and protons are produced through the knock-on process as distinct from the fragmentation process. Kaplon's and the present formulae for the fragmentation alpha particles or protons if applied to all the relativistic alpha particles or protons, would give an underestimation of the primary energy. Mesons are produced more through the isobar than the fireball process in the primary energy interval from 10 to 30 GeV/nucleon, but the meson multiplicity due to the latter process increases faster with increasing energy than for the former process.