Table of contents

It is pointed out that in general relativistic magnetohydrodynamics Ohm's law does not determine the current density J^a in the limit of infinite conductivity, but that it is determined by the electromagnetic field equation as in nonrelativistic magnetohydrodynamics. It is also shown that the relation 2 omega .H= epsilon derived by Yodzis (1971) assuming J^a= epsilon u^a for infinite conductivity, can also be obtained by a modified argument if the above view is taken.

The use of scaling for one-bit correlation processing in optical spectroscopy of nongaussian signals is discussed. A theoretical proof of its equivalence with uniform random clipping, and hence full correlation, is provided in certain cases.

Following the idea of Wu and Yang (1965) that the electromagnetic and nuclear distributions behave similarly at large momentum transfer, the author has studied the differential cross section for pi ^+or-p elastic scattering at high energy within the framework of the parton model. By using the idea of Drell and Yan (1970) he has calculated the electromagnetic form factors of the pion and proton and they are shown to decrease as t^-1 and t/2^-2 respectively at large t.

The new Durham spectrograph, MARS, has been used to study the Coulomb scattering of cosmic ray muons in iron in the momentum range 10-70 GeV/c. The observed root mean square lateral displacement agrees well with that predicted to within the statistical errors, which range from 2% at the lowest momentum to 17% at the highest momentum. Averaged over the whole momentum range the ratio of observed to expected root mean square scattering displacement is 1.023+or-0.019.

A recent evaluation of atomic masses confirms that ⁵⁶Fe has uniquely the 'least' atomic mass per baryon, _Z^AM/A. Thus, with ⁵⁶Fe as the primary standard (₂₆⁵⁶M=56) all other atomic masses would be greater than the mass number A and the corresponding 'mass excesses' would be not only 'positive' but also 'maxima'. Moreover, a mass excess relative to ⁵⁶Fe is potentially the largest 'portion' of the atomic mass that can be transformed into energy (assuming conservation of baryon number); it therefore has a unique physical significance. Accordingly, a plot of the mass excesses against A and Z would provide a unique 'potential-energy surface' which should be useful in the representation of nuclidic transformations that involve a change in A(eg alpha decay) as well as those with A=constant.

The effect of a photon rest mass on the dissipation of magnetic fields in the Galaxy is discussed and an upper limit on the rest mass is obtained: an earlier treatment is corrected and refined.

The authors consider a standard Carnot cycle, except that the reservoirs (of proper temperatures T_H and T_C) are in uniform motion. Two efficiencies for such cycles exist in the literature. Each has the property that it can exceed the usual Carnot efficiency eta _C=1-T_C/T_H for a class of inertial observers. It is shown that a reasonable definition of efficiency leads to the usual Carnot efficiency eta _C for all inertial observers.

The superoperator theory of nonequilibrium statistical mechanics is applied to the Dirac and Klein-Gordon equations. The transformation operators of this theory are found to be closely related to the Foldy-Wouthuysen transformation while the associated subdynamics corresponds to the separation into smooth motion and zitterbewegung.

It is shown that a semiclassical treatment of dispersion forces, based on the dependence of the zero point energy of two oscillators coupled to the electromagnetic field on their distance of separation gives the retarded and nonretarded form of the dispersion forces between them.

In those cases where a direct diagonalization of the energy matrix is not attempted because of insuperable practical difficulties of computation, it is always possible to estimate the gamut of the eigenvalue spectrum by a variational method. A trial state function similar in some respects to a Glauber state is employed. Certain asymptotically exact results due to Tavis and Cummings (1968) are recovered. Finally, ways in which the accuracy might be improved are outlined.

The minimal electromagnetic interaction is introduced into various free, quantum mechanical spin one formalisms, and it is found that the resulting theories are essentially equivalent. The situation does not prevail when, in addition, magnetic dipole or electric quadrupole interactions are considered. For simple such interactions in one formalism are found, in general, to be equivalent to structurally more complicated interactions in the other formalisms considered. Some known results on the acausal propagation of solutions of wave equations for a classical spin one particle in an external electromagnetic field are, with the aid of the above equivalence theorems, which are easily seen to apply to the classical case also, extended to include all the spin one formalisms considered herein.

It is shown how to achieve a finite (and unitary and causal) S matrix for a large class of nonderivative nonpolynomial Lagrangians.

The author takes a chiral SU(2)*SU(2) invariant pion-nucleon interaction to first order in the meson covariant derivative. The covariant derivatives are identified in terms of the Gursey matrix, and choosing the exponential parametrization for this he calculates the matrix superpropagator using Fourier transform techniques.

A model for the cosmological time dependence of weak interactions is discussed and some experimental tests suggested.

An analytical and separable representation for the two-particle S wave t matrix, for the central Yakawa interactions, has been suggested, which is separable and symmetric in momentum variables p and p'. The sturmian eigenfunctions for the S wave Hulthen potential, which form a complete set, have been used as the expansion bases. For the neutron-proton system, the triplet and the singlet states have been considered, including the soft-core repulsion in the singlet interaction. The resulting t matrix has been used as an input in the Faddeev equation for the neutron-deuteron collision problem, the triton binding energy has been computed and compared with the theoretical calculation of Malfliet and Tjon (1969) as well as the experimental findings.

Results of an investigation on muons of energy greater than or equal to 150 GeV associated with extensive air showers are presented. The total number of muons is found to vary with shower size according to the relation n_mu (>or=150, N)=27+or-7)(N/10⁵)^0.47+or-0.05 for 10⁵<or=N<or=5*10⁶. An increase in the power index alpha = delta lnn_mu / delta lnN is indicated for N<10⁵. The energy spectrum of the muons is found to be a power law of the type E^{-1.30+or-0.16}_mu for 150GeV<or=E_mu <or=640GeV. The observed variation of n_mu with N is found to be flatter than the one predicted by known EAS models for constant primary composition.

A discussion is given of various cosmic ray phenomena from the point of view of the hypothesis of 'regenerated showers'. It is shown that the hypothesis, which was originally developed in order to explain muon-poor showers, gives a consistent explanation of various 'unusual' phenomena observed in cosmic rays. The most interesting result is that the hypothesis can explain the apparent discrepancy between the high energy 'muon' spectrum derived from the burst size spectrum and that deduced from other types of observation. With the additional assumption that the passive particle decays into a muon pair with lifetime of the order of 10^-7 s, the hypothesis can also explain the abnormal angular distribution of energetic muons observed by the Utah group (Carlson et. al. 1971).

The analogues of the ⁵²V levels at 0.793 and 0.846 MeV have been examined as resonances in the ⁵¹V (p, gamma )⁵²Cr reaction at proton energies of 1.567 and 1.629 MeV. The resonance at 1.567 MeV and hence the 0.793 MeV ⁵²V level has been assigned J^pi of 3⁺ and the most probable J^pi value for the 1.629 MeV resonance and hence the 0.846 MeV ⁵²V level is shown to be 4⁺. These results are consistent with previous theoretical calculations of the ⁵²V levels.

The proton particle-hole states of ¹¹⁴Sn have been studied by the ¹¹³In(³He,d)¹¹⁴Sn reaction at 37.7 MeV. A ¹¹³In(³He, ³He)¹¹³In elastic scattering experiment provided ³He optical model parameters for the DWBA analysis. The ground state and seven excited states of ¹¹⁴Sn yielded deuteron groups which could be analysed in terms of angular momentum transfers of l=2 or l=4. These transferred protons are believed to occupy 2d_5/2 or 1g_7/2 orbitals and to couple with a 1g_9/2 proton hole. Partial strengths extracted from the angular distributions are consistent with the results obtained on ¹¹⁵In(³He,d)¹¹⁶Sn by Biggerstaff et al. (1967) but not with those of Shoup et al. (1969).

Employing a single well defined approximation, a derivation is given of the nonlinear BGK model. The model is applied to the formulation of equations governing the temporal and spatial variation of macroscopic parameters in the regime where changes in these parameters within a mean free path cannot be neglected. Using the model, an extension is given of earlier results concerning the sign of successive time derivatives of the entropy.