Table of contents

A particular lattice Green function for the simple cubic lattice is evaluated exactly as a square of a Heun function, and as a product of two complete elliptic integrals of the first kind. Applications of these results in lattice statistics are briefly described.

The gamma rays from the ¹⁵⁰Nd ( alpha ,4n) ¹⁵⁰Sm and ¹⁵⁰Nd ( alpha ,2n) ¹⁵²Sm reactions have been studied both in singles and coincidence. The ground state rotational bands in ¹⁵⁰Sm and ¹⁵²Sm are populated up to the state with spin 10⁺. It is found that the nuclear moment of inertia of ¹⁵⁰Sm is substantially lower than that of ¹⁵²Sm for the low spin states, but that it increases with spin and the moments of inertia converge for the high spin states. This supports earlier evidence that the change from spherical to deformed nuclei between N=88 and N=90 is gradual.

Results are presented which show that the classical effect of 'asynchronous excitation of an oscillator' can be applied to the excitation of an ion sound instability in a plasma. Further, the predicted upper and lower threshold values of the asynchronous driving amplitude are observed, for the region in which the instability is excited.

The author treats the absorption of longitudinal electric waves in a cold plasma; upper limits for absorption in propagation from the galactic centre to the Earth are estimated.

The author examines the relation between the Temple, Weinstein and Stevenson bounds for an arbitrary eigenvalues of a Hamiltonian H. It is shown that, in a sense which is defined, the Temple and Stevenson bounds are numerically equivalent, while the Weinstein bound is inferior to either. The Temple bound is reformulated and it is shown that the usual restriction on its validity may be relaxed; the relaxation leads to rather more convenient calculations in the presence of excited states, but not to improved lower bounds. A numerical example demonstrating the extension is given.

The conditions under which class sum operators for a finite group are hermitian are discussed. A class of linear mapping within the group algbra is treated, together with methods of obtaining elements which are symmetry adapted with respect to these mappings. Traditional tensor operators are treated as symmetry adapted elements of the group algebra, and the absence of certain types of tensor operator from the group algebra of direct product groups is discussed. The relevance of the work to operator equivalent theory is briefly indicated.

The forms of the virial and hypervirial theorems are derived when a distribution function, that is, the Laplace transform of a distribution is taken to define a quantum-mechanical system. The validity of the resulting equations imposes necessary (and sufficient) conditions on the distribution and hence the distribution function. Distribution theory is used to establish the existence of an exponential function satisfying the virial theorem for the Yukawa potential for a restricted range of the defining parameters. For hypervirial relations, the method would seem of little practical importance.

The authors give a method of calculating variational trial functions in quantum theory. Applications are made to the discrete spectra of some simple one and two particle systems.

For Pt.I see ibid., vol.5, 1152 (1972). A method given in Part I for the calculation of variational trial functions is applied to the continuous spectra of some simple one and two particle systems.

It is shown that a transfer-matrix method provides a particularly direct solution for a ferromagnetic version of a one dimensional model originally invented by Fisher (1967). An essential feature of this model is the many body potential leading to a phase transition. All the thermodynamical properties of the model may be written down once the dominant eigenvalue and eigenvector of the matrix are known; in particular, surface properties may be obtained in terms of the dominant eigenvector. Typical phase diagrams are obtained, and the singularities at the phase boundaries discussed.

The Gibbs distribution for a polymer molecule contains implicitly the correlation functions for velocity and position of the constituent monomers. The purely spatial part, ignoring potentials, gives the random flight distribution; the velocity correlation function is calculated, exploiting the markovian structure of the problem in phase space. It is shown that the problem can be reduced to an eigenfunction problem and hence solved. The form of the correlation function is quite accurately given by ( nu _n1- nu _n2)²=(2kT/m)(1-exp(-c mod n₁-n₂ mod )) where nu _n1, nu _n2 are the velocities of the n₁th and n₂th monomers and c equivalent to 1.

Results are presented of numerical calculations of the spatial average density distribution inside a simple cubical box containing a random flight polymer. Various lengths of polymer are considered. Included is a correlation to an isotherm calculation in an earlier paper (see abst. A1029 of 1970).

When making thermodynamically based comparisons concerning behaviour in the vicinity of Curie points or Neel points, Pippard's relations are in principle more pertinent than Ehrenfest's. In a discussion supplementing the analyses of Sawatzky and Bloom (1962-64) and Skalyo, Cohen, Friedberg and Griffiths (1967), various magnetic Pippard's relations are considered, and it is re-emphasized that a relation derived by Fisher (1960-62) in statistical mechanical terms (that near an antiferromagnetic Neel point the rise in specific heat closely follows the temperature coefficient of the magnetic susceptibility) amounts very nearly to a relation of the purely thermodynamic type obtained by Pippard for lambda transitions generally. Relevant observations are analyzed in such terms for a number of representative cases, and comparisons made with the dependence of lambda temperatures on hydrostatic pressure and magnetic field. Correspondingly, for lambda transitions associated with a very rapid change of dielectric properties with temperature, the lambda temperature corresponds to a peak in the derivative of electric susceptibility with respect to temperature, and not to a maximum in the susceptibility itself.

The absorption of radiation by inverse bremsstrahlung absorption from a planar single mode monochromatic light beam is considered by nonrelativistic time-dependent perturbation theory, which is equivalent to the Born approximation. The results are of general validity and may be applied to any scattering system which is left unchanged by the collision. Comparison between the results obtained previously by different workers shown the relationship between the different models used to investigate this effect.

It is shown that the S-wave eigenvalues of the Lippmann-Schwinger kernel for the exponential potential can be determined from the zeros of a Bessel function whose order is energy dependent. An asymptotic expansion is obtained for the leading eigenvalue at negative energies.

The sea-level absolute vertical integral cosmic ray muon intensities for three momenta near 1 GeV/c at 12 degrees N were measured with a range spectrometer. The results obtained from this measurement are used to derive the intensities at a latitude of 50 degrees N by applying the latitude correction suggested by Olbert (1954). The integral muon intensities are found to be on the average 3.5% lower and 21.6% higher than the values obtained by Allkofer et al. and Rossi respectively. The differential intensities derived from the integral ones are 20% higher than those calculated from Olbert at the same latitude. The results of the other recent measurements on the differential muon intensities in the low energy region in relation to a form spectrum are also discussed.

The halflife of the 321 keV(9/2^-) state in ¹²⁵Te is measured by the delayed coincidence technique employing a time-to-amplitude converter. On comparing the experimental M1 and E2 transition probabilities with those evaluated by the single particle model, Kisslinger's three-quasiparticle model and the De-Shalit model, it is found that De-Shalit's single particle-core coupling model is applicable in this case.

The decay of radon has been followed in effect over approximately 40 halflives in an effort to detect any deviation from the exponential decay law. The results were fitted to a decay of the form N=N₀ exp(- lambda t(1+bt)) and b was calculated to be (1.9+or-1.0)*10^-6 d^-1+ the halflife was determined to be 3.8235₁+or-0.0003₄d.

The mechanism of the ¹²C(p,p'3 alpha ) reaction at 13 MeV is found to involve the ground state of ⁸Be and the ground state of ⁹B in 24% of the events, and the ⁸Be ground state alone in 51% of the events. The remaining 25% of the events show no clear evidence of levels in intermediate nuclei. The cross section for this reaction is 154 mb.

Neutron capture cross sections leading to the isomeric states in seven nuclei have been measured, for the first time, using the activation technique and absolute gamma counting method, employing an antimony-beryllium neutron source and a calibrated well-type NaI(Tl) crystal. In two reactions, ¹¹⁶Cd(n, gamma )^117m,gCd and ¹⁵¹Eu(n, gamma )^152m1,m2Eu where cross sections have been measured for a pair of states in each case, the 'isomeric cross section ratio' has been employed to extract the spin cutoff factor following Huizenga and Vandenbosch formalism. A comparison is made with theoretical predictions based on various models of level density to throw light on the nuclear moments of inertia.

Beta ray intensity against energy in the decay of ²⁵²Cf has been calculated as a function of time and it is predicted that 7.0 beta rays are emitted per fission. The inner bremsstrahlung radiation from all decaying fragments is shown to be equivalent, in the first 40.96 s after fission, to the radiation from a black body which cools from 1.5*10¹⁰ to 1.2*10¹⁰K.

The authors give a microscopic derivation of a formula of Bottcher's type for the refractive index. In this a macroscopic cavity field replaces the Lorentz internal field and the polarizability is modified by many-body self-interactions. These combine both an Onsager type reaction field and a screened radiation reaction. The microscopic argument resolves apparent conflict between the two different macroscopic approaches to the internal field problem.

The possibility of the variation with time of the electromagnetic and strong coupling constants is investigated using nuclear systematics. Previous work by Dyson (1967) and Broulik and Trefil (see abstr. A57272 of 1971) is re-examined and extended, with the conclusion that Teller's hypothesis of a logarithmic time dependence of the fine structure constant is apparently within the limits discussed if there is a corresponding logarithmic time dependence of the strong coupling constant also. Moreover the recent discovery of naturally occurring ²⁴⁴Pu places the Gamow hypothesis of e² approximately t much nearer the allowable limits than had previously been supposed.