A previous discussion (Feather 1969a) of the energetics of the separation of an α-particle in the ternary fission of an (e, e) nucleus is generalised to cover the case of a light particle of arbitrary mass and charge separating from a fissioning nucleus the nucleon-parity type of which may be any one of the four possible types. A ‘profitability index’ is defined in terms of which certain broad differences in the light-particle spectra from different types of fissioning nucleus are predicted, and the results of detailed calculations of the minimum energy expense of separation are given for various light particles emitted in the fission of and, for comparison, for an α-particle emitted in the fission of , an (o, o) nucleus.

In a previous paper (Jack 1970, § 5) the pre-zonal polynomials were defined by the surface integral (1) below. In that paper they were evaluated using a series of differential type operators acting on the sums of powers of the roots of a matrix.

The present paper, although it is a continuation of Jack (1970), is self-contained and consists of three parts. The first part, §§ 3–7, shows how the pre-zonal polynomials may be calculated, certainly for low degree, using only the first of the differential operators. The next part, §§ 8–11, is devoted to establishing various recurrence relations between the pre-zonal polynomials and to conjecturing similar recurrence relations between the zonal polynomials (James 1964, p. 478). In the final part, §§ 12–14 the pre-zonal polynomials are evaluated directly from the integral (1) below, in terms of the augmented monomial symmetric functions.

The motion of hydrogen atoms due to the internal vibrational modes of a molecule is large and curvilinear. Because of the curvilinear motion the mean displacements of these atoms cannot be described by ellipsoids alone, but higher order terms or cumulants are necessary. Equations determining these terms from the usual riding motion are presented. By analysing a neutron diffraction study of high accuracy it is shown that the size of these higher cumulants is sufficient for them to be determinable. For deuterated samples however really high accuracy will be necessary in the diffraction experiment.

Levels in the ground state bands of 158Dy, 160Dy and 162Dy have been populated by (α, 2n) reactions on metallic targets of separated 156Gd, 158Gd and 160Gd isotopes. Two Ge(Li) detectors were used to study singles gamma-ray spectra, gamma-ray angular distributions, gamma-gamma coincidence spectra and relative yields of gamma-rays for bombarding energies from 20 to 27 MeV. Transitions from all levels in the ground state bands up to the 12+ member were identified and the following level energies in keV established: 158Dy: 0 (0+), 99·0 (2+), 317·4 (4+), 637·9 (6+), 1044·1 (8+), 1520·1 (10+) and 2049·4 (12+); 160Dy: 0 (0+), 86·7 (2+), 283·7 (4+), 581·4 (6+), 967·4 (8+), 1429·0 (10+), 1951·7 (12+); 162Dy: 0 (0+), 80·7 (2+), 265·7 (4+), 548·5 (6+), 921·1 (8+), 1374·8 (10+) and 1901·0 (12+). There is weak evidence for the 14+ levels in 158Dy and 160Dy. The level energies are compared with calculated values using the variable moment of inertia model.

The shape factors of the partial β-spectra of highest end-point energy in the decay of 72Ga and 140La have been calculated and compared with the only previously reported determination of these quantities. For both isotopes the shape factor is consonant with the view that the Blj matrix element controls the decay. Shape factor analysis alone is insufficient to determine the cause of the predominance of a particular matrix element.

The location of the trajectory of a charged nuclear particle can be determined by a number of devices whose operation depends on characteristics of gas counters operated in the region of proportional energy response. Such devices have advantages in precision, speed or available size over other types of position-sensitive counters. The events may be located by observing pulses on one of a set of closely spaced anode wires in a common gas volume, by measuring the drift time of primary electrons to a particular anode wire, or by determining the location of an electron avalanche along the length of a single anode. The operation of the different types of systems and the factors affecting their precision are described. Precision to less than 1 mm can be obtained in a number of ways,

Mirror Gamow-Teller β-decay takes place from members of isospin multiplets to a common final state or to final states that are mirrors of each other. It is found that in these cases the intrinsic speed of the positon emission is systematically lower, by 10–15 per cent, than that of the mirror negaton emission. This difference could be due to a fundamental weak interaction effect, a second-class term in the weak hadronie current, or to a failure of exact symmetry in the nuclear structure. The influence of binding energy differences is studied in the latter context and it is concluded that they cannot be responsible for the empirical asymmetry. The effects of changes of configurational mix across the multiplets is also considered; very few estimates have ben explicitly made but it would be surprising if this effect turned out to be of constant sign and magnitude over the wide range of A involved. No present firm conclusion can be made but none of the empirical evidence is inconsistent with the reality of a largely momentum-transfer-independent second-class current.

The adiabatic invariants associated with the motion of charged particles, trapped in electromagnetic fields with rotational and reflection symmetry, have been studied using classical methods based on the Hamilton-Jacobi equation. It has been shown that results, valid for trapping in purely magnetic configurations, may be applied in the analysis of electromagnetic charged particle traps, provided that suitably modified expressions are used for the angular frequencies in the various dynamical modes. Attention is drawn to circumstances in which the adiabatic conditions may be violated because of cancellation of electric and magnetic terms in the equations.

A search is reported for the relativistic e/3 quark among the cores of Extensive Air Showers initiated by primaries with energies greater than 1014 eV. The detector is a high-pressure cloud chamber filled with helium at 28 atmospheres, and is counter controlled. The experimental conditions avoid the criticisms levelled at the McCusker experiment and are such that the tracks of e/3 quarks cannot be simulated by singly charged shower particles either through statistical variations in primary ionisation or otherwise. The primary ionisation density, measured using a gap-counting technique on post-expansion electron and muon tracks, is compared with predictions from the theory of Budini et al. (1960). The agreement achieved shows that the theory is a reliable foundation for methods of identifying quark candidates, and measuring charges. The experiment has been running for 5000 hours. No quark candidates have been found. With an acceptance angle of 0·3 sr and an area of 140 cm2, this sets the upper limit of flux of e/3 quarks at 4 × 10−9 cm−2 sec−1 sr−1 with 95 per cent, confidence. The experiment is being continued.

Measurement of the frequencies, linewidths and cross-sections of optical phonons in neodymium aluminate by means of inelastic light scattering have permitted the prediction of a trigonal-to-cubic phase transition below the melting point of the crystal. This phase transition was subsequently directly measured via differential thermal analysis.

Theoretical and experimental studies have been made of the scintillation pulse shapes of organic scintillators. In a unitary crystal the pulse shape is characterised by the scintillation decay time τs. In solution scintillators additional parameters are required to describe the pulse shape: Δt, the pulse width (FWHM); tm, the time at which the intensity reaches a maximumpmax; and t½, the time at which the intensity reaches ½pmax. General relations are derived for τs, Δτ, τm, τ½, and pmax for binary liquid solutions in terms of molecular parameters, and the corresponding expression is given for the scintillation pulse shape of a binary plastic solution.

The scintillation pulse shapes of 4 binary liquid solutions and 12 binary and 15 ternary plastic solutions were measured using a single-photon sampling fluorometer. The results confirm the theoretical analysis. A new plastic scintillator (NE 111) with improved timing characteristics has thus been developed, and some of its applications in nuclear physics are briefly discussed. The time association of nuclear events can be measured to within 130 ps with this scintillator, the limiting factor being the time jitter of the photomultiplier itself.

3-Methylfluorene-9-propionic acid (1) with hydrofluoric acid undergoes ring-closure on the substituted ring to give 1,2,3,10b-tetrahydro-5-methylfluoranthen-3-one (II).

Wolff-Kishner reduction of the ketone yielded l,2,3,10b-tetrahydro-5-methylfluoranthene which on dehydrogenation gave 2-methylfluoranthene (III, R=H) identical with a sample prepared according to the method of Tucker (1952) and differing from 8-methylfluoranthene. This proved that ring-closure of (I) had occurred as expected on the methyl-bearing benzene ring. In this instance ring-closure occurs in the position meta to the methyl group and is reminiscent of the similar ring-closure of 2-phenyl-2-p-tolylpropionic acid to give 6-methyl-3-phenylindanone (Pfeiffer and Roos 1941). It thus provided a further example of the limitations of von Braun's statement that Friedel-Crafts ring-closure occurs much less readily at the position meta to a methyl group than on a phenyl ring (von Braun, Manz and Reinsch 1928).

In this paper it is shown that the question of the existence of a classical solution of the first initial-boundary value problem for a non-linear parabolic equation may be reduced to the problem of the derivation of suitable a priori bounds.

This paper considers an extension of the following inequality given in the book Inequalities by Hardy, Littlewood and Polya; let f be real-valued, twice differentiable on [0, ∞) and such that f and f are both in the space fn, ∞), then f′ is in L,2(0, ∞) and

The extension consists in replacing f′ by M[f] where

choosing f so that f and M[f] are in L2(0, ∞) and then seeking to determine if there is an inequality of the form

where K is a positive number independent of f.

The analysis involves a fourth-order differential equation and the second-order equation associated with M.

A number of examples are discussed to illustrate the theorems obtained and to show that the extended inequality (*) may or may not hold.

In an earlier publication [1] we introduced the notion of a Baer assembly and applied it to obtain a coördinatisation theory for semilattices. This was achieved by considering the semigroup of quasi-residuated (i.e. ℴ-preserving and isotone) mappings on a bounded semilattice. In the present paper we consider the semigroup of quasi-residuated ∪-homomorphisms (or hemimorphisms) on a bounded lattice and thus show how a particular type of one-sided Baer assembly can be used to provide a coördinatisation theory for lattices; and in particular for complemented, modular and distributive lattices.

The possibility of α-particle emission from fully accelerated fission fragments is considered. The results of trajectory calculations for such α-particles emitted during the fission of 252Cf are presented, and their significance in relation to the observed energy and angular distributions of the α-particles is discussed.