Table of contents

The Bhabha-Chakrabarty solution of the cascade equations with ionization loss is discussed, and a simplified method of numerical evaluation suggested.

The work of Rochester and Butler, published in 1948, and that of Butler, Rosser and Barker, published in 1950, has been continued. In particular, the interaction properties and the spectrum of the penetrating particles are considered. The interaction length of the shower particles with momenta greater than 10⁹ ev/C. is found to be 18 cm. lead (±20%).

In electron and proton synchrotrons there exists a minimum useful vertical aperture of the vacuum chamber, and for apertures less than this the beam intensity falls to zero. It is considered, on the basis of a comparison of theory and experiment, that this phenomenon is in the main due to free oscillations which arise from gas scattering. The final beam size in proton synchrotrons may be substantial for this reason also, but for cyclotrons the large spread which is known to exist must be attributed to some other phenomenon.

The secondary electron spectrum of ¹⁹⁸Au has been studied using very strong sources, up to 0.3 curie, in a magnetic lens spectrometer. In addition to the well-known γ-ray at 0.411 MeV., evidence of two much less intense higher energy γ-rays at 0.67 MeV. and 1.09 MeV. has been found, both from the Compton and photoelectric spectra. The intensities of these two γ-rays with respect to the one at 0.411 MeV. have been measured. Two photoelectric peaks at low energy, in about the region expected for Kα and Kβ x-radiation from elements in the neighbourhood of gold, have been examined with radiators of different atomic number. The radiation responsible for these peaks has been subjected to critical absorption measurements in the spectrometer. Its behaviour is compatible with the Kα and Kβ x-radiation of gold, and no evidence of platinum x-radiation, such as would suggest K-capture, has been found.

A nuclear photographic emulsion which has been in contact with material containing traces of uranium and thorium shows on processing α-ray stars arising from atoms which have undergone several successive disintegrations during the exposure. The relative frequency of the various multiple stars, which depends on the uranium/thorium ratio, is here evaluated on simple assumptions to show the possibility of determining these elements by star counting.

A careful analysis of the planar modes of vibration of ethylene and ethylene-d₄ is carried out in order (a) to determine finally the value of the C=C stretching force constant in these key molecules, (b) to find what interactions, particularly those between the two ends of the molecules, are real, and (c) to determine the vibrational forms and the potential energy distributions in the normal modes, and how they are affected by altering the potential function. Solutions are obtained both with and without correction for anharmonicity, and estimates are made of the effects of other corrections which may be necessary. The limits found for the C=C stretching constant are 9.336, 9.388 × 10⁵ dyne/cm., with a most probable value of 9.343, the carbon atoms being uncorrected for anharmonicity. The zero-order constant is unlikely to be greater than 9.57. There is detectable real interaction between the two ends of the molecule, for both stretching and bending coordinates. Interactions are discussed.

It is shown that the divergencies in classical electrodynamics may be removed by subtracting the self-energies of isolated electrons by means of a modification of the usual expression for the force density in an electromagnetic field. The results obtained are equivalent to those of Dirac and Wentzel.

The subtraction procedure of Dyson is modified in order to eliminate a certain difficulty in the renormalization programme, namely the so-called `b' divergencies. The conclusions of Dyson concerning the finiteness of the renormalized S matrix are confirmed.

This paper contains a new derivation of the equations of motion of bodies moving slowly in their (weak) gravitational field, up to terms of the order (v/c)². In contrast to the method developed previously by Einstein and co-workers, in which only the field outside the bodies has been considered, in the present paper a new method is used in which the field outside as well as inside the bodies, and the internal structure of the bodies, is taken into consideration. The equations of motion derived by this new method are identical with those obtained by Einstein and co-workers, but the new method is essentially simpler and the necessary calculations much less lengthy

Since the lower excited states of nuclei have very small widths (« 1eV.), resonant scattering of gamma-rays requires precise matching of the energy available from the gamma-ray with the energy necessary to excite the scattering nucleus.

Resonant scattering should be observable if (1) the emitting and scattering nuclei are of identical type, (2) the gamma-transition goes to the ground state, and (3) the source and scatterer are given such a relative velocity that Doppler effect restores the energy lost by the gamma-ray to nuclear recoils Thermal velocities of the emitting and scattering nuclei broaden and correspondingly weaken the resonant scattering peak, and the cross section at the optimum speed of 32E/A cm/sec. is 3.6 × 10^-3(IΓ/E³)(A/T)^1/2 cm², where E and Γ are the energy and intrinsic width of the excited state in electron volts, I the isotopic abundance of the resonantly scattering isotope, A its atomic weight and T the absolute temperature.

Preliminary experiments have been made with the 0.411 MeV. radiation from the nucleus ¹⁹⁸Hg, the source being carried by a high-speed rotor up to a speed of about 7 × 10⁴ cm/sec. and the scatterer being liquid mercury (10% ¹⁹⁸Hg) A small but apparently significant increase of scattering was found, corresponding to a width Γ of the order of 10^-5 eV

No such increase was observed with ¹⁸¹Ta gamma-rays scattered from tantalum carbide.

The negative result for ¹⁸¹Ta and the positive result for ¹⁹⁸Hg are consistent with the latest information about the life-times of the excited states concerned, viz. 1.1 × 10^-8 sec. for ¹⁸¹Ta and less than 2 × 10^-10 sec. for ¹⁹⁸Hg.

The Cerenkov effect has been established for the passage of cosmic-ray μ-mesons through distilled water. The light pulses were observed using a photomultiplier and fast amplifier; the experiments were carried out using the detector alone, and in a coincidence-telescope arrangement The ratio of the light emitted in the downward and upward directions was measured as a function of discriminator bias In addition measurements were carried out at various depths of water and with various orientations of the detector with respect to the vertical Estimates of the absolute efficiency were made and other characteristics of the detector are discussed.