Table of contents

The angular distribution of γ-radiation from a deuteron stripping reaction is given as a Legendre series W(θ) = Σ_νA_νP_ν (cos θ). The coefficients are given in terms of the total angular momentum (orbital plus spin) of the captured nucleon and fully tabulated. Analysis of observed distributions can then test j-j shell model assumptions.

Cascades are discussed and a general theorem for the angular distribution of the nth radiation of a cascade is stated in an Appendix.

Formulae are given relating the parameters of this paper to those used in the channel spin formulation. Their values when the nuclei obey L-S coupling rules are also given.

Some other applications of the theory are indicated and results of interest to experimentalists are summarized.

The occurrence of a nuclear level preceding the 1.9 hour metastable state in ⁸³Kr has been confirmed. The associated transition has been shown to be of magnetic dipole type, of energy 51 keV and half-life less than 5 × 10⁻⁸ second.

Wave functions determined by the variational methods of Hulthén and Kohn are employed in the calculation of the zero order partial cross section for the process He⁺(1s) + e → He⁺(2s) + e by the distorted wave, the Born and the Oppenheimer approximations. The inadequacy of the latter approximation near the threshold is disclosed.

The effect of exchange on the spin paramagnetism of a free electron gas is discussed. It is shown that in general the exchange terms have a marked effect on the susceptibility and can be legitimately neglected only at extremely high temperatures. A comparison is made with the results of a simple treatment due to Stoner, and qualitative similarities are apparent.

Several new band systems have been observed in the absorption spectra of SbSe and SbTe molecules in the vapour state at high temperatures (1000° to 1300°C). All the systems lie in the ultra-violet region. The systems have been analysed and the following constants obtained:

Molecule system	Å	νe	ωe''	ωe''χe''	ωe'	ωe'χe'
SbSe I	3685-3289	28965	326.1	1.04	221.8	1.00
SbSe II	2870-2620	36041	326.1	1.04	418.9	0.48
SbSe III	2456-2360	-	326.1	1.04	-	-
SbSe IV	2335-2222	43756	326.1	1.04	365.74	0.76
SbTe I	2383-2260	43553	284.4	0.20	314.5	0.48

The cross sections associated with transitions from the bound 1sσ_g, 2sσ_g and 3sσ_g states of H₂⁺ to the free pσ_u, pπ_u, fσ_u and fπ_u states are calculated using exact two-centre electronic wave functions. They are tabulated for various values of the energy of the ejected electron and of the distance between the protons (which are treated as fixed in position). In the case of the 1sσ_g state (which, alone of the three, is stable) the investigation is carried further: the vibration and rotation of the molecule are taken into account and curves showing true photo-ionization cross section plotted against wave number are obtained.

The oscillator strengths of the 1sσ_g-2pπ_u, 2pσ_u-3dπ_g and 2pπ_u-3dπ_g transitions of H₂⁺ are calculated from the exact two-centre wave functions. A comparison is made with results obtained from the l.c.a.o. approximation, both the dipole length and the dipole velocity formulae being used. The polarizability of the normal ion perpendicular to the molecular axis is discussed briefly.

It is shown that in a region which is free of currents and charges, any electromagnetic field may be rigorously derived from a single, generally complex, scalar wave function V(x, t). In terms of this function the momentum density g(x, t) and the energy density w(x, t) of the field may be defined in such a way that they are represented by expressions analogous to the formulae for the probability current and the probability density in quantum mechanics; in a homogeneous isotropic medium

g(x,t) = - (1/8πμ₀c)[V*∇V + V ∇V*],

w(x,t) = (1/8π)[(₀/c²)VV* + (1/μ₀)∇V.∇V*]

The densities defined in this way differ from those given by the usual expressions, but the choice is justified since the differences disappear on integration over any arbitrary macroscopic domain. (The corresponding Lagrangian densities differ by a four divergence.) When V is of the form V₀(x)e^-iwt, g is found to form a solenoidal field which is orthogonal to the co-phasal surfaces arg V₀ = constant.

Using three different sources the molecular spectrum of nitrogen has been investigated in the visible and near infra-red. A new infra-red system recently reported by Herman has been studied in greater detail and the vibrational analysis revised. It has been shown that the bands do not arise from the singlet transition ν → q but that states of higher multiplicity are involved. Extensions of the second positive system and the Gaydon-Herman bands in the green are reported. Improved measurements for bands of the First Positive system are given and a new vibrational formula has been derived. A new unassigned band at 8311 Å is reported.

An approximation is made which allows analytic integration of the `overlap', and other, integrals of vibrational wave functions in Morse potentials that arise in the study of the electronic spectra of diatomic molecules. The heavy and lengthy work that goes into numerical integration is thus avoided for many bands of many systems. The necessity for the type of approximation made is discussed from the point of view of the extensive cancellation that occurs in any method of evaluating these integrals. An indication is given of the validity and applicability of the approximation and the formulae thus derived.

In this paper p-values (i.e. overlaps squared) calculated on this approximation are presented for the transitions N₂, B³Π_g → A³Σ_u⁺ (First Positive) and N₂, C³Π_u → B³Π_g (Second Positive), and compared with values calculated with Morse wave functions by numerical methods. The agreement is excellent.

Two improvements in the method of calculating vibrational overlap integrals presented in a previous paper are given here.

The first improvement allows the treatment of cases where|(α₁ - α₂) / (α₁ + α₂)| is so large (greater, similar5%) that the results using the technique of the previous paper are merely indicative of trends. α₁ and α₂ are the parameters in the Morse potentials whose adjustment is the basis of the approximation in the previous paper.

The second improvement is a method of overcoming algebraically the heavy cancellation (intrinsic in the wave functions) that limits the extent of tables of p-values (i.e. overlaps squared). Formulae for the 0, 1, 2 and 3 progressions in either direction are given that allow the overlaps to be calculated for much higher quantum numbers than was previously possible.

It is shown that the deviations of the magnetic moments of all spin ½ nuclei from the Schmidt limits can be adequately accounted for by simple interconfigurational mixing.

The electronic structure of a body-centred cubic metal is considered using the standard excited state extension of the equivalent orbital method. The form of the energy surfaces for both the standard excited state and the ground state is deduced in terms of a small number of parameters using the transformation properties of a determinant wave function. The energy expressions thus found do not depend on any analytical approximation to the wave functions nor on any arbitrary simplification of the theory. Values of the parameters for lithium and sodium are found by fitting the theoretical energies to energies calculated by other methods.

Measurements have been made of the multiple scattering of 7.5 MeV deuterons in a range of metallic elements from aluminium to gold. Satisfactory agreement was obtained between the experimental distributions and those calculated from Moliere's theory. The heavy elements do not show discrepancies similar to those observed in the multiple scattering of electrons and μ-mesons with relativistic velocities in lead.