Table of contents

A number of ferrous and ferric compounds of ⁵⁷Fe enriched rat haemoglobin have been studied by observing nuclear resonant absorption by the iron of the haem group. The ferrous compounds, reduced haemoglobin and haemoglobin carbon monoxide, show only quadrupole splittings at all temperatures, with values characteristic of high and low spin materials respectively. The ferrous compound haemoglobin nitric oxide exhibits a broad spectrum with an effective field value of about 200 kilogauss at all temperatures. This is interpreted in terms of a very strong covalent bond between the π orbitals of the NO molecule and the t_2g orbitals of the Fe ion; this bonding is so strong that the distinction between ferrous and ferric assignments is blurred. The observed quadrupole Mössbauer absorption spectra of oxygenated haemoglobin suggest a similar intermediate assignment.

At 4 °K the ferric compounds with CN^-, N₃^-, OH^-, H₂O and F^- exhibit magnetic hyperfine interactions with characteristic effective magnetic fields of the order of 500 kilogauss. At 195 °K all except the fluoride show simple quadrupole spectra, with splittings which are unusually large for ferric compounds. The spectra are interpreted, with the help of g values where known, to deduce the electronic state of the ion.

The ¹⁹F, ⁸⁵Rb and ⁸⁷Rb nuclear magnetic resonances observed at room temperature in single crystals of RbMnF₃ are described. The hyperfine interaction of a fluorine nucleus with one of its nearest-neighbour Mn²⁺ ions has axial symmetry, the principal values being A_|| = (21.49 ± 0.90) × 10^-4 cm^-1, and A_⊥ = (12.77 ± 0.55) × 10^-4 cm^-1. The part of this interaction which is not due to classical dipole effects has been interpreted in terms of the fraction of unpaired spin in the F^- 2s orbital (f_2s = (0 50 ± 0.02)%), and the F^- 2p orbital ((f_σ - f_π)_2p = (0.33 ± 0 18)%). The rubidium nuclear magnetic resonance indicates a negative spin density at the rubidium nucleus, and can be interpreted in terms of the fraction of unpaired spin in a Rb⁺ 4s orbital (f_4s = -0.0040%). A measurement of the molar magnetic susceptibility of RbMnF₃ at 298 °K gave the value χ_M = (10 40 ± 0 35) × 10^-3 cm³ mole^-1, which is approximately 17% greater than the value previously reported by McGuire. The values of the nearest-neighbour exchange integrals (defined by H₁₂ = JS₁. · S₂) deduced from room temperature magnetic susceptibility measurements are J (RbMnF₃) = (6 7 ± 0.7) °K and J (KMnF₃) = (7.1 ± 0.5) °K.

The exchange interactions in RbMnF₃, KMnF₃ and MnF₂ have been deduced from ¹⁹F nuclear magnetic resonanace linewidth measurements. The calculations were carried through not so much to obtain an accurate value for J, the exchange integral, but to test the theory of linewidth on substances in which J is well known. It is found that the theory gives a better than order-of-magnitude estimate of J, but not precise quantitative results.

The effect of x irradiation on the spin-lattice relaxation times of transitions between the lowest spin levels of Cr³⁺ in α-Al₂O₃ has been examined. The values for the first-order transitions at 4 2 °K are reduced by a factor of ten after x irradiation. Comparison of the properties of orange rubies grown from the vapour phase and produced by x irradiation of pink ruby indicates that this is due to the conversion of some of the Cr³⁺ into Cr⁴⁺ and Cr²⁺.

The formula which has been proposed by Chandrasekhar to express the dependence of the rotatory power on wavelength is given. This quadratic formula was previously derived for crystals with space group of symmetry D⁴₃ or its enantiomorphous D⁶₃. However, Chandrasekhar and other authors have shown that this formula may be used also for crystals which belong to other groups of symmetry.

In this paper we have removed certain simplifying assumptions of Chandrasekhar's model and in this case obtain a more general formula. Only in the special case where K_i⁽²⁾ = 0, that is in the case of the equality of oscillator strengths of both normal modes of vibrations, we obtain Chandrasekhar's formula. The applicability of our equation to known cases is discussed.

The effect of induced quadrupoles on the electric field gradient in metals with hexagonal close-packed structures has been calculated. The case of rare-earth metals has been particularly investigated and the effect stated is found to be not more than 2% of the monopolar contribution to the electric field gradient.

A generalization of two-spinor calculus, useful in the discussion of particles with arbitrary spin, is extended to generally covariant form. The spinor connection and curvature are derived in general form and the analogy between spin and charge is made explicit by consideration of commutators of covariant derivatives. The generation of the gravitational field by the Yang-Mills `trick' is briefly discussed.

The momentum spectrum of cosmic-ray muons has been measured as a function of zenith angle in the range 77.5°-90° and covering the momentum band 3-500 GeV/c. Based on our knowledge of the experimentally determined muon energy spectrum in the vertical direction, an accurate analysis has been made of the inclined muon spectra expected as a function of the ratio of kaons to pions produced in high energy interactions. Inclusion of the various kaon decay modes reduces the sensitivity of the inclined intensities to the K/π ratio and despite the good statistical accuracy of the present measurements only an upper limit can be set to the ratio, the conclusion being that K/π ⩽ 0.4 at production in the nuclear collisions of high energy nucleons in the energy range 6 × 10²-4 × 10⁴ GeV. It is pointed out that an accurate estimate of the ratio will be possible when improved measurements of both the vertical and near-horizontal muon intensities are available in the region of 1000 GeV/c.

This paper describes the construction, testing and performance of an apparatus which consists of six liquid scintillation counters, each of area 1.1 m², interleaved with sheets of lead of thickness 2 5 radiation lengths. The pulse height from each of the counters is converted into digital form and recorded, together with hodoscope information from index counters above and below the stack, on standard five-hole tape. At a depth of 60 m.w.e. below sea level the total event rate is about 2 sec^-1. The classification system used for distinguishing the various types of events is also described.

Using the apparatus described in the previous paper, the probability of a high-energy cosmic-ray muon undergoing an electromagnetic interaction in lead with energy transfer in the range 0 1 to 20 GeV has been determined. The energy transfer in the process is determined by a comparison of the ensuing shower produced in the stack with theoretical shower curves due to Buja. The results indicate that up to energy transfers of 20 GeV there is no significant discrepancy between the theoretical and experimental values for the sum of the electromagnetic cross sections.

The branching ratios of ion-molecule reactions at low kinetic energies are determined from a statistical description of an intermediate complex. Simple estimates are given for the relative probability of two reactions, one of which involves three free particles as products and the other two free particles as products. These estimates show that some highly exothermal ion-molecule reactions are relatively rare. Sufficiently exothermal reactions lead preferentially to dissociative charge transfer. Noble-gas-ion-hydrogen-molecule reactions are treated as examples.

An analytical method, based on some approximations, is given for the calculation of finite-range Coulomb stripping reactions. The case when the captured and emitted particles were initially in arbitrary radial states is considered. Comparison is made with previously derived formulae. Adopting the Morinigo wave function for the final bound state, it is shown that the finite-range interaction leads to an additional angular-dependent factor when the angular momentum of the captured particle is not equal to zero. This correction factor decreases at large angles, which is also observed in the finite-range effects on the non-Coulomb stripping process.

The coefficients of the R^-4, R^-6 and R^-8 terms in the series representation of the long-range interaction between two atomic systems at separation R are evaluated by a two-centre variational procedure, using highly refined ground-state wave functions. Calculations are carried out for all atom-atom and atom-ion pairs drawn from the one- and two-electron systems H, He⁺, He, Li⁺ and H^-. The values for the R^-6 coefficient are in excellent agreement with the values previously derived from oscillator strength data.

The problem of elastic scattering of electrons by the hydrogen ground state is formulated using a variational principle. With trial functions ψ = (1/√2){ψ(r₁)ϕ(r₂) ± ϕ(r₁)ψ(r₂)} where ψ is the ground state functions, one obtains the exchange integro-differential equations for the functions phi. Results from exact solutions of these equations are compared with results obtained using: (a) modified Born-Oppenheimer approximations, with trial functions ϕ(r) = [1/r(4π)^1/2] sin(kr) + αψ(r) and various choices for the parameter α, (b) the approximation of Ochkur, in which one retains only the leading term in the (1/k) expansion of the Oppenheimer exchange amplitudes, and (c) the distorted wave approximation, in which the direct potential is allowed for exactly.

A Monte Carlo calculation of the mean number of elastic collisions involving gas atoms and an electron diffusing between two infinite perfectly absorbing planar electrodes has been carried out. The values obtained agree with those calculated by Bartels and Nordstrom in 1931 to within 12%, throughout the range of gas pressure and electrode separation investigated, but are considerably higher than the values obtained from work based on standard diffusion theory. It is shown that such calculations are unlikely to be reliable except at high gas pressure and large electrode separation.

The mass polarization or specific isotope shift of the 1s²2s ²S and 1s²2p ²P levels of Li and B²⁺ is calculated using the 45-parameter wave functions of Weiss. The specific shifts of the resonance lines of ⁷Li relative to ⁶Li and of ¹¹B²⁺ relative to ¹⁰B²⁺ are calculated to be 0 186 cm^-1 and 0.843 cm^-1 respectively, compared with the observed values 0.157 cm^-1, 0 930 cm^-1 (ΔJ = 0) and 0.970 cm^-1 (ΔJ = 1) of Burke and of Hughes.

The problems of atomic structure and electron scattering from heavy atoms are investigated using the relativistic Hartree approximation. The results obtained from the self-consistent field calculation of structure indicate the necessity for including relativistic effects for heavy atoms. Previously reported scattering calculations, also made using the Hartree approximation, have been extended and it is shown that the approximation ceases to be valid for an incident energy below a few hundred eV.

It is shown that the scattering of a particle by a potential can be described by a Fredholm equation with Hermitian kernel. From this follows an expansion for the reaction matrix, the individual terms of this series having a resonance-type structure. A simple example is given which suggests that a few terms of the series are sufficient to yield a good approximation to the scattering cross section over a wide energy range. A similar expansion is then given for the reaction matrix in the case of electron-hydrogen scattering (or similar three-body scattering problems), the expansion being exact when the total energy of the system is negative and a close approximation for positive energies. Variational methods which may be useful in calculating terms of the expansion are derived and methods of calculating cross sections are briefly discussed.

A comparison is made of the cross sections for ionization of the excited states of hydrogen by electrons calculated using Gryzinski's classical theory with exact velocity distributions and Born's quantal theory. The classical calculations agree with the quantal calculations in all cases to better than 14% and in general the agreement is much better. The classical cross sections do not fall off as log (E)/E at larger impact energies E, but the inclusion of the correct high energy fall-off gives classical results which agree with the Born calculations at high energies.

A differential cross section formula for the 1 ¹S → 2 ¹S excitation of ions belonging to the helium isoelectronic sequence by electron impact has been obtained in the Coulomb-Born approximation. The behaviour of the cross section is discussed both at high energy and at threshold energy. The cross section at threshold energy is finite. An explicit calculation for the differential and total cross section at threshold energy has been done for singly ionized lithium.

The theory is given for the excitation of Li-like ions by electron impact. The transitions of interest in this paper are those in which the optical electron only is excited while the (1s)² core is left unexcited. For such transitions the theory follows closely that for hydrogen-like ions. The theory is applied to transitions induced by electron impact between the 2s, 2p, 3s, 3p and 3d states of N V between threshold and 435.36 eV. The majority of the calculations are carried out in the Coulomb-Born approximation and conclusions are drawn about the accuracy of the results by comparing with strong-coupling and close-coupling calculations. A discussion is given of the importance of these cross sections in the temperature measurement of a laboratory plasma.

A classical velocity distribution function used by Bates and Mapleton is derived and compared with the corresponding distribution of quantum mechanics. This classical distribution is related to other classical distributions for the attractive Coulomb field by an integral over the classical angular momentum. Among these other velocity distributions is the one recently given by Gryzinski.

For a one-dimensional system with liquid-type disorder something is known of the general properties of the wave functions from the work of Roberts and Makinson, and Borland. Utilizing these properties and subject to certain restrictive conditions, an approximate expression has been obtained for the conductivity of a disordered one-dimensional system which would be an intrinsic semiconductor if it were ordered.

In this paper the fluctuations of electron numbers in a general M-level system are discussed. Using a difference equation in the occupation probability, equations are found for the variances of these fluctuating variables, provided they are small. When certain transitions are excluded from consideration these equations reduce to those derived earlier from the Fokker-Planck equation. The present approach lends itself to the derivation of more general expressions for the variances than have so far been obtained. These are given explicitly for a three-level system in terms of the given transition rates. The results are illustrated by some simple examples.

Measurements of the electroreflectance effect on GaAs surfaces in the range of photon energies from 1 3 to 4 5 ev are reported. If an a.c. electric field modulates the surface potential in the reflecting surface, the reflectance responds in a sequence of pronounced peaks at the photon energies of interband transitions, as they are known from previous analysis of the band structure. However, the high resolution and sensitivity of this derivative technique adds a new kind of information. The shift of the observed groups of peaks with electric field establishes an experimental criterion which discriminates between parabolic edges of the M₀ type and saddle-point edges of the M₁ type.

A model for F-centre production in alkali halides by ionizing radiation is discussed. The energy required for the formation of the defect is given to an anion in the radiationless recombination of an electron and a hole, which takes place via an exciton state. The primary products of this mechanism are negative ion interstitials and corresponding vacancies. The separation of the ion from the vacancy is achieved by a replacement sequence along a [110] direction. The radiationless transition is discussed in detail in this paper and its properties are seen to explain many hitherto inexplicable results of experiments in F-centre production. The replacement sequence is discussed in the following paper.

In the previous paper it was shown that radiationless electron-hole recombination in alkali halides might provide energy for the formation of negative ion vacancies. A [110] replacement sequence provides an efficient method for separation of the interstitial from the vacancy and is particularly suitable for defect formation by electron-hole recombination. Two-body calculations of the replacement thresholds, including only short-range repulsive interactions, are discussed. A computer simulation of the [110] replacement sequence, including the effects of long-range Coulomb forces, has been carried out. The results of this simulation indicate that in many of the alkali halides, within broad limits of variation of the interaction forces, replacement thresholds are about 4-5 ev. In other alkali halides, such as NaI, much higher values are calculated, whilst the alkaline earth oxides give values of several tens of electron volts.

Cyclotron resonance signals from thermally generated electrons have been observed with ultra-high purity silicon samples over the temperature range 50-206 °K.

A microwave spectrometer incorporating a confocal cavity and operating at a frequency of 139 Gc/s was used in these experiments. The transverse effective mass parameter m_⊥ is found to increase with temperature by 6±3% at 102 °K. The longitudinal mass m_|| appears to be unaffected by any temperature change. The collision times derived from the width of the resonance lines are in good agreement with mobility data in this temperature range. However, the collision time anisotropy ratio for intravalley acoustic phonon scattering (<τ_||>/<τ_⊥>) was found to be 0.90^+0.05_{-0 11} in disagreement with magnetoresistance measurements which suggest a value of 0 67. The following values for the deformation potential constants are derived from the cyclotron resonance data: Ξ_u = 8.6 eV, Ξ_d = -3.4 eV. A comparison of the deformation potentials quoted above with those derived from the magnetoresistance experiments shows that the cyclotron resonance data give better agreement with the recent theoretical calculations of Goroff and Kleinman. The origin of the above discrepancy is obscure.

A correlation between the thermal conductivity and diffusion coefficients for monatomic gases is presented on the basis of Chapman-Enskog kinetic theory. It is tested for pure, binary and ternary gas systems, the deviation usually being 1 5 per cent. Finally, on the basis of this correlation, thermal conductivity values have been predicted for the Ar-He system at the temperatures 300, 500, 700, 900 and 1100 °K, and for percentages of argon of 20, 40, 60 and 80. These values are also compared with the directly measured values at 100, 316 and 520 °C. The two sets agree within the average absolute deviation of 2 6 per cent. This agreement should be regarded as good in view of the large experimental uncertainty associated with these data.

Evidence for energy transfer from Dy⁺³ to Tb⁺³ ions in CaF₂ is presented. Emission spectra and decay-time measurements are described and discussed.

The C ²Σ⁺_u-X ²Σ⁺_g system of the ¹⁴N⁺₂ molecule has been investigated in the region 2300 to 1300 Å. When a discharge is passed through a mixture of helium and nitrogen, bands having v' ⩾ 3 are the only bands observed. If neon is used as a foreign gas, bands having v' ⩽ 2 also appear quite strongly. Because of the perturbation in the v' = 0, 1 and 2 levels of the C state, the vibrational constants of this state have been calculated by using the bands with v' ⩾ 3 only. Details of the excitation mechanism for this system in the mixture of nitrogen with helium and with neon are discussed. In addition to the bands of the C-X system, a few new bands, which belong to a hitherto unknown system, have been observed in the region 2510 to 2075 Å.

A configuration interaction analysis of the absorption cross-section curve of thallium has been carried out on the autoionization transitions ²P_1/2⁰-⁴P_3/2 and ²P_1/2⁰-²D_3/2 and their associated photoionization continua. Intensity stealing from the E(D) continuum amounts to 80% of the oscillator strength for the ²P_1/2⁰-⁴P_3/2 transition and 5% for the ²P_1/2⁰-²D_3/2 transition. Application of the f-sum rule indicates that a considerable contribution to the oscillator strengths must lie to the high wave number side of the above autoionization transitions. Unperturbed photoionization cross-section values of 8.0 Mbn for the E(D) continuum and 1 7 Mbn for the E(S) continuum at the ionization threshold are indicated.

The results of the companion experimental paper are interpreted in terms of the mechanism proposed in an earlier paper by Anderson in 1957. Using these results and those obtained by Anderson, Kavadas and McKay in 1957, the bimolecular constant of the first afterglow is shown to be k' = 5 6 × 10^-10T^1/2 exp(-3000/T). The bimolecular constant of the second afterglow is similarly k" = 1.0 × 10^-14T^1/2. With these constants, initial populations are found to be 10¹¹ to 10¹² per cubic centimetre in the weaker glows of the experimental paper. Monomolecular constants are evaluated for the second glow; k₁ for the more energetic particle is found to depend through a multiplying constant on the hydrogen impurity concentration. In the present experimental paper k₁ = 0 202T^1/2 exp(-1640/T), while in the previous experimental paper the multiplying factor was 0 163. The monomolecular decay constant of the particle of less energy depends radically on diffusion to the vessel walls being greatly affected by adsorbed water, and only possibly has an activation energy above that which can be measured at the temperature reached. In the earlier experimental work k₂ = 3 4 × 10^-3T^1/2, while in the accompanying paper it was so low that it could only be determined to be within limits: 10^-5 <k₂ <10^-3. These are evaluated at 2 mmHg pressure. With the changed excitation conditions in the companion paper, the initial population ratio of the particles n₂ and n₁ departs widely from unity and becomes about 39 1. This has a large effect on the apparent bimolecular slope of the second glow and its relation to that of the first glow.

A series of measurements of the decay of the long-lived yellow nitrogen afterglow have been made over an intensity range of almost a millionfold. Methods of excitation were the same as those used in a previous paper by Anderson, Kavadas and McKay, though the maximum intensities achieved were much smaller. Electronic digitization and punching equipment was used to accumulate data which were then processed on a computer. The photomultiplier tube was calibrated to give intensities of glow in quanta per cubic centimetre per second. It was shown, using the purest analysed reagent gases, that pure nitrogen gives no afterglow, that oxygen added to nitrogen gives no glow, that hydrogen in small quantities added to nitrogen produces copious glow of the second type as proposed by Anderson in 1957. Quantities in excess of one per cent free hydrogen in the gas kill the afterglow. Further analysis given in the accompanying paper shows that the mechanism previously proposed quantitatively accounts for the very different intensity curves of this work.

Concentrated solutions of naphthalene in toluene and in cyclohexane show a pronounced structureless excimer emission band, whose profile is unchanged in the presence of various quenching agents.

It is shown that the hydrodynamic equations of compressible fluids together with the London equations lead to the macroscopic Ginzburg-Landau equation.

Monte Carlo calculations of the mean number of elastic collisions c undergone by an electron in diffusing through a field-free gas between infinite perfectly absorbing cylindrically symmetrical electrodes have been carried out. Comparison of the results with those obtained using earlier analytical methods shows that the latter are unlikely to be reliable except at high gas pressures and large electrode separations.

MnO₂ is the only iron-group compound having rutile structure in which the magnetic spins of cations along the c axis are not ferromagnetically coupled. The semi-empirical `Goodenough-Kanamori' rules for superexchange interactions, coupled with the direct t_2g-t_2g interactions proposed by Goodenough in certain situations, can satisfactorily account for the magnetic structure of this oxide. A significant modification of the spiral magnetic structure proposed by Yoshimori seems to be required.

An improved method of calculating series limits T_∞ is presented: this consists in varying simultaneously T_∞ and the coefficients in the energy expansion of the quantum defect so as to obtain a least-squares fit to observed series term values. Analysis of the ¹D, ³D and ³F series of helium using this method gives T_∞ = 198 310 74±0 02 cm^-1, compared with 198 310 82±0.05 cm^-1 obtained by Herzberg in 1958, the quoted error estimates being standard deviations in fitting procedures. An independent estimate of 198 310.77±0 02 cm^-1 is obtained for the ³F series using a polarization formula. The best estimate of T_∞ for helium is considered to be 198 310.75 cm^-1, with the error in fitting procedures unlikely to exceed ±0.02 cm^-1.

Values of the mobility and collision cross section obtained for ions of measured mean energy in hydrogen are discussed in relation to other, recently published, values of mobility. The discussion shows that further measurements of mobility are required for ions of experimentally established identity and measured mean energy.