On the thermodynamic limit of the B.C.S. state

We consider vector states in the Fock representation of the C.A.R. algebra, representing condensed pair states. We prove that in the thermodynamic limit these states give rise to a direct integral of gauge-dependent B.C.S. states.Partially supported by C.N.R.Equipe de Recherche associée au C.N.R.S. n^o 154.     

On the mathematical structure of the B.C.S.-model

It is investigated in which sense the Bogoliubov-Haag treatment of the B.C.S.-model gives the correct solution in the limit of infinite volume. We find that in a certain subspace of the infinite tensor product space the field operators show the correct time behaviour in the sense of strong convergence.This work was partly supported by General Atomic Europe, partly by the Ludwig Boltzmann Gesellschaft.     

E.S.R. evidence for the planarity of the t-butyl radical

Monte Carlo calculations are reported for the radial distribution function g ₂(r; λ) of a fluid in which the intermolecular pair potential is [u ^ref(r) + λu ^p(r)], u ^ref(r) being the Weeks-Chandler-Andersen (WCA) reference fluid, and [u ^ref(r) + u ^p(r)] being the Lennard-Jones (6, 12) fluid. The calculations are performed for λ values in the range 0 to 1, at the state condition ρσ³ = 0·80, kT/ε = 0·719. It is shown that at high densities the perturbation expansion of g ₂(r; λ = 1) about g ₂(r; λ = 0) is rapidly convergent, but that the corresponding expansion for y ₂(r; λ) = exp [βu(r; λ)] × g ₂(r; λ) is not. In addition Monte Carlo estimates of the individual terms that contribute to the first-order perturbation term, (?g ₂/?λ)_λ=0, are presented. It is shown that these terms are individually large, but that (?g ₂/?λ)_λ=0 is small because there is strong cancellation between the various terms. Consequently, the calculation of (?g ₂/?λ)_λ=0 is highly sensitive to the approximation used to evaluate the individual terms.     

O.E.E.C. seminar on the use of television for the teaching of science

Under the direction of M. Henri Dieuzeide, who is head of Educational Television in France, the Organization for European Economic Cooperation held a five-day seminar at Ashridge College in July 1960. It was attended by educational authorities concerned with school science television broadcasting, heads of educational television programmes, science producers of schools programmes from 15 countries, and observers from the European Broadcasting Union, the Ford Foundation, the National Science Foundation (U.S.A.), UNESCO., the National Film and Television Council, and the International Scientific Film Association.     

Investigation in the L.C.A.O.-M.O. Framework of the overlap and covalency contribution to the zero field splitting of S state ions

Using the L.C.A.O.-M.O. scheme, we review the different stages of the calculation of the overlap and covalency contribution to the zero-field splitting of ⁶S state ions. We calculate general molecular integrals involved in the non-local spin-spin contribution and derive analytic functions of the metal-ligand distance to fit numerical results of integral calculations for Mn²⁺---F⁻, Mn²⁺---O²⁻, Fe³⁺---F⁻and Fe³⁺---O²⁻ bonds. We use these results to calculate the zero-field splitting of Mn²⁺ and Fe³⁺ ions at Ca²⁺ or Zn²⁺ crystal sites of tetragonal or trigonal symmetry in diamagnetic host lattices (RbCaF₃ and KZnF₃).     

Influence of the surface on the quantum P.E.M. effect in InP

The photoelectromagnetic effect of InP is studied in quantizing magnetic fields at 4·2 K in an energy range 1·4–1·5 eV for linearly polarized light. Depending on the sample surface condition two types of spectral oscillations may appear, those associated with interband transitions between Landau levels or the LO phonon type usually seen in photoconductivity. An analysis of the spectral oscillations gives: E₀ = 1·423±0·001 eV; Δ₀ = 0·102±0·006 eV; hω_L = 0·036 eV.     

A re-examination of the induction (crystal field) energy contribution to the relative stabilities of the f.c.c. and h.c.p. rare-gas crystal structures

A new calculation of the induction (crystal field) energy of the f.c.c. and h.c.p. structures of the rare-gas crystals of neon and argon gives an energy in favour of f.c.c. which is more than sufficient to counter the summed pair-potential which favours h.c.p. Predicted values of (E _f.c.c. - E _h.c.p.)/E _f.c.c. for neon and argon are 0·9 × 10^-3 and 1·3 × 10^-3 respectively. These values are similar to those that have been obtained for a modified dispersion energy and it is concluded that they should be added to these dispersion energies. Calculations on solid helium show a negligible difference in the induction energy for the two close-packed structures.     

Calculation of the E.S.R. spectrum shape of the dynamic biradical system

The E.S.R. spectrum shape of a dynamic biradical system is calculated by means of the density spin-matrix formalism. The biradical is treated as a system which has two conformations characterized by the different values of the exchange integrals J=J ₁ and J=J ₂ and the lifetimes τ₁ and τ₂ respectively. The influence of both the rate and the strength of exchange interactions on the shape of the spectrum is discussed. Criteria to distinguish the spectra of the cases of both slow and fast exchange are discussed.     

The E.S.R. spectrum of the tropolonyl radical

The many-body diagrammatic Rayleigh-Schrödinger perturbation theory (RSPT) is used for the calculation of ionization potentials of open-shell systems with one unpaired electron. This theoretical approach is tested on the simple examples of NO₂ and NF₂ molecules described by the INDO semi-empirical hamiltonian. The first- and second-order results are presented.     

Hall effect studies in ytterbium through the f.c.c.-h.c.p. transformation

The Hall coefficient (R_H) of polycrystalline Yb showing the f.c.c.-h.c.p. transformation has been determined at 20 koe in the range 1.8–420°K. Both the structural and the associated magnetic transformation would separately be expected to modify R_H, but the evidence suggests that the observed behaviour through the transition arises primarily from the effects of the change in structure. A more detailed interpretation is presently not possible, however, because of the lack of knowledge of the band structure of h.c.p. Yb.     

Interatomic forces in the b.c.c. transition metals

Using information obtained from X-ray scattering data, a model for the charge density in the transition metals is constructed. In this model the charge density is given by the sum of the charges situated at the ionic and bond centre sites. Within this framework, expressions for the second order elastic constants and the phonon frequencies in the cubic transition metals are obtained. These quantities have been calculated with and without the bond charge contributions for iron. The comparison with the experimental results shows that the introduction of bond charges, and hence angularity in the force-fields, in iron leads to distinctly better agreement with experiment. From a study of the elastic constants of the other b.c.c. transition metals some observations as to the nature of the angular force fields are made.     

Theoretical models for the interpretation of E.S.C.A. spectra

Three features of E.S.C.A. spectra are discussed: the chemical shift, multiplet splitting, and satellite bands. In the chemical shift effect a perturbation theory treatment shows that the electronic relaxation energy in the hole state of the molecules can be attributed to a flow of electrons on to the ionized atom. Thus the relative abilities of surrounding atoms to “feed” electrons to the ionized atom determines the relative importance of the relaxation energy contribution to the chemical shift. This explains why neutral atom charges don't always determine the direction of the chemical shift. In multiplet splitting the same perturbation treatment shows that the sign and magnitude of the relaxation energy contribution to the multiplet splitting is determined by the direction and magnitude of flow of majority electron spin density in going to the relaxed hole state. Unrestricted Hartree-Fock calculations on the series MF ₂, with M first row transition metals, are compared with E.S.C.A. experiments on the corresponding octahedral complexes to show that complex ion formation has only a very small effect on core level multiplet splitting. Relaxed hole state calculations on a series of first row atom (C,N,O,F) containing radicals leads to the conclusion that in these cases correlation energy effects are larger for the high spin multiplets than for the low spin multiplets. The assignments of satellite structure in transition metal complexes is reviewed and multiconfiguration self-consistent field results are presented and discussed for the satellite structure     

Properties of the vacuum. 2. Electrodynamic

The behaviour of a charged scalar field in an external electric field is discussed. Vacuum polarization is calculated by explicit summation of modes. Instabilities encountered in the external field approximation are absent when back reaction effects are included through a self-consistent semiclassical procedure.     

Vacancies at the surfaces of F.C.C. metals

The vacancy formation energy is calculated using the inserted atom method for faces with high and low indices and in the near-surface atomic layers of aluminum, nickel, copper, palladium, silver, platinum, and gold. The transition of the calculated quantities to the bulk quantities is traced for successive insertion of a defect deeper into the near-surface layer of the material. The relaxation contribution to the energetics is revealed for each type of surface. A correlation is seen between the energies of formation at surfaces with high and low indices. V. D. Kuznetsov Siberian Physicotechnical Institute at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 62–73, March, 1997.     

C. V. Raman and the Discovery of the Raman Effect

In 1928 the Indian physicist C. V. Raman (1888-1970) discovered the effect named after him virtually simultaneously with the Russian physicists G. S. Landsberg (1890-1957) and L. I. Mandelstam (1879-1944). I first provide a biographical sketch of Raman through his years in Calcutta (1907-1932) and Bangalore (after 1932). I then discuss his scientific work in acoustics, astronomy, and optics up to 1928, including his views on Albert Einstein's light-quantum hypothesis and on Arthur Holly Compton's discovery of the Compton effect, with particular reference to Compton's debate on it with William Duane in Toronto in 1924, which Raman witnessed. I then examine Raman's discovery of the Raman effect and its reception among physicists. Finally, I suggest reasons why Landsberg and Mandelstam did not share the Nobel Prize in Physics for 1930 with Raman. RID="*" ID="*"Rajinder Singh is a Diplom-Physiker who is currently working on his doctoral thesis on C. V. Raman and the discovery of the Raman effect in the Department of Higher Education and History of Science in the Faculty of Physics at the University of Oldenburg, Germany.     

A re-interpretation of the E.P.R. spectrum of the 1,2,3,6,7,8-hexahydropyrene anion radical

The γ radiolysis of carbon tetrachloride at 77 K results in the formation of free radicals which are stable at 185 K and have been identified as ?Cl₃. These radicals trapped in crystallites of CCl₄ or at ‘boundaries’ give very different E.S.R. spectra. Their a _13C coupling constants are practically identical (117 G et 114 G). The structure of ?Cl₃ radicals has been determined: it is nonplanar and the angle has a value of 116°. The action of O₂ on the ?Cl₃ radicals leads to the CCl_{3 2} peroxide radicals whose a _13C coupling at 200 K is 6·15 G.

Après irradiation γ à 77 K du tétrachlorure de carbone, le seul radical stable à 185 K est le radical ?Cl₃. Le radical ?Cl₃, suivant qu'il est piégé au sein des cristallites de CCl₄ ou aux joints de grains, donne un spectre R.P.E. très différent.

Pour les deux types de radicaux, les constantes de couplage a _13C sont voisines (117 G et 114 G). On peut ainsi en déduire que le radical CCl₃ est non plan avec une valeur de 116° pour l'angle . Par action de l'oxygène sur le radical ?Cl₃, on a observé à 200 K le radical CCl_{3 2} dont la constante de couplage a _13C est 6,15 G.     

On the internal equilibrium in h.c.p. metals

Recently a number of phenomenological models have been developed to explain the lattice dynamics of h.c.p. metals None of these models takes complete account of equilibrium in this metallic system. Two equilibrium conditions necessary for h.c.p. structure, have to be used with a proper consideration of electrons. We have derived two such conditions, satisfying the condition of rotational invariance, on the basis that the total pressure due to ions and electrons in the metal vanishes in the equilibrium.