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

It is shown for the degenerate B.C.S.-model how in the limit of an infinite system the exact thermal Greens-functions approach a gauge invariant average of the one's calculated with the Bogoliubov-Haag method.Work performed as consultant to General Atomic Europe.     

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.     

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.     

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).     

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.     

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.     

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.