Temperature shift of the CdxHg1−xTe energy gap

The temperature coefficient of the Cd_xHg_1?xTe energy gap dE_g/dT as a sum of lattice dilatation and the phonon-electron interaction terms has been calculated as the function of molar composition x, for 0?x?0.3, in the temperature range 4.2–300 K. A non-linear dependence of $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ vs x and a strong effect of temperature on $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ values have been obtained and a comparison with experimental data is discussed.     

Scaling function for two-point correlations with long-range interactions to order 1/η

The two-point correlation function ? (q, ξ) is calculated in the critical region of momentum space q in terms of a suitable correlation lenght ξ, by means of perturbation expansion to order 1/n, for an n-vector system with long-range interactions decaying as $\text{|}\text{R}\text{/a|}{}^{\mathrm{?(d\; +\; \sigma )}}$, for $\text{|}\text{R}\text{/a|}\text{a}\text{?}\text{1}$, where a is the spacing on a d-dimensional lattice, σ < d < 2σ and 0 < σ ? 2 ? η_SR. The calculations are done in zero field for T ? T_c. Explicit expansions for long-range propagators are developed for $\text{σ « 1}$ and for the neighborhood of σ ? 2 ? η_SR, in terms of which a universal, cut-off independent scaling function is obtained over the whole range of $\text{x = |}\text{q}\text{| ξ}$, and it is shown that the amplitude of the correlation-length dependence of the susceptibility becomes a universal parameter. Both the exponents and the coefficients of the expansion for fixed q as $\text{(T ? T}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{→0}$ are calculated explicitly. The former are shown to require the validity of the operator-product expansion and explicit logarithmic correction terms are obtained for $\text{d = d}{}^1\text{= 3σ/2}$. For these and other dimensionalities, the coefficients are shown to be finite functions of d and σ. The correction to the Ornstein-Zernike form is given explicitly, with non-integer powers of x that have finite coefficients.     

The absorption,magnetic circular dichroism and emission of Eu2+ in cubic elpasolites

The absorption, magnetic circular dichroism (MCD) and emission/excitation spectra of some $\text{4?}{}^7\text{→4?}{}^6\text{5d}$ transitions in Eu²⁺ in several hexachloro and hexabromoelpasolites have been measured. Data were collected between 5 and 300 K and up to energies of 42,000 cm^?1. The absorption and MCD were satisfactorily interpreted using a coupling scheme that treats the d-electron crystal field as being much greater than the f-electron spin orbit coupling and essentially ignores other interactions.     

On the theory of collective motion in nuclei. I. Classical theory

From the assumption that the collective Hamiltonian be invariant under the orthogonal group O(A ? 1, $\text{R}$) it is concluded that classical collective dynamics can be formulated on a symplectic manifold. This manifold is shown to be a coset space of the symplectic group $\text{L}$h(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the dequantization of closed-shell collective dynamics and is described in terms of six complex s- and d-quasiparticles. In the limit A ? 1 it is shown that a transformation leads to interacting s- and d-bosons with the symmetry group $\text{u}$ (6) in the collective phase space.     

Jet analysis in lepton-hadron scattering from QCD

For deep inelastic lepton-hadron scattering we deduce from QCD perturbation theory the cross sections $\text{d}\text{σ}\text{d}\text{T}$ and $\text{d}\text{σ}\text{d}\text{S}$ in terms of the collective jet variables thrust T and spherocity S. We find that the shape of these cross sections depends mainly on the total hadronic energy W. While present data are consistent with the cross sections calculated they do not yet prove or disprove the presence of three-jet contributions. We predict that these contributions will be clearly visible for W ? 12 to 15 GeV.     

Rising dσdt probes pp diffraction mechanisms

The s-dependence of $\text{d}\text{σ}\text{d}\text{t}$ at fixed t reveals important features of the underlying mechanism. In particular, it can clarify the origin of the structure near t = ?1.2 in high-energy pp elastic scattering. If this structure comes from destructive interference between two terms of different energy dependence (e.g. between single and double pomeron exchanges), the plot of ln $\text{d}\text{σ}\text{d}\text{t}$versus ln s in the interference region will show an inflexion or dip; $\text{d}\text{σ}\text{d}\text{t}$ may even rise with increasing s through a limited interval. Other mechanisms have no such feature. We give illustrations and stress the interest of measurements in the NAL and ISR momentum range.     

Analysis of a six-quark model with right-handed currents

A model for the weak interactions using the six-quark model of Harari, right-handed currents, and heavy leptons which was proposed previously by some of us is analyzed in considerable detail. The model is one of a class of “vector-like” theories that are free of gauge theory anomalies. The neutral current is pure vector, which leads to predictions for diffractive production of vector mesons by neutrinos that are different from the predictions of the standard Weinberg-Salam model; the A₁ uncouples and the fractions of ? and ω are enhanced. It is also predicted that relative production of $\text{I =}\text{1}\text{2}$ final states is larger than $\text{I =}\text{3}\text{2}$ final states in vN → vNπ in contrast to the Weinberg-Salam model. The non-leptonic decays of hyperons and mesons and the restrictions imposed by chiral symmetry are discussed. The decays of the charmed mesons are shown to be very rich due to the presence of both V ? A and V + A interactions. The y-anomalies in neutrino interactions are discussed and calculations of $\text{d}\text{σ}\text{d}\text{x}\text{and}\text{d}\text{σ}\text{d}\text{y}$ for both neutrinos and antineutrinos using modified Kuti-Weisskopf distributions are presented. Cross sections and ratios of neutrino and a neutrino cross sections are shown along with available experimental data. The v-distribution of dimuon events is also presented and compared with experiment. It is concluded that the model is not inconsistent with the currently available data.     

Quantizing a classically ergodic system: Sinai's billiard and the KKR method

Sinai's “billiards on a torus,” i.e., free motion of a particle in a plane amongst reflecting discs of radius R centred on points of the unit square lattice, is a classically ergodic system with two freedoms, parametrized by R. Quantal energy levels E_n are given by the vanishing of the Korringa-Kohn-Rostoker (KKR) determinant of solid state theory. This gives a rapid computational scheme for computing E_n as functions of R. Except for the integrable case R = 0, no degeneracies are found, illustrating the theorem that two parameters, not one, are required to make levels cross in a generic system. The same theorem leads to the prediction that the probability distribution of the spacings S of neighbouring levels is $\text{O}$(S) as S → 0, in good agreement with computation. The KKR determinant is transformed analytically to give the level density d(E) semiclassically (i.e., as ? → 0) as the sum of a steady contribution $\text{d}\text{?}\text{(E)}$ and an oscillatory contribution d_osc(E). $\text{d}\text{?}$ is $\text{O}$(?^?2) and is given by the Weyl “area” formula plus “edge,” “corner” and “curvature” corrections, in excellent agreement with computation. d_osc is given by a sum over classical closed orbits (all unstable). Nonisolated closed orbits (not hitting discs) contribute terms with $\text{O}$$\text{(?}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext><mtext>)</mtext>}}$ to d_osc, while isolated closed orbits (bouncing between discs) contribute terms with $\text{O}$(?^?1) to d_osc. The isolated orbits are vastly more numerous than the nonisolated orbits and their contributions cannot be neglected. As a means of calculating the individual E_n (rather than the smoothed spectrum), the KKR method is much more efficient than the classical path sum.     

Doppler-limited dye laser excitation spectrum of the C2 Swan band (v′ − v″ = 1 − 0)

The dye laser excitation spectrum of the Swan band (v′ ? v″ = 1 ? 0) has been observed with Doppler-limited resolution. The C₂ molecule was generated by the reaction of microwave discharge products of CF₄ with CH₄. The high sensitivity of laser excitation spectroscopy has enabled us to observe not only $\text{ΔΩ}\text{= 0}$ transitions, but also $\text{ΔΩ}\text{= ± 1}$ transitions and to determine molecular constants including the spin-orbit coupling constant for both the d³Π_g and a³Π_u states. The parameters thus obtained for a³Π_u were favorably compared with those previously obtained from the Ballik-Ramsay band. The present results on the d³Π_gv = 1 state were combined with those of an earlier Fourier spectroscopic study on the Swan band (v′ ? v″ = 0 ? 0) to derive equilibrium molecular constants for the d³Π_g state. The contributions of the spin-rotation interaction and the centrifugal correction for the spin-orbit coupling to the energy levels in a ³Π state have been discussed in detail.     

Proton 1h112 excitations in odd-mass N = 82 nuclei

The structure of negative-parity states in odd-mass N= 82 isotones (135 ≦ A ≦ 145) is investigated in the framework of a model which is based on coupling one $\text{1h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ proton to π = + 1 states of the appropriate doubly-even isotonic core. It is shown that an effective model-space truncation can be achieved if only core states in the vicinity of the yrast line are taken into account. These have been selected from the several hundreds or even thousands of states obtained from shell-model calculations, where the $\text{1g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{3s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ single- are assumed to be occupied. Spectroscopic data are calculated and predictions on the structure of low-lying π = ? 1 states are discussed and compared as far as possible to experimental findings. Thereby, the particle-core coupling approach is shown to be capable of describing essential properties of negative-parity levels in the N = 82 nuclei considered.     

Regge couplings and intercepts from the planar dual bootstrap

Planar unitarization of dual models is examined in terms of renormalized diagrams. The shift of the Reggeon intercept 1 ? α(0) and the renormalized coupling $\text{g}{}^2\text{N}\text{16π}$ are both expected of order unity in a model with SU(N) Chan-Paton factors. In four space-time dimensions Regge behaviour makes the shift of the dual photon mass reminiscent of Schwinger's mechanism.     

Exact solutions in λϕn theory

Families of exact solutions of the λ?ⁿ theory in d + 1-dimensional space—time are obtained. Certain finite-energy static solutions are found in the case when $\text{n =}\text{2d}\text{(d ? 2)}$.     

Electron drag of dislocations in thin metal plates

The electron force dragging dislocations in a thin metal plate of thickness d has been calculated and the dependence of the drag force F on the parameter $\text{d}\text{l}$ (l is the electron free path length) determined for the cases $\text{d}\text{l ? 1}$ and $\text{d}\text{l ? 1}$. With d ? l, the drag force depends upon the nature of electron scattering on the plate surface. The drag force dependence on the sample size has also been considered for a d.c. magnetic field H parallel to the plate faces. In the case of diffuse scattering the second derivative of F(H) reveals a square root singularity at the value of the magnetic field where the electron orbit diameter is equal to the plate thickness.     

Large perturbative corrections to the Drell-Yan process in QCD

The total cross section $\text{d}\text{σ}\text{d}\text{Q}{}^2$ for the production of a muon pair of invariant mass Q²via the Drell-Yan mechanism and the Feynman x_F differential cross section $\text{d}{}^2\text{σ}\text{d}\text{Q}{}^2\text{d}\text{x}{}_{\mathrm{<mtext>F</mtext>}}$ are calculated in QCD retaining all terms up to order α_s(Q². The calculations are performed using dimensional regularisation of the intermediary infrared and collinear singularities, but we present our results in a form independent of such details. The corrections to both these cross sections coming from radiative corrections to the lowest-order $\text{q}\text{q}$ annihilation diagram are found to be large at present values of Q² and S when the cross section is expressed in terms of parton densities derived from leptonproduction, for all Drell-Yan processes of practical interest. Numerical calculations are presented which show, for any reasonable parametrisation of the parton densities, that the neglect of higher-order terms in α_s(Q²) is not justifiable. The quark-gluon diagrams on the other hand give small corrections in this order and are only important for PP scattering.     

On the determination of α2F(ω) in metals by measuring I–V characteristics of “wide” (non-ballistic) point-contact junctions

For metals with small electron and phonon mean free paths (alloys, deformed or amorphous materials), there exists a possibility of determining α²F(ω) by measuring the V dependence of $\text{d}{}^2\text{I}\text{d}\text{V}{}^2$ or $\text{d}{}^3\text{I}\text{d}\text{V}{}^3$ of wide (d ? 10³ Å) point contacts (PC) and then inverting the linear equation relating these quantities to α²F(ω). The procedure is elaborated numerically and tested successfully for model electron-phonon interaction spectra.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

Delayed onset of 4d photoemission relative to the giant 4d photoabsorption of La

For the giant 4d photoabsorption of La, both the total photoabsorption spectrum and the N_4.5-derived Auger emission intensity spectrum increase significantly above hν ? 112 eV, with spectral peaks at hν = 118 and 119 eV, respectively. However, the predominant 4d photoemission partial cross section shows a delayed onset of ～ 4 eV, with a peak at hν = 121 eV, while the 5s, 5p, and 5d partial cross sections all show a strong resonant enhancement at lower energies, with spectral peaks at hν = 116.6 eV. These results are compared with a recent many-body calculation for Ce. The photon energy dependence of the La 4d_{$\text{5}\text{2}$}/4d_{$\text{3}\text{2}$} photo-emission branching ratio is consistent with a “final-state model.”     

Measurement of the decay-probability of metastable hydrogen by two-photon emission

The two-photon-decay probability of the metastable 2² S_{$\text{1}\text{2}$} level of hydrogen has been measured. The result A(λ)dλ = 1.5 sec^?1 ± 43% in the spectral range dλ = (255.4?232)nm ± 5% is in agreement with the theoretical prediction.     

Dependence on interatomic distance of exchange coupling in rare-earth Al2 compounds

The effect of pressure on the Curie temperature of the heavy rare-earth dialuminides has been measured up to 3.5 kbar. The derivatives dT_c/d_p are 0.00(4), 0.09, 0.21, 0.39, 0.60 and 0.71 K/kbar respectively for TmAl₂ ErAl₂, HoAl₂, DyAl₂, TbAl₂ and GdAl₂ thus indicating a clear positive correlation between dT_c/dp and the de Gennes factor G. The results are discussed in terms of the RKKY model. However, the phenomenological parameter D/d, where D is the nearest-neighbour R-R distance and d the diameter of the 4f orbital, is used to reflect the non-δ-function character of the sf-coupling parameter Г. The experimental values of Г²D² and T_p/G are found to decrease linearly with increasing D/d. This is in keeping with the RKKY proportionality of $\text{T}{}_{\mathrm{c}}\text{?T}{}_{\mathrm{p}}$ to Γ²E^?1_FG. For GdAl₂, TbAl₂ and DyAl₂ the quantity $\text{?}\text{(}\text{d}\text{T}{}_{\mathrm{c}}\text{d}\text{p}\text{)}\text{k}{}_{\mathrm{l}}\text{(}\text{D}\text{d}\text{)}\text{G}$ coincides within the error limits with the slope of the T_p/G vs D/d plot.     

Continuum limit of QED2 on a lattice

A path integral is defined for the vacuum expectation values of Euclidean QED₂ on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields $\text{G}$ on a lattice with spacing proportional to N^?1, N?Z⁺, the Matthews-Salam formula for the vacuum expectation 〈G〉_N has the form ($\text{G}$)_N=∫d_nu;W_N($\text{G}$,f), where dμ is an N-independent measure on a random electromagnetic field ? and $\text{W}{}_{\mathrm{N}}\text{(G, ?)}$ is an N-dependent function of ? determined by $\text{G}$. For a class of $\text{G}$ we prove that as N → ∞, $\text{W}{}_{\mathrm{N}}\text{(C, ?)}$ has a limit $\text{W(G, ?)}$ except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫d_nu;W_N($\text{G}$,f) exists and lim_N→∞∫d_nu;W_N($\text{G}$,f).