Angular distributions and structure functions from two-jet events at the CERN SPS pp collider

The two-jet cross section measured in the UA1 apparatus at the CERN $\text{p}\text{p}$ Collider has been analysed in terms of the centre-of-mass scattering angle θ and the scaled longitudinal parton momenta x₁ and x₂. The angular distribution dσ/d cos σ rises rapidly as cos → 1, independent of x₂ and x₂, as expected in vector gluon theories (QCD). The differential cross section in x₁ and x₂ is consistent with factorization and provides a measurement of the proton structure function $\text{F(x) = G(x) +}\text{4}\text{9}\text{[Q(x) +}\text{Q}\text{(x)]}$ at values of the four-momentum transfer squared, -t? ≈ 2000 GeV². Over the range x = 0.10?0.80 the structure function shows an exponential x dependence and may be parametrized by the form F(x) = 6.2 exp (?9.5x).     

Thermodynamical analysis of the EMC effect

Assuming that the sea quark distribution vanishes for x > 0.3, we analyse the F₂^Fe(x, Q²) and F₂^D(x, Q²) structure functions measured by the European Muon Collaboration in the framework of a thermodynamical model of the valence quarks. The experimental ratio $\text{F}{}_2{}^{\mathrm{<mtext>Fe</mtext>}}\text{(x)}\text{F}{}_2{}^{\mathrm{<mtext>D</mtext>}}\text{(x)}$ is well reproduced over the whole x range by the ratio of two valence quark distributions at different temperatures T and confinement volumes V. We obtain T_D?T_Fe≈3 MeV and $\text{V}{}_{\mathrm{<mtext>Fe</mtext>}}\text{V}{}_{\mathrm{<mtext>D</mtext>}}\text{≈ 1.3}$.     

Inclusive pion distributions in e+e− annihilation from sum rules and duality

The threshold behaviour of pion production presented in our earlier work is successfully compared with the new SPEAR data. By using duality and sum rules we derive F_T^(π+)(x) ≈ F_L^(π+)(x) ≈ F_T^(π0)(x) ? F_L^(π0)(x) for x near 1. An accompanying results is $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>A</mtext>}}{}_2\text{(s) ≈ 2σ}{}_{\mathrm{\pi \omega }}\text{(s) ≈ 4σ}{}_{\mathrm{\pi \pi }}\text{(s) ≈ 9(m}{}_{\mathrm{?}}{}^2\text{/s)}{}^3\text{σ}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}$ for large s.     

Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

Non-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S(q,t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T_I and characterized by the structure factor S(q,0)=x(q,T_I, upon a sudden increase in temperature T_I→T_F at constant coverage, such that the adsorbates equilibrate at T_F in a disordered phase. The initial decay of a peak in x(q,T_I) proceeds exponentially in time, $\text{exp}\text{(−}\text{t}\text{τ}{}_{\mathrm{q}}\text{)}$, where τ_q is a wavevector-dependent lifetime, before it crosses over to a power-law, t⁻¹ decay. When x(q,T_I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S(q,t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T_F, x(q,T_F), in that the ratio $\text{S(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ is independent of q, is dependent on time, approaching unity as t⁻¹ for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ_q strongly depends on q, diverging as q⁻² for q→0. For these systems too, away from the center of the BZ, $\text{S}\text{(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ rapidly evolves to a slowly decaying function of $\text{t}\text{t}{}_{\mathrm{w}}$, independent of q. In this case, however, the characteristic time scale, t_w, is anomalously long, proportional to ξ², where ξ is the correlation length associated with the initial state. This behavior of t_w can be related to the random walk of domain boundaries.     

Ni-Zr amorphous alloys: Low temperature specific heat and superconductivity

The specific heat (C_p) of the amorphous alloys Ni_100-xZr_x for x = 75, 65, 55 and 35 was measured from 0.8K to 40K and the composition trends of the transition temperature T_c, the enhanced density of states at the Fermi level N_γ(_F) and the Debye temperatures θ_D(0), θ_D(T) established. For the three superconducting compositions (x=75, 65, 55) N_γ(E_F increases rapidly with increasing [Zr] in agreement with the trend in amorphous Cu-Zr alloys. However, for the Zr-Ni alloys the bare density of states $\text{N}{}_0\text{(E}{}_{\mathrm{F}}\text{) =}\text{N}{}_{\mathrm{\gamma }}\text{(E}{}_{\mathrm{F}}\text{)}\text{(1 + λ}{}_{\mathrm{p}}\text{)}$ increases strongly with [Zr] in contrast to the Zr-Cu alloys where it is reported to be almost constant. We conclude that for the Ni-Zr alloys the electron-ion matrix element <I²> decreases with increasing [Zr]. Other results are related to recent photoemission studies of these alloys.     

Scaling violation,the Callan Gross relation,and color excitation in electroproduction

The Callan-Gross relation is shown to be consistent with MIT-SLAC data for $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{(Q}{}^2\text{)}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}\text{(Q}{}^2\text{)}$ for x ? 0.33 in deep inelastic eN scattering, despite the fact that these data are taken in the large Q² region where F₁ and F₂ individually exhibit scaling violation. Comparison is made with asymptotic freedom predictions, and color excitation is proposed to explain large values of $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}$ at small x.     

Anomalous optical response with variation in band filling in linear chain conductors

We report the polarized infrared reflectance of ($\text{N}$-methylphenazinium)_x (phenazine)_1-x(tetracyanoquinodimethanide), (NMP)_x(Phen)_1-x(TCNQ) for 0.5≤x≤1.0. We demonstrate that the “Drude edge” in TCNQ salts is related to the conduction electron charge density. An anomalous rapid red shift of the plasma frequency, observed for $\text{x ～}\text{2}\text{3}$, may signal the emptying of the conduction electrons from half of the chains and/or a crossover from small U/W (coulomb repulsion/bandwidth) to large U/W behavior.     

Perturbation theory for the effective interaction in nuclei

Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H₀ + xV, where H₀ is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators $\text{A}\text{?}\text{(x)}$. We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and $\text{A}\text{?}\text{(x)}$ in powers of x is investigated. It is shown that W(x) and $\text{A}\text{?}\text{(x)}$ are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and $\text{A}\text{?}\text{(x)}$ which is closest to the origin and thus defines the radius r₀ of convergence of the expansions of W and $\text{A}\text{?}$. It is shown that r₀ is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

Solving the linearized Φ4 equation in external driving fields

The Φ⁴ equation, linearized about a kink at rest, is solved for external driving fields F(t) = Σ_i=n^∞f_itⁱ. The x-dependent part of the solution $\text{u}\text{?}\text{(x, t)}$ is proportional to the translation mode. This implies that also for large times the kink's dynamics is adiabatic, if the external field is sufficiently weak and $\text{|}\text{u}\text{?}\text{|? z1}$|ν| ? 1.     

Peierls transitions in semimetallic one dimensional charge transfer salts

Peierls transitions in one dimensional charge transfer salts in which both donor and acceptor molecules have even valency such as TTF-TCNQ have been studied. Transitions involving macroscopic occupation of phonon states of wavevector $\text{k}{}_{\mathrm{<mtext>F</mtext>}}\text{(TTF)}\text{+ k}{}_{\mathrm{<mtext>F</mtext>}}\text{(TCNQ)}\text{=}\text{1}\text{2}\text{G}$ and |k_F(TTF) ? k_F (TCNQ)| can occur as well as transitions of wavevector 2k_F(TTF) [and 2k_F(TCNQ)].     

Spectroscopic investigation of [(NH4)xK1−x]2SnCl6 mixed crystals

Polycrystalline samples of the solid solution [(NH₄)_xK_1?x]₂SnCl₆(0?x? 1) have been investigated by DSC, X-ray diffraction and Raman scattering experiments. Substitution of K⁺ by NH⁺₄ depresses the phase transition temperature T₁. For 0? x ?0.05 a linear temperature coefficient $\text{d}\text{T}{}_1\text{dx=?5.16}\text{K/mol}$ % is obtained. The cubic lattice constant roughly obeys Vegard's law, whereas the linewidth of the SnCl₆^2?F_2g internal vibration displays a nonlinear dependence on composition.     

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.     

High ionic conductivity in new fluorine compounds of tin II. II. On the binary system PbF2-SnF2

The Pb_xSn_1?xF₂ solid solutions adopt various structural types following the x value. We observed an evolution from a completely disordered structure for the phases with high lead concentration to an ordered structure for x=0.5. The increase of the logarithm of the conductivity with x is explained by the increase of the number of vacancies in normal anionic positions when the ratio of $\text{Sn}{}^{\mathrm{2+}}\text{Pb}{}^{\mathrm{2+}}$ is increasing.     

The renormalization of the string operator in QCD

We shall observe that the renormalization of the string operator U(x₁, x₂; C) = Pexp{ig∫_x1^x2dx_μA^μ(x)} with an open path C (smooth and non-intersecting) is path-independently performed in any order of perturbation. To demonstrate this, the renormalization constants will be calculated up to order g⁴. Next the renormalization effect on the algebraic identity $\text{U(x}{}_1\text{, x}{}_2\text{;}\text{C}\text{)U(x}{}_2\text{, x}{}_3\text{;}\text{C}\text{) = U(x}{}_1\text{, x}{}_3\text{;}\text{C}\text{∪}\text{C}\text{)}$ will be discussed and it will be proved that the renormalization preserves the algebraic identity in any order of perturbation if the paths C and $\text{C}$ are smoothly connected at x₂. Finally, the string operator renormalization is extended to the case when the path C is smoothly closed (the Wilson loop operator). It is then shown that the renormalization factor which multiplicatively renormalizes the string operator in the case of the open path, is cancelled in any order of perturbation by the divergence appearing in the coincidence of the end points. As a results, the Wilson loop operator can be renormalized by the coupling constant renormalization alone.     

A thermodynamic study of nonstoichiometric cerium dioxide

Thermogravimetric measurements were performed on nonstoichiometric CeO_2?x in the temperature range 750–1500°C and from oxygen pressures of 10^?2 to 10^?26 atm. From this data the deviation from stoichiometry x = x(T, P_o2) was determined. The thermodynamic quantities Δ$\text{H}$_o2 and Δ$\text{S}$_o2 were calculated in the region 0.001? x ? 0.3 and found to be independent of temperature.In the composition region 0.001< x < 0.006, the variation of Δ$\text{S}$_o2 with x is consistent with a defect model involving randomly distributed doubly ionized oxygen vacancies. The experimental dependence of x and σ (electrical conductivity) is shown to be consistent with this model as Δ$\text{H}$_o2 (≈ -10 eV) exhibits a slight dependence on x. It is postulated that the variation in Δ$\text{H}$_o2 may result from lattice parameter increases with x, while the defects remain essentially randomly distributed.In the composition region 0.006 < x < 0.1, x ∝ with 1 < n < 5, and in the region 0.1 < x < 0.3, x ∝ with n increasing rapidly with x to n? 30. This behavior is believed to result from increasing defect interaction with increasing departures from stoichiometry. It is interesting to note that the ordered phase observed by Bevan and Kordis between CeO_1·72 and CeO_1·70 was not observed in this study at temperatures between 1300° and 1500°C.     

Coupled mode behavior of the soft E(TO) phonon of Pb(Ti1-x,Zrx)O3 and (Pb1-3x2, Lax)TiO3

We report the temperature dependence of the low frequency part (ω < 100 cm^?1) of the Raman spectra of the Pb(Ti_1-x, Zr_x)O₃ and $\text{(}\text{Pb}{}_{\mathrm{<mtext>1-</mtext><mtext>3x</mtext><mtext>2</mtext>}}$, La_x)TiO₃ systems. The spectra indicate a coupled mode behavior between the soft E(TO) phonon and a mode which produces an additional band in the spectra. We discuss the possibility that the additional band might be due to zone boundary tranverse acoustical phonons which couple to the q ～ 0 soft E(TO) mode because of the disorder existing in the systems.     

Effect of the frustration to the ground state energy and entropy of the spin-glass in the random bond Ising model on the square lattice

The energies and the entropies of the spin-glass state and the paramagnetic state at T = 0 of the random-bond Ising mixture of the ferromagnetic bond (concentration p) and the antiferromagnetic bond (concentration 1 ? p) on the square lattice are calculated by the method of the square approximation in the simple version. A self-consistent relation that the partial trace of the normalized density matrix of the square cluster is equal to that of the vertex ($\text{tr}\text{(}{}_{\mathrm{jkl}}\text{?}\text{?}{}^{\mathrm{(4)}}\text{(i,j,k,l) =}\text{?}\text{?}{}^{\mathrm{(1)}}\text{(i)}$) leads to an integral equation for the distribution function of the effective fields, and it is solved exactly at T = 0. The symmetric solution of the integral equation contains the paramagnetic state and two spin-glass states, SG1 and SG2. The energies and the entropies of these states are obtained as functions of the concentration p. The values of the energies per spin at $\text{p =}\text{1}\text{2}$ are -0.75|E_F|, -0.72746|E_F|, -0.72543|E_F|, and correspond to a minimum, a saddle point, and a maximum, respectively, and the values of the entropies are 0, 0.082886k_B, and 0.054457k_B, respectively. The present results are compared with those of the pair approximation and discussed.