Topological characteristics of electronic spectra of single crystals

The paper considers the topological characteristics of dispersion functions ɛ_s(p) in energy bands in single crystals related to classical electron trajectories in uniform magnetic fields. Specifically, the topological properties of open trajectories in p-space on various energy levels within one energy band and related physical effects are described. Zh. éksp. Teor. Fiz. 112, 371–378 (July 1997)     

Calculation of the ion transverse velocity distribution function under ion cyclotron resonance heating

The ion transverse velocity distribution functions and the fraction η of ions heated above a certain energy W ₁ are calculated as applied to the ion cyclotron resonance heating method of isotope separation. It is assumed that the longitudinal ion velocity distribution in a plasma source is nonequilibrium. Under high heating temperatures, the averaged ion transverse velocity distribution becomes essentially nonequilibrium and exhibits two maxima. The ion heating efficiency η is calculated for W ₁=40 eV and various values of the parameter p=λ/L, where λ is the wavelength of the electric field of an antenna and L is the heating zone extension. The relative contributions of the time-of-flight and Doppler broadenings are evaluated.     

SPRITE MRI with Prepared Magnetization and Centrick-Space Sampling

A technique for imaging materials with short transverse relaxation times and prepared longitudinal magnetization is proposed. The technique is single-point ramped imaging withT₁-enhancement (SPRITE) MRI with centrick-space sampling. The effects of transient state behavior on image resolution and signal/noise are estimated. Centric sampling in the basic SPRITE sequence gives increased signal-to-noise and permits a quantitative determination of the MR parameters associated with longitudinal spin preparation. Spin-lock and inversion recovery preparation experiments are presented.     

Network topology and subgap resonances observed by Fourier transform scanning tunnelling microscopy of cuprate high-temperature superconductors

Fourier transform scanning tunnelling microscopy (STM) on Bi₂Sr₂CaCu₂O_{8+ δ} (BSCCO) subgap resonances has deciphered an octet of ‘quasiparticle’ states that are consistent with the Fermi surface and energy gap observed by angle-resolved photoemission spectroscopy (ARPES), but the origin of the high-intensity k-space octets and the sharply defined r-space chequerboard is unexplained. The filamentary ferroelastic nanodomain model that predicted the r-space chequerboard also explains the k-space octets and the origin of the apparent anisotropic surface d-wave gap by using strong electron–phonon interactions outside the CuO₂ planes. The topological model identifies the factors that stabilize high-intensity k-space octets in the presence of a very high level of irregular r-space chequerboard noise.     

Fine-structure effects in relativistic calculations of the static polarizability of the helium atom

We use the relativistic configuration-interaction method and the model potential method to calculate the scalar and tensor components of the dipole polarizabilities for the excited states 1s3p ³ P ₀ and 1s3p ³ P ₂ of the helium atom. The calculations of the reduced matrix elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron-electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. Zh. éksp. Teor. Fiz. 115, 494–504 (February 1999)     

Molecular electronic distribution functions and correlation holes Theory and application to H2, LiH and BH

The one-electron density functions for the diatomic hydrides H₂, LiH and BH, defined with respect to a limited STO basis set, are partially integrated to yield longitudinal and transverse distribution functions which admit of a simple pictorial representation. The maxima in the longitudinal distribution functions occur in regions conventionally ascribed to core pairs, lone pairs or bond pairs.

The correlation between pairs of electrons of given spin is then analysed in terms of the analogous partially integrated pair density functions and in terms of the associated hole functions. In the case of LiH and BH, the Fermi hole functions are similar in form to the negatives of the one-electron distribution functions for the appropriate singly occupied molecular orbitals; but the differences between the two functions are more marked in BH, where there is increased spatial interpenetration of the valence electron pairs. The results also show, in a simple way, how the electron motion is over-correlated in H₂ when the Heitler-London wavefunction is used.     

A new basis set for molecular wavefunctions

A new basis set is proposed for molecular self-consistent field and configuration interaction calculations. Expansion functions are proposed in the form sin (r _A · p) exp (-ar_A ²) and cos (r _A · p) exp (-ar _A ²) and it is suggested that they are used as an alternative to the gaussian basis set x_A ⁱy_A ^jz_A ^k exp (-ar _A ²).

It is shown how the new basis can have the same effects, for suitable vectors p, as the gaussian basis. It is further shown that all the one and two-electron integrals in the new basis are evaluable in terms of exponentials, square roots and the complex error function erf (z). First calculations, using the new basis, are presented in LiH, HF and H₂O.     

Scaling of semi-inclusive cross sections with respect to longitudinal and transverse momenta

The semi-inclusive one-particle transverse and longitudinal momenta spectra of π^± mesons have been studied in the centre-of-mass system for π^?p interactions at 40 GeV/c. These data are compared with similar data from pp interactions at 300 GeV/c and lower energies. Distributions in the variables p_T/〈p_T〉 and p_L/〈p_L〉 reveal scaling properties, which are found to be substantially independent of the nature of the projectile, of the incident energy and of the prong multiplicity. These spectra are reasonably described by universal functions.     

12C(e,e′ p) missing momentum distributions in HF-Sk3 and RPA-Sk3 continuum theories

We study the momentum distribution or reduced cross-section for electron induced 1p _3/2 proton knockout from¹²C in parallel kinematics. We refer to continuum self-consistent HF-Sk 3 and RPA-Sk 3 theories with a full treatment of the one-nucleon energy continuum. The PWIA limit is also shown. The¹²C(e, e′p ₀) missing momentum distribution is analyzed in connection with the energy dependence at fixed momentum transfer of the¹²C(e, e′) longitudinal and transverse responses. We compare our theoretical results with the available experimental data.     

Stress-Induced Changes in the Optical Parameters in Copper Chloride

We have calculated the stress-induced variations in refractive indices (of the index of refraction Δn and of the extinction coefficient Δk) of CuCl by the means of the Kramers–Kronig relationship from the piezoreflectance spectra of the 1s Z₃ and 1s Z₁₂ excitons. In the two studied configurations corresponding with the applied stress p //[001] and p //[111] the spectrum of the differential parameters Δk consist of two principals absorption lines in the region of the Z₃ band. The corresponding energetic separation is comparable with the transverse-longitudinal splitting. The longitudinal Z₃ exciton Γ_5L is mixed with the transverse exciten Γ_5T by virtue of the stress-induced k-linear term and became optically active.     

Maximum entropy principle and power-law tailed distributions

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution p_i by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. Indeed, the Maxwell-Boltzmann distribution is obtained by maximizing the Boltzmann-Shannon entropy under proper constraints. The second link is algebraic and imposes that both the entropy and the distribution must be expressed in terms of the same function in direct and inverse form. Indeed, the Maxwell-Boltzmann distribution p_i is expressed in terms of the exponential function, while the Boltzmann-Shannon entropy is defined as the mean value of -ln (p_i). In generalized statistical mechanics the second link is customarily relaxed. Of course, the generalized exponential function defining the probability distribution function after inversion, produces a generalized logarithm Λ(p_i). But, in general, the mean value of -Λ(p_i) is not the entropy of the system. Here we reconsider the question first posed in [Phys. Rev. E 66, 056125 (2002) and 72, 036108 (2005)], if and how is it possible to select generalized statistical theories in which the above mentioned twofold link between entropy and the distribution function continues to hold, such as in the case of ordinary statistical mechanics. Within this scenario, apart from the standard logarithmic-exponential functions that define ordinary statistical mechanics, there emerge other new couples of direct-inverse functions, i.e. generalized logarithms Λ(x) and generalized exponentials Λ^-1(x), defining coherent and self-consistent generalized statistical theories. Interestingly, all these theories preserve the main features of ordinary statistical mechanics, and predict distribution functions presenting power-law tails. Furthermore, the obtained generalized entropies are both thermodynamically and Lesche stable.     

Microwave transport approach to the coherence of interchain hopping in (TMTSF)2PF6

We report a microwave study of the longitudinal and transverse transport properties of the quasi-one-dimensional organic conductor (TMTSF)₂PF₆ in its normal phase. The contactless technique have provided a direct measurement of the temperature profile of the resistivity along the b' direction and in magnetic fields up to 14 T. A characteristic energy scale ( K) has been observed which delimits a transient regime from an insulating to a metallic behavior. This anomalous profile is discussed in terms of the onset of coherent transport properties along the b' direction below 40 K. This is also supported by the observation of a finite longitudinal and transverse magnetoresistances only below 40 K, indicative of a two-dimensional regime. Below T_x, however, strong deviations with respect to a Fermi liquid behavior are evidenced. Received 27 January 1999     

J/ψ gluonic dissociation revisited: III. Effects of transverse hydrodynamic flow

In a recent paper [B.K. Patra, V.J. Menon, Eur. Phys. J. C 44, 567 (2005)] we developed a very general formulation to take into account explicitly the effects of the hydrodynamic flow profile on the gluonic breakup of J/ψs produced in an equilibrating quark–gluon plasma. Here we apply that formulation to the case when the medium is undergoing a cylindrically symmetric transverse expansion starting from RHIC or LHC initial conditions. Our algebraic and numerical estimates demonstrate that the transverse expansion causes enhancement of the local gluon number density n_g, affects the p_T-dependence of the average dissociation rate through a partial-wave interference mechanism and makes the survival probability S(p_T) to change with p_T very slowly. Compared to the previous case of a longitudinal expansion the new graph of S(p_T) is pushed up at LHC but develops a rich structure at RHIC, due to a competition between the transverse catch-up time and the plasma lifetime.PACS 12.38.Mh     

Study of relativistic bound state wave functions in quasielastic (e,e′ p) reactions

The unpolarized response functions of the quasielastic ¹⁶O(e,e′ p)¹⁵N reaction are calculated for three different types of relativistic bound-state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density-dependent relativistic Hartree calculations that reproduce the experimental rms charge radius of ¹⁶O. The sensitivity of the unpolarized response functions to the single-particle structure of the different models is investigated in the relativistic plane-wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single-particle states. The interference responses R_LT and R_TT reveal a strong sensitivity to the small component of the relativistic bound-state wave function.     

Semi-inclusive structure functions in the spectator model

We establish the relationship between distribution and fragmentation functions and the structure functions appearing in the cross-section of polarized 1-particle inclusive deep-inelastic scattering. We present spectator model evaluations of these structure functions focusing on the case of an outgoing spin- baryon. Distribution functions obtained in the spectator model are known to fairly agree at low-energy scales with global parameterizations extracted from totally inclusive DIS data. Therefore, we expect it to give good hints on the functional dependence of the structure functions on the scaling variables x _B, z and on the transverse momentum of the observed outgoing hadron, P _h . Presently, this dependence is not very well known, but experiments are planned in the near future. Received: 26 May 2000 / Accepted: 29 August 2000     

Single Particle Distributions from Veneziano Amplitudes I

The single particle distribution for the inclusive reaction A + B → C + anything is calculated from the discontinuity of the Veneziano six point function in the tree approximation and investigated in different kinematical regions. Power series expansions around x = 1 and Barnes-Mellin integral representations suitable for expansions around x = 0 are presented. For large transverse momenta the single particle distribution shows an exponential decrease in p_⟂² with an x dependent slope assuming the value 4 α′ for x = 0. For small transverse momenta the behaviour of the distribution function in the pionization region is determined by a logarithmic singularity at the unphysical point p_⟂² = −m_c². In addition single particle distributions following from two special types of Pomeron-background modified B₆ functions are studied. Most of the results are similar to those obtained with the unmodified B₆ function. This applies in particular to the pionization region, where the asymptotic p_⟂²-slope 4α′ is replaced by a “background slope” 4β′.     

The Spin Structure of the Nucleon; A COMPASS Perspective

The COMPASS experiment at CERN is carrying on an experimental investigation of the spin structure of the nucleon, covering both longitudinal and transverse spin phenomena. In the first case, the central topic is the direct measurement of the gluon polarisation with the hope to solve the spin crisis first observed by EMC. The result shows that Δg/g is small around x _g ≃0.1, and its first moment should not be larger than 0.2—0.3 in absolute value. About transverse spin effects, evidence is given for new phenomena, associated with transverse momentum dependent distribution and fragmentation functions.     

The transverse momentum profile of a quark jet

The first and second moments of the transverse momentum distribution of pions ine ⁺ e ^?-annihilation at fixed longitudinal momentum with respect to the jet axis are discussed, treating the hadronic final state evolving from the 2-quark system in the framework of a fireball-model. Good agreement with the published data is found. A comparison with thep _T -distribution of electroproduction is made, showing qualitative agreement. This casts serious doubts on previous conclusions favoring a large partonk _T inside the proton.