On the role of the Δ(1232) on the transverse nuclear response in the (e,e′) reaction

The transverse nuclear response to an electromagnetic probe which is limited to create (or destroy) a particle-hole (ph) or delta-hole (Δh) pair is analyzed. Correlations of the random phase approximation (RPA) type and self-energy insertions are considered. For RPA correlations we have developed a scheme which includes explicitly the Δ and the exchange terms. Self-energy insertions over ph and Δh bubbles are studied. Several residual interactions based on a contact plus a (π + ϱ)-meson exchange potential are used. All calculations are performed in non-relativistic nuclear matter. The main effect of the Δ is to reduce the intensity over the nuclear quasi-elastic peak. Exchange RPA terms are very important, while the terms with self-energy insertions depend strongly on the residual interaction employed. Our results are compared with data for ⁴⁰Ca at momentum transfer q = 410 and q = 550 MeV/c, where the longitudinal response is also briefly discussed.     

Parton densities beyond perturbation theory

I compute non-perturbative corrections to the kernel governing the evolution of non-singlet parton densities. The model used is QED in the limit of many charged particles. I find an infrared renormalon at b₀t = −1, where t is the Borel variable and b₀ is the first coefficient of the β-function. This term has a non-trivial dependence on the variable x = -q²/(2p · q) and its coefficient scales as x³/(1 − x)² (p is the momentum of the hadron and q is the momentum transfer). An extrapolation of my results to QCD implies a breakdown of the parton model near the elastic region.     

Elliptic flow in the nuclear interaction of an astroparticle with an energy of ∼10<Superscript>16</Superscript> eV

A total of 107 cascades formed by secondary particles of the nuclear interaction of an astroparticle with an energy of ～10¹⁶ eV are detected in a stratospheric emulsion chamber. Their azimuthal distribution revealed a distinct anisotropy. The elliptic flow coefficient V₂ was estimated at 0.35 ± 0.02. The average transverse momentum of cascades in the direction of the impact parameter exceeded 3 GeV/c.     

Neutron inelastic scattering study of transverse spin fluctuations in CsNiF3: A soliton-only central peak

We have observed a quasi-elastic contribution to the spectrum of the transverse spin fluctuations S^perp;(Q, ω), perpendicular to an applied magnetic field in the easy plane of the one-dimensional ferromagnet CsNiF₃. According to the present theoretical understanding this contribution is due solely to soliton quasi-particles and it should not contain two-magnon scattering. The observed dependence on momentum transfer is as expected for soliton scattering with zero intensity at q_c = 0 rising through a maximum with increasing q_c.     

Weitere Messungen zur Anisotropie der intermolekularen Wechselwirkung durch Streuung von Molekülen in definiertem Quantenzustand

The interaction between diatomic molecules and rare gas atoms can be described by the realistic, though simplified potentialV=?[(r_m/r)¹²(1 +q₁₂P₂(cosθ))?2(r_m/r)⁶(1+q₆P₂(cosθ))] The determination of the parameters?, r _m andq ₆has been treated in the two previous parts of this series. The present final paper describes the determination of the anisotropy parameter in the repulsive part of the potential, q₁₂, for the system CsF-He. Whileq ₆ could be derived using only the dependence of the total scattering cross section on the molecular rotational state, the determination ofq ₁₂ requires, in addition, knowledge of the velocity dependence. The comparison of the experimental data for CsF in the rotational states ¦J, M〉=¦1, 1〉 and ¦1, 0〉 with cross sections calculated by means of the “high energy” approximation yields the result:q ₁₂=0.9±0.2. The validity of the “high energy” approximation in the velocity range covered by the experiment is discussed.     

Effect of pressure on the temperature dependence of the thermal conductivity of InSb

The dependence of the thermal conductivity of indium antimonide on temperature (in the range 300–450 K) and hydrostatic pressure (up to 0.4 GPa) has been investigated. It is shown that the phonon thermal conductivity λ_ph obeys the law T ^?n (n ≥ 1). Hydrostatic pressure affects the magnitude and temperature dependence of the thermal conductivity of InSb: with an increase in pressure, the thermal conductivity increases, while the parameter n in the dependence λ_ph ≈ T ^?n decreases.     

Weitere Messungen zur Anisotropie der intermolekularen Wechselwirkung durch Streuung von Molekülen in definiertem Quantenzustand

Improved measurements of the ratio of scattering cross sections for various molecular rotational states are reported for scattering of TlF in rotational states ¦J, M〉=¦1, 0〉 and ¦1, 1〉, and CsF in rotational states ¦2, 0〉 and ¦2, 2〉 by rare gases. The results are interpreted in terms of an angle dependent attractive potentialV=?2ε(r _m /r) ⁶(1+q ₆ P ₂(cosΘ) in which the repulsive part of the interaction is neglected. The “high energy” approximation is used to calculate the cross section, which contains the velocity dependence and the state dependence as factors. The experiments show for all scattering partners with the exception of He and Ne, that the state dependence is velocity independent. In those cases this result provides a justification for the neglect of the repulsive potential term. The results for the anisotropy parameterq ₆, which to a good approximation depends only on properties of the moleculus, are:q ₆=0.23±0.01 for TlF,q ₆=0.28±0.02 for CsF.     

Extrapolation from positive to negative energy of the Woods-Saxon parametrization of the n-208Pb mean field

The real part V(r); E) of the nucleon-nucleus mean field is assumed to have a Woods-Saxon shape, and accordingly to be fully specified by three quantities: the potential depth U_v(E), radius R_V(E) and diffuseness a_v(E). At a given nucleon energy E these parameters can be determined from three different radial moments [r^q]_v = (4π/A) ∝V(r; E)r^q dr. This is useful because a dispersion relation approach has recently been developed for extrapolating [r^q]_V(E) from positive to negative energy, using as inputs the radial moments of the real and imaginary parts of empirical optical-model potentials V(r; E) + iW(r; E). In the present work, the values of U_v(E), R_v(E) and a_v(E) are calculated in the case of neutrons in ²⁰⁸Pb in the energy domain −20 < E < 40 MeV from the values of [r^q]_V(E) for q = 0.8, 2 and 4. It is found that both U_V(E) and R_v(E) have a characteristic energy dependence. The energy dependence of the diffuseness a_a(E) is less reliably predicted by the method. The radius R_V(E) increases when E decreases from 40 to 5 MeV. This behaviour is in agreement with empirical evidence. In the energy domain −10 MeV < E < 0, R_V(E) is predicted to decrease with decreasing energy. The energy dependence of the root mean square radius is similar to that of R_V(E). The potential depth U_v slightly increases when E decreases from 40 to 15 MeV and slightly decreases between 10 and 5 MeV; it is consequently approximately constant in the energy domain 5 < E < 20 MeV, in keeping with empirical evidence. The depth U_v increases linearly with decreasing E in the domain −10 MeV < E < 0. These features are shown to persist when one modifies the detailed input of the calculation, namely the empirical values of [r^q]_v(E) for E > 0 and the parametrization [r_q]_w(E) of the energy dependence of the radial moments of the imaginary part of the empirical optical-model potentials. In the energy domain −10 MeV < E < 0, the calculated V(r; E) yields good agreement with the experimental single-particle energies; the model thus accurately predicts the shell-model potential (E < 0) from the extrapolation of the optical-model potential (E > 0). In the dispersion relation approach, the real part V(r; E) is the sum of a Hartree-Fock type contribution V_HF(r; E) and of a dispersive contribution ΔV(r; E). The latter is due to the excitation of the ²⁰⁸Pb core. The dispersion relation approach enables the calculation of the radial moment [r^q]_ΔV(E) from the parametrization [r^q]_w(E): several schematic models are considered which yield algebraic expressions for [r^q]_ΔV(E). The radial moments [r^q]_HF(E) are approximated by linear functions of E. When in addition, it is assumed that V_HF(r; E) has a Woods-Saxon radial shape, the energy dependence of its potential parameters (U_HF, R_HF, a_HF) can be calculated. Furthermore, the values of ΔV(r; E) can then be derived. It turns out that ΔV(r; E) is peaked at the nuclear surface near the Fermi energy and acquires a Woods-Saxon type shape when the energy increases, in keeping with previous qualitative estimates. It is responsible for the peculiar energy dependence of R_V(E) in the vicinity of the Fermi energy.     

B → πlΝ form factors calculated on the light-front

A consistent treatment of B → πlν decay is given on the light-front. The B to π transition form factors are calculated in the entire physical range of momentum transfer for the first time. The valence-quark contribution is obtained using relativistic light-front wave functions. Higher quark-antiquark Fock-state of the B-meson bound state is represented effectively by the ¦B*π〉 configuration, and its effect is calculated in the chiral perturbation theory. Wave function renormalization is taken into account consistently. The ¦B*π〉 contribution dominates near the zero-recoil point (q ² ? 25 GeV²), and decreases rapidly as the recoil momentum increases. The calculated form factor ?+(q ²) follows approximately a dipole q ²-dependence in the entire range of momentum transfer. We estimate that ¦V _ub¦=0.003.     

Dispersive viscosity coefficient of nuclear matter

By application of Landau's kinetic theory of a Fermi liquid in non-equilibrium, we have deduced a dispersive, momentum and frequency dependent shear viscosity coefficient η(q, ω) for symmetric nuclear matter. The resulting formula for η is found to be complicated for arbitrary q, ω; however, simple interpretation is possible in the limit of small momentum q → 0. In the static limit, ω → 0, η reduces to the well known kinetic formula for the hydrodynamic viscosity coefficient η_o, while in the high frequency (zero sound) limit, ωτ ? 1, η(ω) is found proportional to (?iω)^? indicating elastic behaviour of nuclear matter. As is discussed shortly, application of these results to finite nuclei unfortunately does not seem justified.     

Brillouin zone effects on the critical temperature of superconductors and some related normal metal properties

A Fermi surface passing through a set of Bragg planes gives rise to variations of several normal metal properties, e.g. the electronic density of states N(0), the magnetic susceptibility, the Seebeck coefficient, the Debye temperature and the electron-phonon interaction strength V_ph, and consequently also to variation of the critical temperature for superconductivity, T_c.This behaviour is analysed on the basis of a nearly free electron model and a comparison is made with experimental results in various alloy systems. These systems include alloys of non-transition metals and pseudo-binary alloyed compounds with Cu₃Au- and CuAl₂-type structure.The observed variations of normal metal properties are in reasonable agreement with the theoretical estimates. The variations in T_c indicate that enhancements not only of N(0) but probably also of V_ph occur near Bragg planes.     

Current transport mechanism in Al/Si3N4/p-Si (MIS) Schottky barrier diodes at low temperatures

The current-voltage (I-V) and capacitance-voltage (C-V) characteristics of metal-insulator-semiconductor (Al/Si₃N₄/p-Si) Schottky barrier diodes (SBDs) were measured in the temperature range of 80-300 K. By using the thermionic emission (TE) theory, the zero-bias barrier height Φ_B0 calculated from I-V characteristics was found to increase with increasing temperature. Such temperature dependence is an obvious disagreement with the negative temperature coefficient of the barrier height calculated from C-V characteristics. Also, the ideality factor decreases with increasing temperature, and especially the activation energy plot is nonlinear at low temperatures. Such behaviour is attributed to Schottky barrier inhomogeneties by assuming a Gaussian distribution of barrier heights (BHs) at interface. We attempted to draw a Φ_B0 versus q/2kT plot to obtain evidence of a Gaussian distribution of the BHs, and the values of Φ_Bo = 0.826 eV and α_o = 0.091 V for the mean barrier height and standard deviation at zero-bias, respectively, have been obtained from this plot. Thus, a modified ln(I_o/T²) − q²σ_o²/2(kT)² versus q/kT plot gives Φ_B0 and Richardson constant A^* as 0.820 eV and 30.273 A/cm² K², respectively, without using the temperature coefficient of the barrier height. This value of the Richardson constant 30.273 A/cm² K² is very close to the theoretical value of 32 A/cm² K² for p-type Si. Hence, it has been concluded that the temperature dependence of the forward I-V characteristics of the Al/Si₃N₄/p-Si Schottky barrier diodes can be successfully explained on the basis of TE mechanism with a Gaussian distribution of the barrier heights. In addition, the temperature dependence of energy distribution of interface state density (N_SS) profiles was determined from the forward I-V measurements by taking into account the bias dependence of the effective barrier height and ideality factor.     

Continuum RPA correlations in quasielastic electron scattering from 12C decay on (e,e'p) and (e,e'n) reaction channels

We investigate the rôle of RPA correlations in longitudinal and transverse response functions for inelastic electron scattering from ¹²C at momentum transfers ranging between 200 MeV/c and 550 MeV/c. We refer to a continuum self-consistent RPA theory with a SK3 interaction. Electromagnetic operators are taken for uncorrelated nucléons. The partial response on (e, e'p) and (e, e'n) reaction channels is also calculated. Since energy-weighted sum rules are conserved, we can control the effect of the Hartree-Fock non-locality expressed by the SK3 nucleon effective mass as well as the action of creation and descruction of 1p 1h pairs on the true ground state induced by the RPA residual interaction.     

Transverse momentum of charged hadrons observed in deep inelastic muon scattering

The transverse momenta of charged hadrons produced in high energy muon-proton scattering have been studied. The average squared transverse momentum 〈p²_⊥〉 shows a strong dependence on z = E_h/v characteristic of intrinsic momentum effects and a significant rise as a function of s = W². The W², q², x and z dependences of the data are compared with the predictions of a perturbative QCD model.     

The Ruderman-Kittel-Kasuya-Yosida interaction in amorphous La80Au20 alloys with dilute Gd impurities

From magnetization measurements on some amorphous dilute La_80?xGd_xAu₂₀ alloys with x ? 1 we have shown that the magnetic behavior follows the scaling laws of a spin-glass system, characteristic of the 1/r³ dependence of the pairwise interaction. We have also determined the strength of the Ruderman-Kittel-Kasuya-Yosida interaction V(r) = (V₀cos 2k_Fr)/r³, to be V₀ = 0.20 × 10^?37 ergcm³. The corresponding value of the s-f exchange integral is |J_sf| = 0.14 eV, which is compared with values determined from other experiments.     

Pion-nucleus inelastic scattering and charge exchange

Using a separable fixed scatterer pion-nucleon interaction and the distorted wave impulse approximation we have made predictions for medium energy pion inelastic scattering from ¹⁶O and (π^?, π⁰) charge exchange from ⁴⁸Ca. An optical potential based on the pion-nucleon interaction adopted in this work has been shown previously to provide good fits to pion-nucleus elastic scattering. After a discussion of the basic formulae, we present results of calculations for pion inelastic scattering from ¹⁶O for initial pion lab kinetic energies of 70 and 180 MeV. Because of the strong energy dependence of the pion-nucleon interaction there are qualitative differences between the predictions for the nuclear response in the momentum transfer, energy loss plane for T_π^lab = 70 and 180 MeV. At these energies, states not prominently excited by other probes are predicted to be observable. In particular, J^π = 3^? and 4^?, T = 0 states appear prominently in the excitation spectrum region at large momentum transfer. A comparison of π^? and π⁺ scattering showing the effects of the Coulomb interaction is presented. The predictions for pion single-charge exchange on ⁴⁸Ca indicate that this interaction would be useful for studying the location of the T_> states arising from the splitting of the giant dipole resonance in T ≠ 0 nuclei.     

A microscopic description of nuclear molecules: Application to the 12C + 12C system

The interaction energy between two oblate ¹²C ions is calculated by means of the constrained Hartree-Fock method. The influence of the mutual orientation of the ions is investigated by considering two extreme configurations: an axial symmetric one where the two ions approach each with their symmetry axes aligned with the collision axis and a triaxial one where the axes of the fragments are perpendicular to the collision line. The corresponding potentials V₁ and V₂ display very distinct features. In particular the minima of the potentials occur for quite different interdistances. A method is devised for constructing from V₁ and V₂ the potentials and coupling factors between two ions rotating with definite angular momentum. Using these quantities in a coupled channel calculation, we explain the gross features of the elastic, single 2⁺ inelastic and double inelastic cross sections. The same calculation yields good agreement with the fusion data.     

TDPAC studies of the intercalation compound Li x TiS2 in the region 0≤x≤1

The electrochemical intercalation of Li⁺ into hafnium-doped TiS₂ was studied using time-differential perturbed angular correlations (TDPAC). The¹⁸¹Ta nuclear quadrupole interaction was monitored as a function of the charge transfer,n _F. For low uptakes, 0≤n _F≤0.03, a two-phase region was found with an empty host interaction, characterized byV _q=458(4) MHz, η=0.19(3) and δ-0.083(5), and a second interaction corresponding to lithiated material withv _q=597(5) MHz, η=0.13(4) and δ=0.061(5). No evidence was found for intermediate phases.     

Analytic proton-nucleus scattering amplitudes

Analytic expressions for the elastic nucleon-nucleus amplitudes F(q) and G(q) are derived. They are based on analytic approximations of the nuclear profile functions in the Glauber formulation. Our amplitudes are sums of terms with a familiar structure, black-sphere Bessel functions multiplied by form factors accounting for the diffuseness of the nuclear surface. Their accuracy is tested with the Woods-Saxon density and found to be excellent for momentum transfers q? 5fm^?1.     

Electron-electron interaction and instabilities in one-dimensional metals

The possible instabilities of a 1-dimensional itinerant electron gas are discussed, assuming electron-electron interaction to play the dominant role. As is well known, in the RPA, a 1-dimensional metal is prone to spin density wave (SDW), charge density wave (CDW) and Cooper pair (CP) instabilities. The spin channel decomposition of the irreducible scattering amplitude I is made and the spin channel projections are evaluated in terms of the matrix elements of bare electron-electron interactionV(x) for momenta of interest. It is found that if the bare electron interactionV(x) is repulsive and decreases monotonically with separation, only the SDW instability will occur. If the small separation (x?(2k _F )^?1) part of the interaction is greatly reduced or is made attractive,V(x) is non-monotonic,V _q (q?2k _F ) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [V _q (0<q<k _F )+V _q (q?2k _F )]<0. The above RPA results serve only as rough indicators, since in general there are important two-electron configurations with two-electron momentum close to zero and with electron hole momentum close to 2k _F , an example being the near Fermi energy configurationk ₁?k _F ,k ₂??k _F ,k ₃??k _F k ₄?k _F . Therefore as pointed out first by Bychkov, Gorkov and Dzhyaloshinskii (BGD), cross channel coupling is especially significant. It is shown that the cross channel coupling is constructive is some cases,eg., exchange of CD fluctuations leads to an effective electron-electron spin singlet attraction and vice-versa. A formalism for studying such effects is set up, and the particular example mentioned above is discussed. An RPA-like approximation is made for the form of the reducible singlet electron hole scattering amplitudeγ _s ^d and the resulting induced Cooper pair attraction is calculated to be $$\begin{gathered} [I_s ^e ]_{ind.} \rho _{{}^\varepsilon F} = [ln(\lambda \beta \omega _c )]^{ - 1} ln\{ [1 + 2\pi ^{ - 1} ln(\lambda \beta \omega _c )^2 ]/ \hfill \\ 1 + [8\pi ^{ - 1} \gamma _s ^d (q = 2k_F )^{ - 1} )^2 ]\} \hfill \\ \end{gathered} $$ where λ=1.14,β=(k _B T)^?1 andω ₀ is an electronic energy cut-off ～ε _F . The induced electron hole attraction due to the exchange of virtual Cooper pairs has a similar expression, but with a factor of (1/4) and withγ _s ^e (q=0) replacingγ _s ^d (q=2k _F ). The induced Cooper pair attraction is seen to be quite large over a broad range of temperatures close to but aboveT _CDW [i.e., aboveT such thatγ _s ^d (q=2k _F )^?1=0]. There is no requirement thatγ _s ^d (q=2k _F ) andγ _s ^e (q=0) become singular at the same temperature, as found by BGD. The BGD prediction is seen to arise from the neglect of real particle hole and particle-particle excitations while calculatingγ _s ^d andγ _s ^e . The effect of impurities, of electron-phonon coupling, of interchain coupling and of interaction between thermal order parameter fluctuations is discussed. The results are then applied to a discussion of the properties of TTF-TCNQ, where it is suggested that a CDW instability occurs becauseV _q (q=2k _F )<0,i.e., because the small separation electron repulsion is strongly reduced by the highly polarizable TTF. Because of substantial interchain coupling, the bulk CDW instability occurs close to the RPA instability temperature. The giant conductivity observed by Colemanet al is attributed to superconductive fluctuations in a 1-dimensional system with large mean field superconductive transition temperatureT _CP ^MF of order 300°K. Such a largeT _CP ^MF is shown to result from the induced Cooper pair attraction due to CD fluctuation exchange.