On the energy dependence of elastic scattering

The energy dependence of elastic scattering is discussed and it is shown that it is compatible with geometrical scaling of the inelastic overlap function. The importance of the real part of the elastic amplitude for the energy dependence is emphasized.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

Temperature dependence of phonon energy spectra with nuclear resonant scattering of synchrotron radiation

Summary The phonon energy spectra of a polycrystalline α-Fe foil were observed at 150 K and 300 K by using the nuclear resonant scattering of synchrotron radiation. In each spectrum, inelastic scattering was observed at both sides of the elastic peak. It was found that the ratio of the elastic-scattering component and the asymmetry of the intensity of the side bands observed at 150 K are larger than those observed at 300 K, respectively. The observed temperature-dependent spectra are in good agreement with the spectra calculated from the phonon energy distribution function. One of the advantageous features of this method is that the excitation of only a specific element is possible. Our results show that this method is applicable to the study of lattice dynamics and opens a new field of the nuclear resonant scattering spectroscopy. Paper presented at ICAME-95, Rimini, 10–16 September 1995.     

Nonperturbative corrections of quark and gluon condensates to QCD inspired quark potentials

We adopt the Lorentz gauge to derive the non-local two-gluon vacuum expectation value (VEV) with translational invariance. By means of the obtained non-local two-gluon VEV, the leading nonperturbative QCD corrections to one gluon exchange quark-quark, quark-antiquark and pair-excitation potentials are given by employing non-vanishing vacuum condensates of quarks and gluons to modify the free gluon propagator. The linear, cubic and Yukawa-type terms in quark-quark potential appear automatically. In the pair-excitation potential with , the linear, square and cubic terms arise from the nonzero quark and gluon condensates. Received: 22 June 1998 / Revised version: 10 August 1998 / Published online: 29 October 1998     

Analysis of intermediate energy nucleon-deuteron elastic scattering

We present a theoretical analysis of a broad range of aspects of intermediate energy nucleon-deuteron scattering. This analysis is based on a multiple scattering approach using knowledge of the deuteron's structure and nucleon-nucleon interactions. Conversely, comparison of this theory with experiment can yield information about low and intermediate energy strong interactions. The relationship of this multiple scattering type of approach to the complementary Faddeev equation approach is discussed. Our program consists of calculating the single scattering and one nucleon exchange contributions in a realistic way then parametrizing the remaining contributions as an S-wave. We argue that the largest error in this analysis is the P-wave part of the double scattering and we give estimates of its size. The single scattering integral is evaluated numerically. Coulomb effects are neglected. We derive the relativistic expressions for single scattering and nucleon exchange and discuss the approximations made, including the off-mass-shell extrapolation of the nucleon-nucleon scattering amplitude. Fits are made to experimental measurements of differential cross sections, nucleon polarizations, and total elastic cross sections. Unitarity is maintained. We tabulate the partial waves for $\text{J ?}\text{5}\text{2}$, L ? 2. They are consistent with recent Faddeev calculations. We argue that with the additional calculation of double scattering the deuteron D-state percentage can be determined to the same relative uncertainty as the differential cross section. Even without the calculation of double scattering, our results indicate a D-state percentage around 8%. In an effort to provide benchmarks for future work, we have tried to be conscientious in describing our techniques and in tabulating numerical results. Comparisons are also made with earlier analyses.     

Proton-deuteron elastic scattering at medium energy and relativistic models of multiple scattering

We have constructed a simple model of proton-deutron elastic scattering which can incorporate either a two-dimensional Pauli matrix or four-dimensional Dirac matrix parametrization of the nucleon-nucleon scattering amplitude. The model includes the S-and D-wave components of the deuteron wave function but neglects interactions with the spins of the target nucleons and is intended to provide an estimate of the magnitude of the differences between relativistic and non-relativistic treatments. We find these differences to be quite large and attribute them primarily to the intermediate negative energy states which are present only in the relativistic calculation.     

A study of radiation damage by elastic scattering experiments

Abstract

Chaneling measurements are used to study the structure and configuration of defects produced in CdS under irradiation by 50–150 KeV Na⁺ ions at room temperature with a current density of 1 μA/cm² and irradiation dose 3.10¹⁵ ion/cm².

The results of studies of 1.8 MeV He⁺ ion dechaneling along the <1120> and <0001> axes are probably indicative of the defect structure extended along the <0001> axis.

For the dependence of the dechaneling cross-section on the ⁴He energy in the energy range 1.2 to 2.4 MeV we found E^?1, which characterizes the produced defects as randomly distributed complexes of interstitial atoms straining the crystal lattice.

The fact that the defects are mostly located along the <0001> direction can possibly be explained by strong anisotropy of CdS therefore the defects form the region of elastic stresses in the crystal which are maximum along the <0001> axis.     

The odderon in high energy elastic pp scattering

We study the odderon contribution to elastic pp and scattering at high energies. Different models for the odderon–proton coupling are considered and their effects on the differential cross section in the dip region are investigated. We use a Regge fit by Donnachie and Landshoff as a framework and replace its odderon contribution by the different models. We consider two models for the odderon–proton impact factor proposed by Fukugita and Kwieciński and by Levin and Ryskin. In addition we construct a geometric model of the proton which allows us to put limits on the size of a possible diquark cluster in the proton. All models are able to describe the data well. The two models for the impact factor require the strong coupling constant to be fixed rather precisely. In the geometric model a relatively small diquark size is required to describe the data. Received: 1 February 2002 / Published online: 14 June 2002     

Baryon scattering at high energies: wave function,impact factor,and gluon radiation

The scattering of a baryon consisting of three massive quarks is investigated in the high energy limit of perturbative QCD. A model of a relativistic proton-like wave function, dependent on valence quark longitudinal and transverse momenta and on quark helicities, is proposed, and we derive the baryon impact factors for two, three and four t-channel gluons. We find that the baryonic impact factor can be written as a sum of three pieces: in the first one a subsystem consisting of two of the three quarks behaves very much like the quark–antiquark pair in γ^* scattering, whereas the third quark acts as a spectator. The second term belongs to the odderon, whereas in the third (C-even) piece all three quarks participate in the scattering. This term is new and has no analogue in γ^* scattering. We also study the small x evolution of gluon radiation for each of these three terms. The first term follows the same pattern of gluon radiation as the γ^*-initiated quark–antiquark dipole, and, in particular, it contains the BFKL evolution followed by the 2→4 transition vertex (triple pomeron vertex). The odderon term is described by the standard BKP evolution, and the baryon couples to both known odderon solutions, the Janik–Wosiek solution and the BLV solution. Finally, the t-channel evolution of the third term starts with a three-reggeized gluon state, which then, via a new 3→4 transition vertex, couples to the four-gluon (two-pomeron) state. We briefly discuss a few consequences of these findings, in particular the pattern of unitarization of high energy baryon scattering amplitudes.     

The elastic scattering of low energy electrons from Xenon

Calculations are presented of angular distributions for electrons elastically scattered from xenon in the energy range 5.5 to 10 eV. The potential describing the xenon atom is determined by the X_α-approximation. The relative dependence with energy of the differential cross section at 30° scattering angle has been calculated in the range 30 to 200 eV. The theoretical results are in very good agreement with experimental data.     

The dipole picture of high energy scattering,the BFKL equation and many gluon compound states

The relationship and equivalence between the BFKL and dipole equation kernels are investigated by means of explicit calculations in light-cone perturbation theory. A dipole equation, equivalent to the usual equation, for interactions between four reggeized gluons is given in the large N_c limit. The leading trajectory of the four-gluon system is bounded by 2αp − 1 with αp the BFKL pomeron intercept.     

Polarization of gluon jets in photon-photon scattering

We show that the linear polarization of a gluon emerging from the reaction $\text{e}\text{+}\text{e}\text{→}\text{e}\text{+}\text{e}\text{+}\text{g}\text{+}\text{g}$ is large - on the order of 20%. This polarization arises from the process γ + γ → quark loop → g + g, which is expected to dominate the two gluon jet cross section. The polarization can be used to test quantum chromodynamics (QCD), even if the gluon jets cannot be distinguished clearly from the background of quark jets. If the QCD prediction is accepted, our result can be used to enhance the signal of gluon jets, thereby aiding in the study of their properties.     

Detailed energy dependence of the elastic and inelastic12C +12C scattering between 5 and 10 MeV/nucleon

Excitation functions for¹²C+¹²C elastic and inelastic scattering to 2⁺ level have been measured over the energy range 30–60 MeV (cm) by 250 keV steps using the kinematical coincidence method. The intermediate structure resonances disappear aboveE _cm=35 MeV while the broad and irregular structure becomes a general feature of the interaction at higher energies.     

Backward elastic pd scattering in the resonance energy region

The cross section for backward elastic pd scattering in the proton kinetic energy interval from 0.4 to 1.0 GeV is calculated from a double-triangle diagram with intermediate Δ(1232) excitation. Different approximations for the loop integrals are discussed. The predicted cross sections reproduce quite well the enhancement observed in the experimental data at about 600 MeV.     

Intermediate changes in high energy elastic scattering from atoms

Correction of the Glaubner T-matrix to account for target particle motion and energy change in elastic scattering of charged particles from atomic systems is found to vanish to leading order.     

A study of gluon scattering and gluon fragmentation in highp T interactions at the ISR

Gluon scattering processes are studied in hadronic highp _T events using data obtained with the Split Field Magnet detector (SFM) at the CERN ISR. The experimental set-up allowed the scanning of a wide range of parton energies and scattering angles. It is shown that for positive pions as trigger particles, the parton composition of the recoil jet is correlated with the polar angle and transverse momentum of the triggering pion. Over the kinematical region studied, the recoil jet originates predominantly from scatered gluons, with an increasing prevalence of the gluon component towards forward triggering angles. The variation of the momentum structure of the recoil jet with the trigger angle indicates that the fragmentation function of gluons is softer than that of quarks.     

QCD scattering processes with hard gluon emission

2→3 QCD scattering processes are studied in kinematical regions which are free from infrared and mass singularities. Anomalously large hard gluon emission corrections are found to gluon-gluon annihilation \(gg \to q\bar q\) . It is pointed out that in a kinematical region where azimuthal angel correlations of large transverse momentum π⁰'s have been measured at ISR, the 3-jet production rate is large and the contribution of the subprocessgq→ggq is greater than the contributions from quark-quark scatteringqq→qqg.     

Azimuthal dependence of impact scattering in electron energy loss spectroscopy

The azimuthal dependence of electron energy loss spectroscopy (EELS) dipole and impact scattering intensity has been measured. Spectra for a saturation coverage of H adsorbed on W(110) exhibit loss peaks due to impact scattering from adsorbate vibrational modes. The intensity of the 160 meV loss peak has been measured as a function of the azimuthal angle between the scattering plane and a mirror plane of the $\text{s}$urface. The angular pattern has strong maxima oriented perpendicular to the <111 > rows of atoms on the surface, and has the C_2v symmetry of the W(110) surface. This azimuthal dependence is strikingly different from the nearly isotropic angular dependence of dipole scattering from Cl adsorbed on W(110). Selection rules for impact scattering account for the general features of the angular pattern based on asymmetric stretch modes associated with bridge site H atoms.We have shown that the azimuthal dependence of the 36 meV Cl/W(110) dipole scattering loss peak is isotropic and that the 160 meV H/W(110) impact scattering loss peak exhibits a striking azimuthal pattern with C_2v symmetry. The symmetry and deep minima suggest that selection rules play a central role in determining the azimuthal pattern. Application of these rules to two orthogonal directions (as in ref. 6) may be misleading, as is clear from Fig. 2, because essential features of the pattern will not be observed. Our analysis of the full pattern has suggested two bridge sites may be occupied at saturation coverage, but has still not resolved certain questions about the H/W(110) system.

1. Impact scattering selection rules for potential adsorbate sites. The listed directions are the intersections of the planes with the (110) surface for the mirror planes and the scattering planes, and the displacement directions for the adsorbate vibrational modes. Modes are assumed to be strictly parallel to the surface. The long bridge site is between two W atoms along the <001 > direction, the short bridge site is between two W atoms along the <$\text{111}\text{-}$ > direction, and the distorted bridge site is displaced from the long bridge site along the <$\text{110}\text{-}$ > direction (ref. 6) The asterisks (*) denote that the scattering amplitude is zero for all directions in the scattering plane, otherwise it is zero only in the specular direction. The <$\text{110}\text{-}$ > mode of the distorted bridge is not covered by the selection rules of ref. 2.

     

20.

Temperature dependence of inelastic ultracold-neutron scattering at low energy transfer     

E. V. Lychagin  A. Yu. Muzychka  V. V. Nesvizhevsky  G. V. Nekhaev  R. R. Tal’daev  A. V. Strelkov 《Physics of Atomic Nuclei》2000,63(4):548-550

The temperature dependence of inelastic ultracold-neutron scattering on beryllium and copper surfaces at low energy transfers (about 10^?7 eV) is investigated, and the results of this investigation are presented. The recorded flux of neutrons inelastically scattered by these surfaces at liquid-nitrogen temperature is less than that at room temperature by a factor of about two.     

SITE	LONG BRIDGE	SHORT BRIDGE	DISTORTED BRIDGE
MIRROR PLANES	[001], [1$\text{1}\text{-}$0]	NONE	[1$\text{1}\text{-}$0]
2-FOLD ABOUT Z	YES	YES	NO
PARALLEL MODES	[001]	[1$\text{1}\text{-}$0]	[1$\text{1}\text{-}$1]	[$\text{1}\text{-}$12]	[001]	[1$\text{1}\text{-}$0]
DIRECTIONS OF ZERO SCATTERING	[001] * [1$\text{1}\text{-}$0]	[001] * [1$\text{1}\text{-}$0]	[1$\text{1}\text{-}$1] [$\text{1}\text{-}$12]	[1$\text{1}\text{-}$1] [$\text{1}\text{-}$12]	[001] * [1$\text{1}\text{-}$0]	NA

Temperature dependence of inelastic ultracold-neutron scattering at low energy transfer

The temperature dependence of inelastic ultracold-neutron scattering on beryllium and copper surfaces at low energy transfers (about 10^?7 eV) is investigated, and the results of this investigation are presented. The recorded flux of neutrons inelastically scattered by these surfaces at liquid-nitrogen temperature is less than that at room temperature by a factor of about two.