Microscopic approach to calculating cross sections and optical potentials for nucleus-nucleus interaction at intermediate energies

Nucleus-nucleus scattering is considered in the high-energy approximation and on the basis of Glauber-Sitenko microscopic theory in the optical limit. Analytic expressions for eikonal phase shifts are given for the case of Fermi-type realistic potentials and nuclear-density distributions. The effect of taking into account the distortions of the trajectories of the nuclei involved and the nuclear-density dependence of nucleon-nucleon forces on the total reactions cross sections is illustrated. The sensitivity of the reaction cross sections to the choice of model for the ⁶He projectile nucleus, which involves a neutron halo, is explored. Semimicroscopic optical potentials are introduced in order to describe differential cross sections for elastic scattering. The results of the present calculations are compared with available experimental data.     

Eikonal representation in the momentum-transfer space

By means of empirical fits to the differential cross section data on pp and elastic scattering, above 10 GeV (center-of-mass energy), we determine the eikonal in the momentum-transfer space (q ²- space). We make use of a numerical method and a novel semi-analytical method, through which the uncertainties from the fit parameters can be propagated up to the eikonal in the q ²- space. A systematic study of the effect of the experimental information at large values of the momentum transfer is developed and discussed in detail. We present statistical evidence that the imaginary part of the eikonal changes sign in the q ²- space and that the position of the zero decreases as the energy increases; after the position of the zero, the eikonal presents a minimum and then goes to zero through negative values. We discuss the applicability of our results in the phenomenological context, outlining some connections with nonperturbative QCD. A short review and a critical discussion on the main results concerning “model-independent” analyses are also presented. Received: 19 August 2004, Revised: 12 November 2004, Published online: 14 January 2005 PACS: 13.85.Dz, 13.85.-t     

Interactions of cosmic neutrinos with nucleons in the RS model

We consider the scattering of brane fields due to t-channel massive graviton exchanges in the Randall-Sundrum model. The eikonal amplitude is analytically calculated and both differential and total neutrino-nucleon cross sections are estimated. The event rate of quasi-horizontal air showers induced by cosmic neutrinos, which can be detected at the Pierre Auger Observatory, is presented for two different fluxes of cosmogenic neutrinos.Received: 27 December 2004, Published online: 8 June 2005     

Factorization theorems for high energy nn, \gamma p and \gamma\gamma scattering

The robustness of the factorization theorem for total cross sections, for nn (the even portion of pp and scattering), and scattering, originally proved by Block and Kaidalov using an eikonal formalism, is demonstrated. Factorization theorems for the nuclear slope parameter B and , the ratio of the real to the imaginary portion of the forward scattering amplitude, are derived under very general conditions, using analyticity and the optical theorem.Received: 19 February 2003, Revised: 10 July 2003, Published online: 19 September 2003Work partially supported by Department of Energy contract DA-AC02-76-Er02289 Task D.     

On factorization, quark counting and vector dominance

Using an eikonal structure for the scattering amplitude, Block and Kaidalov [1] have derived factorization theorems for nucleon-nucleon, and scattering at high energies, using only some very general assumptions. We present here an analysis giving experimental confirmation for factorization of cross sections, nuclear slope parameters B and -values (ratio of real to imaginary portion of forward scattering amplitudes), showing that: – the three factorization theorems [1] hold, – the additive quark model holds to , – and vector dominance holds to better than . Received: 6 November 2001 / Revised version: 29 November 2001 / Published online: 8 February 2002     

Momentum-space optical model for K+-nucleus scattering

The momentum-space optical model of K⁺-nucleus scattering is analyzed and comparison with other conventional models is shown. The model is based on the multiple scattering formalism in which the optimal factorization approximation is used. Off-energy-shell extension of the elementary K⁺-nucleon amplitude is neglected which reduces non localities in the optical potential. Predictions of the model are sensitive to the definition of the K⁺-nucleon energy (energy shifts) but they are independent (1–2%) of a particular form of the covariant K⁺-nucleus scattering equation (relativistic Lippmann-Schwinger, Gross, Erkelenz-Holinde). The Coulomb distortion in the total cross section is important for²⁸Si and⁴⁰Ca at low momenta (≈10%). Off-energy-shell effects in the optical potential are discussed too. Results for the total and reaction cross sections are systematically below the data. The reaction cross sections are in a larger disagreement with the data than the total cross sections. This work was supported by grants ASCR A1048703 (P. Bydžovsky) and GACR 202/96/1566 (M. Sotona).     

Neutron total and scattering cross sections of 6Li in the low-MeV range

Neutron total cross sections of ⁶Li are measured at intervals of ? 10 keV from ≈ 0.1 to 4.8 MeV with precisions of ≈ 1 to 3 %. Differential elastic scattering cross sections are measured at intervals of ? 100 keV from 1.5 to 4.0 MeV at 10 or more scattering angles distributed between ≈ 20 and 160 deg. Differential inelastic scattering cross sections are measured at selected angles in the energy range 3.5 to 4.0 MeV. The experimental results are analyzed in terms of R-matrix theory and the model parameters used to deduce the ${}^6\text{Li(n}\text{,α)}$ cross sections. The implications of the measurements and their interpretation on the level structure of ⁷Li and the reaction mechanisms are discussed.     

Second-order eikonal corrections for

The first-order eikonal approximation is frequently adopted in interpreting the results of A(e,e^′p) measurements. Glauber calculations, for example, typically adopt the first-order eikonal approximation. We present an extension of the relativistic eikonal approach to A(e,e^′p) which accounts for second-order eikonal corrections. The numerical calculations are performed within the relativistic optical model eikonal approximation. The nuclear transparency results indicate that the effect of the second-order eikonal corrections is rather modest, even at Q²≈0.2 (GeV/c)². The same applies to polarization observables, left–right asymmetries, and differential cross sections at low missing momenta. At high missing momenta, however, the second-order eikonal corrections are significant and bring the calculations in closer agreement with the data and/or the exact results from models adopting partial-wave expansions.     

Streuung von Helium-Atomstrahlen in Edelgasen

The scattering of Helium atomic beams in rare gases is investigated by measurements of total elastic scattering cross sections. With the device described the dependence of total scattering cross sections of the relative velocity of the scattering atoms was measured. For variation of the beam velocity in the range of 1:8 a He beam source was used which could be cooled down with liquid helium from room temperature to 4.8 °K. The detector is of the universal-detector-type. A Wien filter is used as mass filter. The lowest detectable particle density is 6.3 · 10³ He-atoms/cm³. The measured scattering cross sections are in qualitative agreement with the theory ofBernstein.     

Coulomb corrections for coherent electroproduction of vector mesons: Eikonal approximation

Virtual radiative corrections due to the long-range Coulomb forces of heavy nuclei with charge Z may lead to sizeable corrections to the Born cross-section usually used for lepton-nucleus scattering processes. An introduction and presentation of the most important issues of the eikonal approximation is given. We present calculations for forward electroproduction of rho-mesons in a framework suggested by the VDM (vector dominance model), using the eikonal approximation. It turns out that Coulomb corrections may become relatively large. Some minor errors in the literature are corrected.Received: 3 October 2003, Revised: 2 December 2003, Published online: 6 July 2004PACS: 25.30.-c Lepton-induced reactions - 25.30.Rw Electroproduction reactions - 13.40.-f Electromagnetic processes and properties - 25.30.Bf Elastic electron scattering     

H+,He2+与Li原子碰撞中电子俘获总截面的程函近似计算

采用Li原子价电子的有效势对前置形式程函近似振幅公式进行了修正,提出有效势修正程函近似方法,并对H^＋和He²⁺与Li原子碰撞中的电子俘获总截面进行了计算,取得了与实验比较吻合的结果. 关键词：     

Cross sections for multi-particle final states at a linear collider

In this paper total cross sections for signals and backgrounds of top- and Higgs-production channels in e ⁺ e^- collisions at a future linear collider are presented. All channels considered are characterized by the emergence of six-particle final states. The calculation takes into account the full set of tree-level amplitudes in each process. Two multi-purpose parton level generators, HELAC/PHEGAS and AMEGIC + + , are used, and their results are found to be in perfect agreement.Received: 26 November 2003, Revised: 15 January 2004, Published online: 3 March 2004     

Discording power of Hamiltonian interactions

In this paper, we report the coherent scattering cross sections of some lanthanides at low momentum transfer in four angular ranges of (0°?4°), (0°?6°), (0°?8°) and for ²⁴¹Am (59.54 keV) and ¹³⁷Cs (661.6 keV) gamma rays. The coherent scattering cross sections were derived by subtracting the small contribution of the corresponding angle integrated incoherent scattering cross sections from the experimentally measured total (coherent + incoherent) scattering cross sections for the elements and energies of interest. The coherent scattering cross sections were found to agree with the corresponding theoretical cross sections within the range of experimental errors. The theoretical coherent scattering cross sections were computed by numerically integrating the S-matrix data of the elements in the angular ranges of interest. The incoherent scattering cross sections were based on the compilations which make use of the non-relativistic Hartree-Fock (NRHF) model for the atomic charge distribution.     

Soft diffraction at the LHC: a partonic interpretation

We present a ‘new generation’ model for high energy proton–proton ‘soft’ interactions. It allows for a full set of multipomeron vertices as well as for including multichannel eikonal scattering. It describes the behaviour of the proton–proton total, σ_tot, and elastic, dσ_el/dt, cross sections together with those for low- and high-mass proton dissociation. Although the model contains a comprehensive set of multipomeron diagrams, it has a simple partonic interpretation. Including the more complicated multipomeron vertices reduces the absorptive effects as compared to the predictions in which only the triple-pomeron vertex is considered. Tuning the model to describe the available ‘soft’ data in the CERN ISR–tevatron energy range, we predict the total, elastic, single- and double-diffractive dissociation cross sections at the LHC energy. An inescapable consequence of including multichannel eikonal and multipomeron effects is that the total cross section is expected to be lower than before: indeed, we find σ_tot≃ 90 mb at the LHC energy. We also present differential forms of the cross sections. In addition, we calculate soft diffractive central production.     

$\mbox{Log}(1/x)$ gluon distribution and structure functionsin the loop-loop correlation model

We consider the interaction of the partonic fluctuation of a scalar photon with an external color field to calculate the leading and next-to-leading order gluon distribution of the proton following the work done by Dosch-Hebecker-Metz-Pirner. We relate these gluon distributions to the short and long distance behavior of the cross section of an adjoint dipole scattering off a proton. The leading order result is a constant, while the next-to-leading order result shows a enhancement at small x. To get numerical results for the gluon distributions at the initial scale Q²₀ = 1.8 GeV², we compute the adjoint dipole-proton cross section in the loop-loop correlation model. Quark distributions at the same initial scale are parameterized according to Regge theory. We evolve quark and gluon distributions to higher Q² values using the DGLAP equation and compute charm and proton structure functions in the small-x region for different Q² values.Received: 13 September 2003, Revised: 22 November 2003, Published online: 15 January 2003     

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π ^±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π ^± scattering from ⁶Li and ¹²C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of ⁶Li and ¹²C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.     

Shielded fixed-pole Pomeranchon model for high energy total and differential cross sections

A Regge model with a fixed-pole Pomeranchon and its associated shielding cut is used for π^±p, K^±p and pp scattering at small t and from 6 GeV to NAL and ISR energies. No additional parameters are associated with the cut. The model produces rising total cross sections and anti-shrinkage or non-shrinking diffraction peaks for some s and t. Good fits to total cross sections and to Serpukhov and ISR pp slope parameter data are obtained, and predictions about cross sections and shrinkage at NAL energies are made.     

Electron-impact detachment from S<Superscript>-</Superscript>

Absolute cross sections for single and double electron-impact detachment of the S^- ion have been investigated over collision energy ranges of 0-60 eV and 0-30 eV, respectively. The experiment was performed at the ion storage ring, CRYRING. The threshold energies were measured to be 6.6 eV for single detachment and 19.8 eV in the case of double detachment. The single detachment cross section has a maximum of 6.7 x 10^-16 cm² at 30 eV. The double detachment cross section was studied only in the threshold region. No sharp structures were observed in either of the cross sections.Received: 24 April 2003, Published online: 29 July 2003PACS: 34.80.Dp Atomic excitation and ionization by electron impact - 34.80.Kw Electron-ion scattering; excitation and ionization     

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order 1/k ², where k is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.