Sum rules for forward elastic photon scattering

Relations between integrals over forward elastic photon scattering amplitudes, forward elastic cross sections and total cross sections are derived from dispersion relations. A new photon-proton interaction sum rule is derived and evaluated.     

Sum rules for forward elastic pion-nucleon scattering

A number of energy weighted sum rules relating amplitudes and differential cross sections for forward elastic and charge exchange scattering to the total pion-nucleon cross section are derived from dispersion relations.     

Dispersive treatment of low-energy pion-nucleus forward elastic scattering

The amplitudes for pion-nucleus forward elastic scattering are studied by means of dispersion relations, with emphasis on the low-energy and unphysical regions. The importance of the threshold behaviour of inelastic pion scattering is pointed out, and effective coupling constants, a news-wave parameter and the real part of thep-wave scattering length are determined.     

Spin effects in proton-proton elastic scattering near the forward direction

We have analysed the several sets of experimental data on pp elastic scattering in the Coulomb interference region in the range p_lab between 9 and 500 GeV/c, in order to estimate the size of the spin dependent part of the strong amplitude. Calling β the ratio of this spin-dependent part to the spin-dependent amplitude in the forward direction, we find all the data strongly suggest but do not conclusively prove a non-negligible β whose value is around 10% and approximately constant with energy. This result cannot be explained theoretically in terms of exchange of any simple factorising Regge pole. We suggest important pomeron cut contributions. Implications of our analysis for some experiments at ISR energies which appear to give rising total cross sections are discussed.     

Dispersion relation for elastic electron-hydrogen atom forward scattering amplitude

The elastic e + H forward scattering amplitude is an analytical function in the complex energy E plane and has two cuts on the real axis: 0 < E < ∞ and ?∞ < E < ?B, B being the hydrogen ionization potential. The e+H dispersion relation contains two integrals over the right and left cuts.     

Analytical properties of the forward elastic scattering amplitudes following from microcausality

The forward elastic scattering amplitudes T_i(v,q²), (i = 1,2), of the virtual photon with the mass q² are considered in variables σ and ? where σ and ? are related to q² and v by the formulae q² = exp (2σ) and v = exp (σ) ch?. It has been proved that microcausality requirement implies the analyticity of amplitudes in the tube region [Im σ + π/2] + |Im?| < π/2 as a function of both complex variables σ and ?. Formulae are obtained expressing amplitudes T_l(v,q²) at arbitrary v and q² through functions W_l^(?)(v, q²) describing the electroproduction process ?2v < q² < 0.     

The pion-nucleon forward scattering amplitude

The pion-nucleon forward scattering amplitude has been calculated from new data of the total cross sections, using several assumptions on the energy dependence above 20 GeV. The results are presented as complex diagrams of the forward amplitude, which are of interest for the discussion of the nucleonic resonances and the non-resonant background scattering. In addition the predictions for the elastic forward cross sections are given as well as the contributions of the real parts to this quantity. A comparison with the new Saclay data of the charge exchange forward cross section leads to the estimate αρ≈0.6, if a Regge behaviour is assumed above 20 GeV. There are indications in favour of a new\(T = \tfrac{1}{2}\) resonance at the total c.m. energyW≈2.8 GeV.     

The pomeron in elastic meson-baryon scattering

We show that a pomeron (P) trajectory with α_P(t) ≈ 1.07 + 0.22t provides a simple and satisfactory fit to π^±p and K^±p elastic scattering data (as well as pp and $\text{p}$p considered in an earlier publication) for |t| < 1.2 GeV², including the rising total cross sections. The destructive term needed to explain the diffraction minimum in pp may be explained as a weak P ? P cut effect provided that the Gribov vertices are given suitable structure, and the prediction is then made that similar minima should be observed in meson-baryon scattering at FNAL somewhere in the region 1.5 < |t| < 2.5 GeV². The P ? P cut does not seem to be related (at least directly) to the unitarization effects which must eventually make σ_tot ～ log²s (but not until s > 10⁸GeV²). Thus the “effective” J-plane singularity structure, at currently available energies seems to be much simpler than it can be asymptotically.     

Influence of multiple elastic scattering on the shape of the elastically scattered electron peak

The influence of multiple elastic scattering on the shape of the energy distribution of elastically scattered electrons is investigated. The energy of the maximum intensity of the detected electrons differs from the probe electron beam energy due to the elastic energy loss. The experimentally observed spectrum is adequately described by a Gaussian distribution with a maximum at the elastic energy loss value. In this paper the peak-broadening mechanisms due to energy-analyzer spread function, probe beam energy distribution and atomic vibration-induced broadening are considered to be independent and of random nature. Analysis of multiple elastic scattering shows some mechanisms leading to the broadening and a shift of the elastic scattering electron energy spectrum from the value defined by single elastic scattering at the certain angle. It is revealed that the magnitude of this shift and the width of energy distribution is determined by ratio (_lin/_ltr)$(l_{\text{in}}/l_{\text{tr}})$, where _lin$l_{\text{in}}$ is inelastic mean free pass, _ltr$l_{\text{tr}}$ is the transport length.     

π p forward elastic scattering near 1 GeV/c

We have measured the differential cross section of the reaction π⁻p→π⁻p in the range 0.92 ? cos θ_c.m. ? 0.99 at 15 momenta between 0.875 and 1.580 GeV/c. The results we report complete the available data; previous measurements of this reaction do not extend beyond cos θ_c.m.=0.90. We compare our experimental results with dispersion relation predictions. A comparison of our results for B, the slope of the differential cross section, with earlier results shows many discrepancies.     

Forward glory and the determination of the nuclear forward amplitude from heavy-ion elastic scattering

It is shown that a forward glory phenomenon is present in the elastic scattering angular distribution of heavy ions. The general properties of the glory determine the conditions under which it is possible to obtain both the amplitude and phase of the nuclear forward amplitude ?_N(0) from elastic angular distributions. Examples are given which show that even in strongly absorbing systems this amplitude is relatively large and can be easily measured. It is demonstrated that the knowledge of ?_N(0) provides a unique piece of information on the origin of the backward rise and of the resonances observed in heavy-ion-induced reactions.     

The analysis of forward scattering channeling data

The use of large angle forward scattering offers the advantage of performing dechanneling measurements at low beam fluences in comparison to the backscattering technique. Here, we present the method for the analysis of forward scattering channeling data and discuss the advantages of the technique.     

Contribution of the radiative tail from the elastic peak to deep inelastic scattering at HERA

The formulae for the contribution of the elastic radiative tail (photon- andZ-boson exchange are included) to the measured cross section of deep inelasticep→eX scattering are derived, using a simple procedure of smoothing the integrand. The numerical results in the kinematical region of smallx at HERA energies are presented.     

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     

The role of absorption in large-angle elastic scattering

The measurements of energy loss distributions obtained in electron scattering experiments at high momentum transfer are presented for Xe, Ar and methane. The spectra show a large variety of intensity distributions, clearly different from those obtained in measurements at the dipole limit. The fraction of the intensity present in the energy loss distribution compared to the elastic peak is significant, but is in line with the reduction of the elastic cross section due to absorption. It is argued that, if similar effects are present in the condensed phase, they should be dealt with in any quantitative analysis of electron transport in matter, as is often done using Monte Carlo simulations. This argument is worked out in some detail for Reflection Electron Energy Loss Spectroscopy.