Sum rules including first order quantum corrections for neutron scattering experiments on isotopic mixtures of monatomic fluids

The sum rules for neutron scattering experiments on monatomic isotopic mixtures are studied. The scattering is separated into a self part and a distinct part rather than into an incoherent part and a coherent part. Exact expressions for the moments are derived in terms of polynomials in ? ². The coefficients in these polynomials are sums of averages of hermitean operators that have a classical analogue. For the interpretation, the coefficients are approximated including first order quantum corrections.

It is argued that the separation into coherent and incoherent scattering is not justified in the presence of ‘isotopic incoherence’. Approximate expressions for the sum rules are proposed, in which combined averages (over the isotopic composition) appear of the scattering amplitudes and masses of the scattering atoms. These expressions, including first order quantum corrections to the sum rules, are not available in the literature.

The importance of correct averaging over the isotopic composition of expressions that involve scattering amplitudes and masses is discussed for the case of a maximum incoherent mixture of ³⁶Ar and ⁴⁰Ar.     

Antiproton-nucleus scattering with self-consistent model for medium corrections

The antiproton-nucleon t-matrix with propagation in the nuclear medium is calculated selfconsistently and applied to the construction of optical potentials for the elastic scattering of antiprotons from nuclei. We find that this treatment gives results that are sensitive to medium corrections even though the strong absorption acts to mask these corrections partially. The agreement with scattering experiments at 46.8 MeV on ¹²C is very good. We compare potentials containing medium corrections to those based on free $\text{p}\text{N}$ amplitudes for ¹²C and ⁴⁰Ca. The local approximation to the optical potential is found attractive at low energies, becoming shallower with increasing bombardment energy in the range considered here (up to about E_L = 120 MeV).     

Non-eikonal effects in high-energy scattering IV. Inelastic scattering

We calculate amplitudes of inelastically scattered high-energy projectiles. For the example of scattering on ¹²C (T_p = 1 GeV) we demonstrate sizeable non-eikonal corrections in diffraction extrema even for relatively small q². At least part of the anomaly in the 3-distribution may be due to these non-eikonal effects.     

A new technique for the evaluation of Feynman diagrams in the high energy,large momentum transfer limit

The problem of finding scattering amplitudes in the high energy, large momentum transfer limit is reconsidered. We propose a novel technique of evaluating Feynman diagrams in this regime with higher order perturbative corrections in mind. The relation to other methods is discussed and the ladder diagrams in φ³ theory, recalculated up to sixth order, serve as examples.     

Binding corrections for reactions on the deuteron in the 3-3 resonance region

Binding corrections evaluated to all orders in a phenomenological nucleon-nucleon potential are compared with the leading term and with a double scattering correction in the Watson expansion for breakup and for coherent reactions on the deuteron at intermediate pion or photon energies. As principal result, we establish that for charged pion photoproduction, and for certain pion induced “spectator” reactions, the binding correction remains sufficiently small that truncation of the Watson expansion at terms of second order in the projectile-nucleon amplitudes is justifiable, but sufficiently large that it cannot be neglected in comparison with multiple scattering corrections. For the reactions π⁺d → π⁺p + spectator neutron and π^?d → π^?n + spectator proton, our theory predicts deviations from the simplest impulse approximation which become very large in well-defined kinematical regions, and should be easily accessible to experimental investigation.     

Light-light scattering in vector electrodynamics

Expressions for scattering amplitudes with definite polarizations in the approximation ω² ? m² are found. The asymptotic γγ→γγ total cross section is evaluated for the scattering of unpolarized photons. Also the forward scattering amplitudes and the differential cross section for forward scattering are obtained.     

Eikonal and Fresnel corrections to the Glauber theory of nuclear multiple scattering

Starting from a Watson-type multiple scattering series we study first-order corrections to the Glauber high-energy collision model. These are obtained by replacing the free-space Green function between successive scatterings by the second-order eikonal propagator. We distinguish between Fresnel corrections and eikonal-type corrections. Due to large cancellation effects the eikonal contribution is very small compared to the Fresnel contribution. First-order corrections to Glauber theory are calculated explicitly for high-energy elastic scattering of protons from light nuclei (⁴He, ¹²C, ¹⁶O).     

Target-mass and finite <Emphasis Type="Italic">t</Emphasis> corrections to diffractive deep-inelastic scattering

The quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering given in a previous paper (Blümlein et al. in Nucl. Phys. B 755:112–136, 2006) is discussed in detail using an equivalent formulation with the aim to derive a representation suitable for data analysis. We consider the off-cone twist-2 light-cone operators to derive the target-mass and finite t corrections to diffractive deep-inelastic scattering and deep-inelastic scattering. The corrections turn out to be at most proportional to x|t|/Q ², xM ²/Q ², x=x _BJ or x _ℙ, which suggests an expansion in these parameters. Their contribution varies in size considering diffractive scattering or meson-exchange processes. Relations between different kinematic amplitudes which are determined by one and the same diffractive GPD or its moments are derived. In the limit t,M ²→0 one obtains the results of (Blümlein and Robaschik in Phys. Lett. B 517:222, 2001) and (Blümlein and Robaschik in Phys. Rev. D 65:096002, 2002).     

Perturbative and non-perturbative QCD corrections to wide-angle Compton scattering

We investigate corrections to the handbag approach for wide-angle Compton scattering off protons at moderately large momentum transfer: the photon–parton subprocess is calculated to next-to-leading order in and contributions from the generalized parton distribution E are taken into account. Photon and proton helicity flip amplitudes are non-zero due to these corrections, which leads to a wealth of polarization phenomena in Compton scattering. Thus, for instance, the incoming photon asymmetry or the transverse polarization of the proton is non-zero, although small. Received: 31 October 2001 / Revised version: 11 December 2001 / Published online: 8 February 2002     

Ground state reorientation effects in elastic scattering cross sections

Elastic scattering cross sections are shown to be quite sensitive to ground state reorientation amplitudes and cross sections. These effects are dramatically evident when comparing scattering from even-even nuclei with that from high-spin odd-A nuclei, and may affect choices of potentials for odd versus even nuclei. Neutron scattering data from ²³⁵U and ²³⁸U are analyzed via coupled channels methods. The diffraction minima in elastic scattering from ²³⁵U are found to be dominated by reorientation cross sections. The majority of this reorientation is shown to follow from second order virtual nuclear excitations rather than proceeding through amplitudes for direct ground state reorientation.     

Elastic deuteron scattering on 12C and 16O nuclei in the alpha-cluster model

On the basis of the dispersive alpha-cluster model for target nuclei and the theory of multiple diffractive scattering, differential cross sections and analyzing powers for the elastic scattering of 400 and 700-MeV deuterons on ¹²C and ¹⁶O target nuclei were calculated in the pointlike-deuteron approximation. In these calculations, the amplitude for incident-deuteron scattering on nuclei was constructed with the aid of amplitudes for dα scattering that were obtained from a fit to data on d ¹⁶O scattering. The same features were calculated on the basis of the diffraction approximation with allowance for the internal deuteron structure by using the amplitudes obtained earlier for nucleon scattering on ¹²C and ¹⁶O nuclei within the same dispersive alpha-clustermodel. The latter made it possible to perform calculations without employing adjustable parameters. The observables calculated on the basis of either approach agree with available experimental data.     

Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

Pion scattering on 3H and 3He nuclei in the Δ33(1232) region

Elastic scattering of π ^± mesons on ³H and ³He nuclei at energies around the Δ₃₃(1232) resonance is considered. The amplitudes for single and double scattering are calculated on the basis of the nonrelativistic diagram technique. The spin and isospin structure of pion-nucleon amplitudes is fully taken into account. The resulting theoretical predictions for the differential cross sections are compared with available experimental data.     

Theory of pion-nucleus scattering lengths

We calculate the scattering lengths for pions on light nuclei, in a multiple scattering theory given earlier. We include all effects through second order in the pion-nucleon scattering amplitudes, using a simple nuclear model. We show how to calculate the binding corrections (BC) consistently, and find large cancellations between differentBC terms. The resulting scattering lengths are smaller than those obtained from measurements of pi-atomic level shifts. The size of the difference is consistent with the contribution of pion absorption, which we estimate.     

Relativistic corrections to electron scattering by the deuteron and triton

Relativistic corrections to electron-deuteron and electron-³He scattering have been calculated. the deuteron corrections agree substantially with the results of Gross and the ³He corrections are approximately equal in magnitude to those of Cocho and Flores.     

Holomorphy of the scattering matrix with respect toc −2 for Dirac operators and an explicit treatment of relativistic corrections

We prove holomorphy of the scattering matrix at fixed energy with respect toc ^–2 for abstract Dirac operators. Relativistic corrections of orderc ^–2 to the nonrelativistic limit scattering matrix (associated with an abstract Pauli Hamiltonian) are explicitly determined. As applications of our abstract approach we discuss concrete realizations of the Dirac operator in one and three dimensions and explicitly compute relativistic corrections of orderc ^–2 of the reflection and transmission coefficients in one dimension and of the scattering matrix in three dimensions. Moreover, we give a comparison between our approach and the firstorder relativistic corrections according to Foldy-Wouthuysen scattering theory and show complete agreement of the two methods.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich by an E. Schrödinger Fellowship and by Project No. P7425     

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.     

Elastic transfer in the scattering of 16O by 28Si

It is shown that the interference of potential scattering and elastic transfer amplitudes can account for the recently observed gross structure in the excitation function for elastic scattering of ¹⁶O by ²⁸Si at 180°.