Unitarity and the BFKL pomeron

High energy onium-onium scattering is calculated as a function of impact parameter in the one- and two-pomeron exchange approximation. Difficulties with using the multiple scattering series to unitarize single pomeron exchange at high energy are noted. An operator formalism which sums all numbers of pomeron exchange is given. A toy model which has a similar operator structure at high energy as QCD is presented and the S-matrix is evaluated. Estimates of the energies and impact parameters at which blackness occurs in onium-onium scattering are given. It is emphasized that the problem of unitarity in high energy onium-onium scattering can be solved in a purely perturbative context, with a non-running coupling if the onium is heavy enough.     

Unitarization of the elastic amplitude on the SO(2, 1) group

We obtain the solution of the unitarity equation for the elastic processes in terms of the expansion coefficients of the amplitude as a function on theSO(2, 1) group. This approach is a generalization of the eikonal representation to the case of small impact parameters and large transverse momenta. We show how the unitarity relation is modified when the contributions of the backward scattering are taken into account. We discuss the simplest models of the profile functions in the following cases: full reflection, full absorption and the combination of these two cases.     

A class of scattering amplitudes which satisfy the unitarity condition

The unitarity condition is applied to the Regge representation of the scattering amplitude. This leads to a linear inhomogeneous algebraic equation for the residua of Regge poles and to a linear inhomogeneous integral equation (with Cauchy kernel) for the conical amplitude which can be solved exactly.     

Relativistic and close-coupling effects in the spin polarization of low-energy electrons scattered elastically from cadmium

The measurements of the Sherman function in elastic electron-cadmium scattering by Bartsch et al. [J. Phys. B 25, 1511 (1992)] have been in serious disagreement with scattering theories for nearly two decades. The recently developed relativistic convergent close-coupling method is applied to the problem and found to be in excellent agreement with experiment over the complete energy range measured. The unusually rapid variation in the spin asymmetry parameter in the vicinity of 4 eV projectile energy is now explained in terms of unitarity of the close-coupling formalism.     

On causality,unitarity and perturbative expansions

We present a pedagogical case study how to combine micro-causality and unitarity based on a perturbative approach. The method we advocate constructs an analytic extrapolation of partial-wave scattering amplitudes that is constrained by the unitarity condition. Suitably constructed conformal mappings help to arrive at a systematic approximation of the scattering amplitude in a quantum-field theoretical context. The technique is illustrated at hand of a Yukawa interaction. The typical case of a superposition of strong short-range and weak long-range forces is investigated.     

A Soliton Perturbation Theory for the MNLS Equation with Corrections in terms of an Auxiliary Spectral Parameter

Based on the lakharov-Shabat equation of the inverse scattering transform for the MNLS equation, a perturbation theory for the MNLS equation with corrections is developed in terms of an auxiliary spectral parameter ζ. All necessary formulae for calculating the scattering data are derived without any assumption beyond the usual conditions for the inverse scattering transform. Based upon these formulae, the effects due to the corrections can be calculated.     

A multiperipheral model with continued cross channel unitarity

We derive, by using a spectral representation in momentum transfer, t, an integral equation, similar in structure to a multipheral equation, with continued cross channel unitarity, for the absorptive part for a composite particle scattering amplitude from a Bethe-Salpeter equation describing composite particle scattering in the s channel. At high energy in the t channel, the equation becomes homogeneous and has a Reggeized solution. We indicate how this equation may be solved using determinental techniques. We also show how the composite particle amplitude resulting from the original equation may be used to construct production and three body amplitudes. We also infer the possibility of studying, using the amplitude from the cross channel problem, the effect of extra unitarity on Reggeon-Reggeon-particle vertices.     

Eikonal expansion in electron scattering: I. Elastic scattering

A systematic eikonal expansion for the scattering of high-energy electrons from nuclei is derived which starts from the iterated Dirac equation. The resulting scattering amplitude is written in an impact parameter representation depending on eikonal phases which are proportional to inverse powers of the energy. The first two correction terms to the leading Glauber-Baker amplitude are calculated. For a Coulomb potential they agree with a sinθ-expansion of the relativistic Coulomb scattering amplitude. In the case of scattering from an extended charge distribution at sufficiently high energies numerical partial wave calculations are accurately reproduced.     

微扰论与解析性

本文对近年来用微扰论来讨论散射振幅的解析性的理论,作了简单的介绍。在附录AⅠ中,计算了N-π,N-N散射的最简单图的奇异曲面上各点的相应临界α_c,证实了除了在谱函数边界上的点外,临界α_c都不落在实轴的(0,1)段中。在附录以AⅡ中,提出了色散关系的一个不受动量输送限制的证明方法。方法为对介子动量的方位角(讨论时取Breit系,核子动量取为极轴)进行平均。在附录AⅢ中,提出了一个可以带来么正条件的式子,以便在用微扰论进行对解析性的研究时考虑到么正条件。     

Ultracold two-component fermionic gases with a magnetic field gradient near a feshbach resonance

We study theoretically the ultracold two-component fermionic gases when a gradient magnetic field is used to tune the scattering length between atoms. For 6Li at the narrow resonance B0=543.25 G, it is shown that the gases would be in a coexistence of the regimes of BCS, Bose-Einstein condensation (BEC), and unitarity limit with the present experimental technique. In the case of thermal and chemical equilibrium, we investigate the density distribution of the gases and show that a double peak of the density distribution can give us a clear evidence for the coexistence of BCS, BEC, and unitarity limit.     

Unitarity and the optical potential

The optical potential for the elastic scattering of two nuclear fragments with the full inclusion of the Pauli principle is considered. It is shown using unitarity that the optical potential, defined in terms of the Alt, Grassberger and Sandhas off-shell extension of the transition operator, has no singularities across the elastic unitarity cut. Similar results are obtained for general rearrangement scattering.     

Jacobian transformed and detailed balance approximations for photon induced scattering

Photon emission and scattering are enhanced by the number of photons in the final state, and the photon transport equation reflects this in scattering–emission kernels and source terms. This is often a complication in both theoretical and numerical analyzes, requiring approximations and assumptions about background and material temperatures, incident and exiting photon energies, local thermodynamic equilibrium, plus other related aspects of photon scattering and emission. We review earlier schemes parameterizing photon scattering–emission processes, and suggest two alternative schemes. One links the product of photon and electron distributions in the final state to the product in the initial state by Jacobian transformation of kinematical variables (energy and angle), and the other links integrands of scattering kernels in a detailed balance requirement for overall (integrated) induced effects. Compton and inverse Compton differential scattering cross sections are detailed in appropriate limits, numerical integrations are performed over the induced scattering kernel, and for tabulation induced scattering terms are incorporated into effective cross sections for comparisons and numerical estimates. Relativistic electron distributions are assumed for calculations. Both Wien and Planckian distributions are contrasted for impact on induced scattering as LTE limit points. We find that both transformed and balanced approximations suggest larger induced scattering effects at high photon energies and low electron temperatures, and smaller effects in the opposite limits, compared to previous analyzes, with 10–20% increases in effective cross sections. We also note that both approximations can be simply implemented within existing transport modules or opacity processors as an additional term in the effective scattering cross section. Applications and comparisons include effective cross sections, kernel approximations, and impacts on radiative transport solutions in 1D geometry. The additional computing time for processing opacities (cross sections) within these approximations is negligible as induced terms are merely added (multipliers) to cross sections at the end of the processing cycle.     

Unitarity structure of scattering amplitudes

As a first step towards constructing scattering amplitudes satisfying unitarity, analyticity and crossing symmetry, we derive a linear non-singular integral equation for the total scattering amplitude which is equivalent to the unitarity condition. For this purpose we use the partial-waveN/D representation (with inelasticity) and the convolution theorem for Legendre transforms. We also discuss briefly the choice of two functionsN(s, cos Θ),C(s, cos Θ) which determine the unitary scattering amplitude through the integral equation. These functions may hopefully be chosen so that the analyticity and crossing symmetry requirements are satisfied.

     

DC and AC Josephson effects with superfluid Fermi atoms across a Feshbach resonance

We show that both DC and AC Josephson effects with superfluid Fermi atoms in the BCS-BEC crossover can be described at zero temperature by a nonlinear Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS calculations, we find that the NLSE is reliable in the AAN side of the crossover up to the unitarity limit. The NLSE can be used for weakly-linked atomic superfluids also in the BCS side of the crossover by taking the tunneling energy as a phenomenological parameter.     

A New Approach to the 3D Faddeev Equation for Three-body Scattering

A novel approach to solve the Faddeev equation for three-body scattering at arbitrary energies is proposed. This approach disentangles the complicated singularity structure of the free three-nucleon propagator leading to the moving and logarithmic singularities in standard treatments. The Faddeev equation is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation for identical bosons, which we are using, is an integral equation in five variables, magnitudes of relative momenta and angles. The singularities of the free propagator and the deuteron propagator are now both simple poles in two different momentum variables, and thus can both be integrated with standard techniques.     

The tunneling phenomena of the Fermi superfluid gases in a double-well potential by manipulating the s-wave scattering length

In the present work, we have investigated tunneling dynamics of superfluid Fermi gas in a double-well potential in deep BEC regime and in the unitarity regime by adjusting the scattering length or the interaction parameter y. The scattering length a _sc or y could affect the quantum transition dramatically. At certain regime, the complete population transfer between two modes can be obtained. However, at some other regimes, the quantum transition can be completely blocked.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Quantum corrections from nonresonant WW scattering

An estimate is presented of the leading radiative corrections to low energy electroweak precision measurements from strong nonresonant WW scattering at the TeV energy scale. The estimate is based on a novel representation of nonresonant scattering in terms of the exchange of an effective scalar propagator with simple poles in the complex energy plane. The resulting corrections have the form of the corrections from the standard model Higgs boson with the mass set to the unitarity scale for strong WW scattering.