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.     

Construction of diffractive amplitudes

Starting from a simple parametrization of production amplitudes an explicit construction of the diffractive elastic amplitude through multiparticle unitarity is given. It is shown that the phase cancellation effect is essential in order to obtain an elastic amplitude which display a diffractive peak in qualitative agreement with the data.     

Quantal description of inelastic heavy-ion scattering

A model Schrödinger equation for scattering with energy loss is discussed. The equation is linear and is closely related to the coupled-channels approach to elastic and inelastic scattering. A possible parametrization of the model for applications to heavy-ion scattering is considered.     

A new “parametrization” of the differential cross section for elastic scattering

A new parametrization of the differential cross section for elastic scattering is proposed. The parametrization incorporates correct analytic properties of the differential cross section and is based on optimized polynomial expansions of an analytic function. It is, in principle, valid for all energies and all angles. The parametrization has been tested for pp, $\text{p}\text{p}$, pd, π^± and K^±p elastic scattering at high energies and small angles. The results of the new fits are compared with those of the old ones. It has been found that with the same number of parameters one obtains practically the same values of χ². However, the new values of physical quantities, such as slope, α and (dσ/dt)₀, in most cases differ considerably from those obtained by the old parametrization. In particular, it has been found that the slope of the differential cross section for pp, $\text{p}\text{p}$, pd and K^±p elastic scattering increases continuously as the forward direction is approached.     

Radiative corrections to deep inelastic electron-deuteron scattering: The case of tensor-polarized deuteron

Model-independent radiative corrections to deep inelastic scattering of an unpolarized electron beam off the tensor-polarized deuteron target are considered. The contribution to the radiative corrections due to the hard photon emission from the elastic electron-deuteron scattering (the so-called elastic radiative tail) is also investigated. The calculation is based on the covariant parametrization of the deuteron quadrupole polarization tensor. Radiative corrections to the polarization observables are estimated numerically for the kinematical conditions of the current experiment at HERA.     

Isobar doorway approach to pion scattering on open shell nuclei

Delta-hole approach developed for the pion scattering on closed shell nuclei is extended to be applied to the case of open shell nuclei. The doorway space is spanned by the states of the form |Ψ^(A−1)ψ^(Δ) which correspond to |Δ h states in the usual delta-hole approach for closed shell nuclei. In this approach, the effects of the couplings between elastic and inelastic channels are incorporated in a natural way. As a first application of this approach, some numerical calculations have been done for the elastic and inelastic pion scattering on ¹²C and the elastic scattering on ¹⁴N and ¹⁴C. The effects of the nuclear structure and the coupling between elastic and inelastic channels are discussed.     

Exclusive Scattering from Unpolarized and Polarized Deuteron

We present results for exclusive electron scattering from polarized and unpolarized deuteron. We employ the Gross equation to describe the deuteron ground state, and we use the SAID parametrization of the full NN scattering amplitude to describe the final state interactions. We discuss properties of various asymmetries accessible with a polarized deuteron target and/or a polarized beam.     

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

1 Introduction Though one-dimensional (1D) systems may clearly exhibit many features of quan-tum mechanics, systems with many degrees of freedom provide more opportunities tostudy many other important features, e.g. the degeneracy of energy eigenstates, whichneed a complete set of commuting observables to characterize an energy eigenstate. Inparticular, two-dimensional (2D) systems with two spatial degrees of freedom may ex-hibit symmetries not present in 1D systems, e.g. the rotational symme…     

Elastic pion-deuteron scattering in the resonance region as a three-body problem

We study elastic pion-deuteron scattering in the Δ(1236) energy region by means of the three-body Faddeev equations. We present a compact angular momentum reduction of the Faddeev integral equation for separable amplitudes, neglecting the nucleon spin, and solve the resulting coupled integral equations. We examine the dependence of the elastic scattering amplitude on the deuteron structure, on the pion-nucleon scattering amplitude, and on the various orders of multiple scattering. The differential cross section is very sensitive to multiple scattering effects at backward angles. We find that a number of conventional approximations do not well reproduce these multiple scattering effects in the resonance region.     

Unitary amplitudes with cut-plane analyticity from given scattering data

We continue the study of constructing the scattering amplitude for scalar particles from elastic scattering data at a given energy. Here we require the scattering amplitude, f (z), to be analytic in a suitably cut z-plane; (z is the cosine of the scattering angle). We find that, in the elastic domain, the unitarity constraint is satisfied by a continuum of amplitudes, all corresponding to the same elastic scattering data. This continuum ambiguity in determination of f (z), which was noted earlier in formulations based on a smaller domain on analyticity, is associated with lack of knowledge of the contribution to unitarity from inelastic channels. We discuss the problem of incorporating smooth energy dependence in the determination of the scattering amplitude over some range of energy, and show that, under certain restrictions on the scattering data, there is a continuum of amplitudes having smooth energy dependence.     

Theoretical remarks for the analysis of electron scattering experiments on rotational nuclei

A convenient parametrization of longitudinal and transverse form factors of rotational nuclei is presented. This parametrization is model independent up to the order considered. It is intended to extract information on the intrinsic structure of ground state rotational bands by expressing the form factors for elastic and inelastic scattering within the band in terms of intrinsic charge and current multipoles, weighted by angular momentum dependent coefficients. The importance of the experimental measurements of transverse form factors is stressed as providing unique information on the distribution of the rotational current and hence, a unique test of the different rotational models. A qualitative comparison of three different models—rigid rotor, cranking and projected Hartree-Fock approach—is also presented in this context.     

Optical model potential of 800 MeV/c K+ meson for12C and40Ca by the method of inversion

The elastic scattering differential cross-sections of 800 MeV/c K⁺ mesons from¹²C and Ca have been analyzed using the Ericson’s parametrization for the phase shift. It is found that the parameter values obtained by our analysis are significantly different from those obtained from the closed expression for K⁺-nucleus amplitude derived by the strong absorption approximation. Next, using the phase shift obtained from the present analysis we calculate the K⁺ optical model potentials for¹²C and⁴⁰Ca by the method of inversion. The calculated potentials are compared with the recently determined phenomenological ones.     

Structure of the antiproton-proton elastic scattering amplitude

It is found that the simple expression [(πcq)/sinh(πcq)][J ₁(Rq)/(Rq)] for the elastic scattering amplitude makes it possible to well describe differential cross sections over a broad range of energies from 100 MeV to \(\sqrt s \) = 1800 GeV. This parametrization can be used to calculate antiproton-nucleus and antinucleus-nucleus amplitudes and cross sections, which are necessary in accelerator experiments and in cosmic ray physics. The generalization of the wavelet expansion to the case of functions defined on a semi-infinite interval is also proposed.     

Physics (and technique) of gas jet experiments

Recently gas jet targets have been used for the study of small momentum transfer p-p and p-d elastic and inelastic scattering. In these experiments, which were performed at Serpukhov in the USSR and at the Fermilab in the USA, the gas jet is introduced in the main ring of the accelerator. We review the techniques associated with these measurements and summarize the published results which cover 4-momentum transfers 0.001< |t|< 0.12 (GeV/c)^?2 and incident energies 8<E< 400 GeV. Elastic scattering data have yielded precise values for the slope of the nuclear scattering amplitude and for the ratio of the real to imaginary part as a function of energy. The implications of these data on the understanding of high energy hadronic interactions are discussed in some detail. We also present and discuss information on the diffractive dissociation of the proton to low mass states, obtained from inelastic scattering using the gas jet target.     

Stable, strongly attractive, two-state mixture of lithium fermions in an optical trap

We use an all-optical trap to confine a strongly attractive two-state mixture of lithium fermions. By measuring the rate of evaporation from the trap, we determine the effective elastic scattering cross section 4pia(2) to show that the magnitude of the scattering length |a| is very large, in agreement with predictions. We show that the mixture is stable against inelastic decay provided that a small bias magnetic field is applied. For this system, the s-wave interaction is widely tunable at low magnetic field, and can be turned on and off rapidly via a Raman pi pulse. Hence, this mixture is well suited for fundamental studies of an interacting Fermi gas.     

Possible Odderon exchange in pp and ■p elastic collisions at the TOTEM experiment

Based on the Froissart-Martin theorem,the Regge theory and the possible Odderon exchange,the total cross-sectionσtot and the ratio of the real to imaginary parts of the forward scattering amplitude p in the pp and pp elastic collisions in the TOTEM energy region are studied in the FPO model.We consider the contributions of the Froissart bound and of the Pomeron,Reggeon and Odderon exchange terms in the scattering amplitude of the pp and pp elastic collisions.Using the Odderon interceptαo(0)=0.5,our theoretical predictions are in good agreement with the recent results of the TOTEM experiment.These results show that the Odderon,corresponding to the odd elastic scattering amplitude,is likely to exist.     

Elastic and charge exchange scattering of pions on3He in the (3,3)-resonance region

The elastic scattering of pions from³He and the single charge exchange reaction³He(π ^?,π ⁰)³H are calculated in the energy domain of the (3,3)-resonance within the framework of Glauber's theory, including spin and isospin degrees of freedom in all orders. It is pointed out that, from the first minimum on, the differential cross section strongly depends on the parametrization of theπN amplitude, especially on its continuation into the unphysical region of momentum transfer. Single and double spin flip contributions prove to be very important in the charge exchange reaction. Within a modified version of Glauber's formalism, directly usingπN phase shifts rather than amplitudes, the³He charge exchange scattering is reexamined. Whereas the shape of the angle-integrated cross section as a function of pion energy is confirmed, the magnitude is still uncertain within a factor of 2.     

$ \alpha$ -nucleus elastic scattering in the energy range 25-70 MeV/nucleon

Working within the framework of the Coulomb-modified Glauber model for nucleus-nucleus collisions, we analyse the elastic scattering of -particles on ⁴He at 25, 30, 35, 40, 50, and 70MeV/nucleon. Emphasis has been put on the parametrization of the basic (input) NN amplitude that preserves the low-q behavior at the desired energy, whereas the higher momentum transfer components are treated phenomenologically. The analysis also considers the medium modification of the NN amplitude due to Pauli blocking. Using the realistic form factors for colliding nuclei, it is found that the data are reproduced satisfactorily well up to the fairly large value of momentum transfer. We also discuss the suitability of the extracted NN amplitude for other target nuclei in the energy range under consideration. Our analysis suggests that the proper account of the higher momentum transfer components of the NN amplitude may push down the Glauber model to lower energies, and increase its validity in the region of relatively large momentum transfers.     

Measurement of np elastic scattering at high energies and very small momentum transfers

The np elastic differential cross section has been measured for incident neutron momenta 100–400 GeV/c in the |t| range 6 · 10^?6 ? 5 · 10^?1 (GeV/c)². The np data of this experiment provide a first direct measurement of the hadronic amplitude for |t| < 10^?2 (GeV/c)², which is consistent with the extrapolations from higher |t| values. Our data for |t| < 10^?4 (GeV/c)² are consistent with a rise which can be attributed to Schwinger scattering, caused by the interaction of the neutron magnetic moment with the proton.     

Ballistic electron transport in wrinkled superlattices

Inspired by the problem of elastic wave scattering on wrinkled interfaces, we studied the scattering of ballistic electrons on a wrinkled potential energy region. The electron transmission coefficient depends on both wrinkle amplitude and periodicity, having different behaviors for positive and negative scattering potential energies. For scattering on potential barriers, minibands appear in the electron transmission, as in superlattices, whereas for scattering on periodic potential wells the transmission coefficient has a more complex form. Besides suggesting that tuning of electron transmission is possible by modifying the scattering potential via voltages on wrinkled gate electrodes, our results emphasize the analogies between ballistic electrons and elastic waves even in scattering problems on non-typical configurations.