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.     

Microscopic theory of multiple scattering for open-shell nuclei

We consider the scattering of a distinguishable projectile from a nucleus assuming that the underlying interaction Hamiltonian is a sum of two-body potentials. We show that the effective interaction of the projectile with the nucleus in a truncated nuclear model space can be calculated as a linked-cluster expansion. The rules for evaluating this expansion are given in terms of the nucleon-nucleon and projectile-nucleon potentials and the exact eigenstates of the (effective) shell-model interaction. The shell-model interaction is required to be an energy-independent, Hermitian potential; its expression in terms of the underlying two-body potential is given by folded diagrams. The terms in the expansion of the effective projectile-nucleus interaction must also contain folded diagrams but, unlike the shell-model potential, these are energy-dependent in order to describe the singularities associated with the crossing of the scattering thresholds as the projectile energy is varied. Once the effective interaction is known, elastic and inelastic scatterings may be evaluated numerically by solving a finite-dimensional coupled-channel equation.     

Color Conductivity at High Resolution: A New Phenomenon of Nuclear Physics

In this paper we discuss in detail the hyothesis that nuclei show extended quark and gluon modes when explored with a high resolution probe. We call this color conductivity at high resolution. We relate color conductivity to the behaviour of proton-proton total and elastic cross sections at high energies. For deep inelastic muon-nucleon scattering we discuss in detail the nuclear evolution equation following from color conductivity and introduced by us previously. The EMC Fe/d data are well described by our theory if due allowance is made for the quoted systematic error. We predict striking effects from color conductivity in the final state of deep inelastic lepton-nucleus scattering. The possibility of making fundamental tests of quantum chromodynamics in leptonnucleus scattering is emphasized. We connect the shadowing phenomenon to the volume and surface terms in the Bethe-Weizsäcker formula for the nuclear binding energy. Finally we point out that deep inelastic scattering on deformed nuclei may be crucial to distinguish between different theories of the EMC effect.     

The need for a state dependent interaction in proton inelastic scattering from 24Mg

The calculated angular distributions for proton elastic and inelastic scattering can be greatly improved by using an imaginary potential which depends upon the nuclear state. We demonstrate that this is just the effect expected from the coupling of deuteron channels and the phenomenon therefore provides a signature for multistep processes which is not dependent on detailed calculations. The obvious application to the usual DWBA calculations of inelastic proton scattering is mentioned.     

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.     

Antiproton-Nucleus Interaction and Coulomb Effect at High Energies

The Coulomb effect in high energy antiproton-nucleus elastic and inelastic scattering from ¹²C and ¹⁶O is studied in the framework of Glauber multiple scattering theory for five kinetic energies ranged from 0.23 to 1.83 GeV. A microscopic shell-model nuclear wave functions, Woods-Saxon single-particle wave functions, and experimental pN amplitudes are used in the calculations. The results show that the Coulomb effect is of paramount importance for filling up the dips of differential cross sections. We claim that the present result for inelastic scattering of antiproton-¹²C is sufficiently reliable to be a guide for measurements in the very near future. We also believe that antiproton nucleus elastic and inelastic scattering may produce new information on both the nuclear structure and the antinucleon-nucleon interaction, in particular the p-neutron interaction.     

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.     

Isobar-hole doorway states and π-16O scattering

We describe and apply the isobar-hole approach to intermediate energy pion-nucleus reactions. Pion propagation, nucleon and isobar binding, Pauli restrictions and Δ propagation are calculated explicitly within a shell model framework. Intermediate coupling to multihole channels, for example through pion absorption, is treated phenomenologically through an isobar spreading potential. We find strongly collective Δ-hole states, leading to a reformulation of the approach in an extended schematic model. This entails systematic construction of a Δ-hole doorway state basis within which the Δ-hole propagator is evaluated. We find that this doorway space can be truncated at very low dimensionality while preserving accuracy, thereby simplifying the calculations appreciably. We make a detailed comparison between the theoretical results and recent data for π⁺ — ¹⁶O scattering in the pion energy range 50–340 MeV. Nonresonant πN interactions and the π-nucleus Coulomb interaction are included in the calculations. The data is reproduced quite well both below and in the resonance region, and we discuss in detail the role of various dynamical mechanisms. Above the resonance, the calculations are far less successful. We discuss possible shortcomings, stressing the role of inclusive pion-nucleus reactions for revealing the important dynamics. As a test of the Δ spreading potential used for describing elastic scattering, we calculate the total cross section for pion absorption. The result agrees reasonably well with the available data.     

Sensitivity of inelastic pion scattering to non-local interactions

We show that the excitation of nuclear electric dipole states by small angle inelastic scattering of pions can be used to detect the degree of non-locality of pion nucleus scattering matrix.     

Elastic scattering and fusion cross-sections in 7Li + 27Al reaction

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the ⁷Li + ²⁷Al reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies (E _lab?=?8.0–16.0 MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured α-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of 1n-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.     

Crossing symmetric amplitude with Regge poles

We obtain a representation for a pion scattering amplitude that incorporates analyticity in the Mandelstam variables, and meromorphy in the right half of the l-plane. Full crossing symmetry and elastic unitarity in the three elastic regions are built into the equations; and we show how to derive the expected Regge asymptotic behavior as one Mandelstam variable tends to infinity, while another is held fixed at any real or complex value. Moreover, we demonstrate that the inelastic unitarity bound is respected by the partial wave amplitudes, even though the Regge trajectories are allowed to rise indefinitely.     

The local field correction to the optical potential at high energy

A key assumption in the derivation of the optical potential for high energy hadron-nucleus scattering is that no target nucleon is struck more than once. The local field (rescattering) amplitude gives the probability for the projectile to strike a target nucleon twice with an intermediate interaction with another nucleon. This rescattering amplitude generates a correction to the basic high energy optical potential, and it must be small for the above assumption to be valid. We evaluate the local field correction to the optical potential using the formalism of Foldy and Walecka. The projectile-nucleon potential is assumed to have a finite range, and the target nucleons are kept sufficiently far apart by a hard core correlation function that there is no overlap between target particles, and all off-energy-shell effects vanish. With a specific form for the high energy behavior of the on-shell projectile-nucleon scattering amplitude, we find that the local field correction vanishes rapidly at high energy.     

Closed-form quantal description of inelastic heavy ion scattering

The amplitude for inelastic heavy ion scattering, given by the distorted-wave theory for excitation of low-lying collective states, is evaluated in closed form. Use is made of the Austern-Blair relation and of other approximations appropriate for strongly absorptive interaction to express the inelastic partial-wave amplitude entirely in terms of the elastic S-matrix elements in the initial and final channels. The resulting formulae display explicitly the various contributions to the transition amplitude, whose superposition gives rise to the variety of interference patterns observable in the angular distributions and excitation functions of inelastic heavy ion scattering. It is shown that, as for elastic scattering, the dominant mechanism in inelastic heavy ion collisions near and above the Coulomb barrier is diffractive scattering of Fresnel type.     

Evidence for resonance and absorption effects in positron-atom differential elastic scattering

This review focuses on recent positron-atom elastic differential cross section (DCS) measurements which reveal evidence that interference effects may be occurring between the elastic and inelastic scattering channels. These effects appear as (1) absorption effects which are observable in relative elastic DCSs by the washing out of structure in the DCS versus angle as the positron energy is increased above the positronium formation threshold, and (2) a new type of resonance-like structures at intermediate energies (well above the normal inelastic thresholds) that have been observed in absolute elastic DCS measurements when plotted at a fixed scattering angle versus energy. A discussion is provided of possibly relevant information on positron-atom scattering that also indicates that coupling is occurring between various scattering channels.     

Eikonal model description of forward energy distribution in oxygen-induced reactions at 60 A GeV and 200 A GeV

The forward energy flow cross section is described in terms of the projectile-nucleon abrasion probability which is calculated in the impact parameter representation within the framework of the Glauber multiple scattering formalism. Realistic nuclear densities and the nucleon-nucleon inelastic cross section have been used in the calculation. The recent WA80 data are in reasonable agreement with the calculation. A simple relationship has been obtained between the abrased nucleons from the target and projectile and the zero degree energy.     

Pion-nucleus inelastic scattering and charge exchange

Using a separable fixed scatterer pion-nucleon interaction and the distorted wave impulse approximation we have made predictions for medium energy pion inelastic scattering from ¹⁶O and (π^?, π⁰) charge exchange from ⁴⁸Ca. An optical potential based on the pion-nucleon interaction adopted in this work has been shown previously to provide good fits to pion-nucleus elastic scattering. After a discussion of the basic formulae, we present results of calculations for pion inelastic scattering from ¹⁶O for initial pion lab kinetic energies of 70 and 180 MeV. Because of the strong energy dependence of the pion-nucleon interaction there are qualitative differences between the predictions for the nuclear response in the momentum transfer, energy loss plane for T_π^lab = 70 and 180 MeV. At these energies, states not prominently excited by other probes are predicted to be observable. In particular, J^π = 3^? and 4^?, T = 0 states appear prominently in the excitation spectrum region at large momentum transfer. A comparison of π^? and π⁺ scattering showing the effects of the Coulomb interaction is presented. The predictions for pion single-charge exchange on ⁴⁸Ca indicate that this interaction would be useful for studying the location of the T_> states arising from the splitting of the giant dipole resonance in T ≠ 0 nuclei.     

On the spin-isospin response at intermediate energies

We have calculated the response function of infinite nuclear matter to a spin-isospin probe in the transverse and longitudinal channels. The two channels are distinguished by the meson exchanged (ρ or π, respectively) in the ph and Δh interactions, in addition to the effective g′ interaction. In the intermediate-energy region the response is particularly sensitive to the Δ-dynamics in the nuclear medium. We have applied the results of a previous calculation, which is based on a self-consistent treatment of π- and Δ-propagation in nuclear matter, to obtain Δ-self-energy corrections in the medium. Due to the opening of many-body decay channels, the self-consistent mechanism supplies a strong quenching and spreading effect on the Δ-peak in the transverse channel and we find a remarkable contribution to the response function in the energy region corresponding to the dip in inelastic electron scattering. A comparison with the experimental data for the ¹²C(e, e') cross section is given. In the longitudinal channel, on the other hand, the coherent propagation of the intermediate pion has the effect of splitting the Δ-peak into two parts, due to the vanishing of the polarization propagator at the energy corresponding to the on-mass-shell pion. The self-consistent calculation again yields a quenching effect on the response which is particularly strong on the lower peak and pushes up the other one to higher energies.     

Debye-Waller factor in atom-surface scattering: Elastic and inelastic channels

Explicit expressions for the Debye-Waller factor for the elastic and one-phonon channels are presented to lowest order in the phonon displacement, using a hard wall model to represent the atom-surface interaction. The periodicity of the crystal is accounted for; thus we explicitly generalize to all elastic channels the reflectance result found by Garcia et al. within the plane-surface model, and we include the contribution of the umklapp processes to the inelastic channels. We show how for high incident energy of the atom all Debye-Waller factors reduce to the standard result.     

Combined nuclear-molecular resonance inelastic scattering of x rays

We report on theoretical and experimental studies of nuclear inelastic scattering in a molecular crystal, whose atoms experience both molecular and lattice vibrations. In this case scattering proceeds as combined nuclear-molecular resonance inelastic scattering. The lattice vibrations give rise to inelastic scattering around the molecular resonances with an energy dependence identical to that around the nuclear resonance. The incoherent nature of the scattering in the molecular resonances results in a proper balance of elastic and inelastic components, which has important implications for studies of heterogeneous systems.