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.     

Application of one body dissipation to deep inelastic heavy ion scattering

The one body dissipation mechanism is employed to couple the relative motion of two heavy ions to the internal degrees of freedom. Trajectories, energy and angular momentum losses are calculated, and compared with experimental data on deep inelastic scattering.     

Semiclassical treatment of heavy ion elastic scattering

A generalized semiclassical treatment for the elastic scattering of heavy ions is developed in the presence of a complex optical potential. The scattering phase shift and its derivatives with respect to the impact parameter are calculated after extending the JWKBL approximation. The results are compared with experimental data for the elastic scattering of¹⁶O from medium and heavy target nuclei and relation between the present treatment and that of the optical model and Regge pole analysis is established     

Optical potentials for elastic heavy ion scattering

The zero-field level crossing effect in selective reflection from an atomic vapour is calculated for normally incident radiation using a theory which, unlike the conventional dispersion theory, includes the effect of transient polarization behaviour due to diffuse wall collisions of vapour atoms. Both longitudinal and transverse magnetic fields are considered. At low vapour densities we find a narrowing of the level crossing curve in selective reflection relative to its width in the conventional dispersion theory. The narrowing is calculated as a function of the ratio of the homogeneous and inhomogeneous line width of the vapour for a Maxwellian velocity distribution of the vapour atoms and spectrally uniform incident radiation. The theory of this paper offers an explanation for recent observations of narrowing of level crossing curves in selective reflection.     

Multistep transfer processes in inelastic heavy ion reactions

Multistep transfer contributions in inelastic heavy ion scattering are investigated in a coupled channels model for the reaction ${}^{17}\text{O}\text{(}{}^{16}\text{O}\text{,}{}^{16}\text{O}\text{)}{}^{17}\text{O}\text{(}\text{1}\text{2}{}^{\mathrm{+}}\text{, 0.871}\text{MeV}\text{)}$. We find that only the interference of the one- and two-step transfer contributions gives agreement with recent experimental results. This is interpreted as strong evidence for multistep processes in heavy ion scattering.     

Rainbow interference effects in heavy ion elastic scattering

It is shown that the oscillatory behaviour of differential cross section of heavy ion elastic scattering, which satisfies the semi classical conditions, is well described in terms of interference effects due to a rainbow.     

Effects of relativistic kinematics in heavy ion elastic scattering

Relativistic corrections to the reaction kinematic parameters were made for elastic scattering of ⁶Li, ¹²C and ⁴⁰Ar from ⁴⁰Ca, ⁹⁰Zr and ²⁰⁸Pb targets at incident energies between 20 and 100 MeV/nucleon. The results of optical model calculations show that the effects of such corrections are important when describing the angular distributions of elastic scattering cross sections for heavy ion scattering at incident energies as low as around 40 MeV/nucleon. The effects on the total reaction cross sections on the other hand, were found to be small within the energy range studied when the optical model potential is fixed.     

The optical potential for the elastic heavy ion scattering

For the elastic scattering of heavy ions a microscopic model is developed which uses shell model wave functions which are localised at a certain distance both in coordinate and momentum space. The antisymmetrization is treated exactly. Using oscillator functions and the Brink-Boeker force the energy dependent real part of the optical potential for O₁₆- O₁₆ scattering is numerically determined. The results are compared with the analysis of experiments.     

Total reaction cross sections from heavy ion elastic scattering

A model-independent method of obtaining total reaction cross sections has been applied to α-particle and ¹⁶O, ⁴⁰Ar and ⁸⁴Kr elastic scattering. Results are compared with total reaction cross sections determined by other means.     

Pick-up and inelastic scattering contributions to the proton optical potential

The contributions from couplings with the available inelastic (p, p′) and pick-up (p, d) channels to the elastic scattering of 30 MeV protons from ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb were studied. The equivalent non-local potentials were constructed and attempts were made to find local equivalents to them. These potentials are dependent upon angular momentum. Inelastic scattering produces an attractive contribution to the real potential but pick-up results in a much larger repulsive term. The main features of the observed scattering from ²⁰⁸Pb can be reproduced by coupling to 24 channels provided a supplementary absorptive term is included. The explicit couplings by themselves can produce 90 % of the observed absorption cross section but only about one-half of the empirical absorptive potential strength.     

Importance of longitudinal contributions to backward inelastic electron scattering

Coulomb contributions of multipolarity 2 are calculated for backward (θ = 180°) inelastic electron scattering by our improved DWBA code. General features are studied such as nuclear charge (Z) dependence, energy transfer dependence, momentum transfer dependence as well as the angle dependence near θ = 180°, with the help of a simple model for the transition charge density. We compare these features with PWBA and other simple approximations. We show, as a specific example, that the C2 contribution is comparable to the M1 and E2 multipole form factors for inelastic scattering to the rotational excited states of ¹⁸¹Ta.     

Contribution of the elastic radiative tail to the deep inelastic muon scattering on heavy targets

Improvement of the radiative correction scheme for the deep inelastic scattering on the heavy targets is discussed. Arguments that the contribution of the radiative tail from the elastic peak should be calculated without the use of the Born approximation in the case of the heavy target scattering are presented. The semianalytical approach based on the classical solution of the old bremsstrahlung problem is shortly described. The numerical results for the new correction factor η are presented for the scattering on tin and lead.

     

Diffractive,refractive and interference effects in heavy ion elastic scattering

The elastic scattering amplitude is divided into contributions arising from the “near” and “far” sides of the interaction region. Each of these contributions is further divided into a diffractive component arising from strong absorption and refractive components arising from the repulsive Coulomb and attractive nuclear fields. Damped orbiting of the projectile around the target is also allowed for. Simple closed form expressions are derived for the various contributions by assuming specific forms for the elastic scattering matrix. The results are discussed by analysing several typical elastic scattering data.     

Shape effects in heavy ion (Li) elastic scattering

The elastic scattering of aligned ⁶Li and ⁷Li on ⁵⁸Ni at E_cm = 12.7 MeV displays an “isotopic” effect which can be traced to the very different (mass) quadrupole moments of both isotopes. The elastic scattering of aligned ⁶Li and ⁷Li on ^12,13C at E_Li = 9 MeV displays large effects, but the angular dependence is much more complicated compared to the scattering on ⁵⁸Ni.     

Kinetic energy contributions to heavy ion potentials

It is shown that the change in the intrinsic kinetic energies of two interacting heavy ions gives a repulsive contribution to the heavy ion interaction potential. It is proposed that this effect explains a major part of the discrepancy between folded and experimentally determined HI potentials.     

Heavy flavour contributions to the deep inelastic scattering sum rules

We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in φ³ theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading order contributions are also studied. We show that the small-x approximation does not deliver the dominant contributions.