Semiclassical derivation of a local optical potential for heavy-ion elastic scattering

A semiclassical method to determine the contribution to the optical potential in the elastic channel due to the coupling to other processes taking place in heavy-ion collisions is developed. An application is made to the case of Coulomb excitation. The lowest-order term of our potential is shown to be identical to the potential derived by Baltz et al.     

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     

Nearside-farside analysis of aligned heavy-ion elastic scattering

The nearside-farside decomposition of scattering amplitudes is brought to bear upon analysing powers for polarized heavy-ion elastic scattering. Results for aligned ⁷Li on ⁵⁸Ni and on ¹²C show that at an incident centre-of-mass energy slightly above the Coulomb barrier all observables provide a clear signature of a nearside-dominated process. This is in consonance with the so-called shape-effect ideology which relates second-rank analysing powers with the orientation of aligned, deformed projectiles solely at the point of closest approach. At higher energies, however, the advent of Fraunhofer interference as observed in cross section and analysing powers is found to be coupled with increasing deviations from the shape-effect relations.     

Semiclassical theory of potential scattering for massless Dirac fermions

In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different regimes of scattering. To find the reflection and transmission coefficients in these regimes, we apply the Wentzel–Kramers–Brillouin (WKB), also called semiclassical, approximation. We use the method of comparison equations to extend our prediction to nearly normal incidence, where the conventional WKB method should be modified due to the degeneracy of turning points. We compare our results to numerical calculations and find good agreement.     

Estimation of nuclear effects in heavy-ion elastic scattering

The elastic scattering of heavy ions interacting by a central complex nuclear potential is calculated in first-order perturbation theory. The differential cross section can be expressed by simple analytical formulas for a Yukawa-type potential as well as for a Woods-Saxon potential. This leads to a very easy estimate of the nuclear effects, if the energy of the projectile is in the neighbourhood of the Coulomb barrier. It is shown that the derived expressions are quite accurate compared to a full numerical solution of the Schrödinger equation, as long as the elastic cross section deviates less than about 50 % from the pure Rutherford cross section.     

Strong coupling effects in near-barrier heavy-ion elastic scattering

Accurate elastic scattering angular distribution data measured at bombarding energies just above the Coulomb barrier have shapes that can markedly differ from or be the same as the expected classical Fresnel scattering pattern depending on the structure of the projectile, the target or both. Examples are given such as ¹⁸O + ¹⁸⁴W and ¹⁶O + ^{148, 152}Sm, where the expected rise above Rutherford scattering due to Coulomb-nuclear interference is damped by coupling to the target excited states, and the extreme case of ¹¹Li scattering, where coupling to the ⁹Li + n + n continuum leads to an elastic scattering shape that cannot be reproduced by any standard optical model parameter set. An early indication that the projectile structure can modify the elastic scattering angular distribution was the large vector analyzing powers observed in polarised ⁶Li scattering. The recent availability of high-quality ⁶He, ¹¹Li and ¹¹Be data provides further examples of the influence that coupling effects can have on elastic scattering. Conditions for strong projectile-target coupling effects are presented with special emphasis on the importance of the beam-target charge combination being large enough to bring about the strong coupling effects. Several measurements are proposed that can lead to further understanding of strong coupling effects by both inelastic excitation and nucleon transfer on near-barrier elastic scattering. A final note on the anomalous nature of ⁸B elastic scattering is presented as it possesses a more or less normal Fresnel scattering shape whereas one would a priori not expect this due to the very low breakup threshold of ⁸B . The special nature of ¹¹Li is presented as it is predicted that no matter how far above the Coulomb barrier the elastic scattering is measured, its shape will not appear as Fresnel like whereas the elastic scattering of all other loosely bound nuclei studied to date should eventually do so as the incident energy is increased, making both ⁸B and ¹¹Li truly “exotic”.     

Description of elastic heavy-ion scattering within the Glauber-Sitenko approach

Analytic expressions for the amplitudes of elastic nucleus-nucleus scattering for various collision regimes are derived within the Glauber-Sitenko approach. The procedure used to do this employs an extended optical potential of the Woods-Saxon type and takes into account the deflection of trajectories by a strong Coulomb field. A comparison of the analytically calculated cross sections with numerical results and experimental data shows that the approach in question can be successfully used in the energy range from 10 to 100 MeV per nucleon. It is demonstrated that, for a preset potential, it is possible to find angular ranges dominated by specific patterns of scattering, such as classical or rainbow scattering and Fresnel or Fraunhofer diffraction.     

Quantal theory of Coulomb absorption in heavy-ion scattering

The component in the heavy-ion optical potential due to the Coulomb coupling to inelastic channels has been calculated using the on-energy-shell approximation for the intermediate-channel Green's functions. Closed expressions were derived for the Coulomb polarization potential representing coupling to all orders in the K = 0 rotational band. As a test of this general aproach for coupling to higher states, elastic-scattering calculations were performed with a truncated expression which included reorientation in the 2⁺ state and coupling to the 4⁺ state to all orders. Comparison with coupled-channels calculations indicate the increasing importance of off-shell effects with increasing coupling strength. An analytical estimate of offshell effects is presented. Limits on the range of validity of the optical-potential approach are determined.     

Semiclassical theory of superradiant scattering from a Bose-Einstein condensate

A semiclassical theory of superradiant scattering of light from a Bose-Einstein condensate of a dilute atomic gas is proposed. Choosing atomic states with definite values of the momenta as a basis, we derive a nonlinear Schrödinger equation. Its solutions describe the evolution of the scattered light intensity and of the populations of the coherent atomic states with different recoil momenta.     

Phase shift analysis of heavy-ion elastic scattering measured at intermediate energies

An elastic scattering phase shift analysis based on McIntyre parametrization is presented. It has been applied to¹²C+¹²C system at 360- and 1,016 MeV incident energies as well as to¹⁶O scattering on¹²C,⁴⁰Ca,⁹⁰Zr and²⁰⁸Pb targets at 1,503 MeV. The success of this model allows the interplay between diffraction and refraction to be pinned down: a presence of a nuclear rainbow is clearly evidenced in several cases.     

Complete set of deuteron analyzing powers for dp elastic scattering at intermediate energies

With the aim of clarifying roles of the 3NFs in nuclei experimental programs with polarized deuterons beams at intermediate energies are in progress at RIKEN RI Beam Factory. As the first step, we have measured a complete set of deuteron analyzing powers (iT ₁₁, T ₂₀, T ₂₁, T ₂₂) in deuteron-proton elastic scattering at 250 and 294 MeV/nucleon. The obtained data are compared with the Faddeev calculations based on the modern nucleon-nucleon forces together with the Tucson-Melbourne’99, and UrbanaIX three nucleon forces.     

Differential cross sections and analyzing powers for pd elastic scattering below 1.0 MeV

Differential cross sections for the elastic pd scattering were measured at seven energies between 0.4 and 1.0 MeV for scattering angles from θ_c.m. = 44.5° to 149.2°. A mixture of D₂ and Kr was used as target gas and the pd differential cross sections were determined relative to those of pKr scattering with a statistical error of $\text{Δσ}\text{σ}$ ～5 × 10^?3. Analyzing powers for $\text{p}$d scattering were measured at 0.8, 0.9 and 1.0 MeV with a statistical error of ΔA_y ～5 × 10^?4.     

Precision measurement of vector and tensor analyzing powers in elastic deuteron-proton scattering

High-precision vector and tensor analyzing powers of elastic deuteron-proton ( d + p) scattering have been measured at intermediate energies to investigate effects of three-nucleon forces. Angular distributions in the range of 70^°-120^° in the center-of mass frame for incident-deuteron energies E _d ^lab = 130 and 180 MeV were obtained using the RIKEN facility. The beam polarization was unambiguously determined by measuring the ^12C (d, α)^10B(2⁺) reaction at 0^°. Results of the measurements are compared with state-of-the-art three-nucleon calculations. The present modeling of nucleon-nucleon forces and its extension to the three-nucleon system is not sufficient to describe the high-precision data consistently and requires, therefore, further investigation.