Asymmetric deflection functions and the extinction of rainbows: A comparison of α-particle scattering from 40Ca and 44Ca

Dynamic polarization effects on the angular distributions of protons channeled through carbon nanotubes in dielectric media

“…The system under investigation is a proton moving through an (11,9) SWNT surrounded by a dielectric medium. The z-axis coincides with the nanotube axis and the origin lies in its entrance plane.…”

“…However, ions moving with medium (MeV) energies will induce strong dynamic polarization of valence electrons in the nanotubes which in turn will give rise to a sizeable image force on the ions, as well as a considerable energy loss due to the collective, or plasma, electron excitations. The dynamic image force has been recently shown to give rise to the rainbow effect in the angular distributions of protons channeled through short (11,9) single-wall [6] and double-wall carbon nanotubes [7] in free space, which is not otherwise observable in simulations of ion channeling through chiral carbon nanotubes using the continuum approximation for the interaction potential [1]. Obviously, the presence of dielectric media may affect these dynamic polarization forces, as well as the resulting ion trajectories, making the analysis of such effects in ion channeling through carbon nanotubes a timely task, which we take up in this contribution.…”

“…The rainbow effect occurs and plays an important role in photon scattering from water droplets [8,9], nucleusnucleus collisions [10,11,12], atom or ion collisions with atoms or molecules [13], electron-molecule collisions [14], atom or electron scattering from crystal surfaces [15,16], and ion channeling in crystals [17,18]. Moreover, the rainbow effect has been investigated recently in the context of grazing scattering of atoms from metal surfaces under channeling conditions by Schüller et al [19] who showed that precise measurements of the well-defined maxima in the angular distributions of scattered atoms, attributed to the rainbow effect, can give detailed information on the interaction potential of the atoms with the metal surfaces.…”

Interpretation of airy minima in 16O+16O and 16O+12C elastic scattering in terms of a barrier-wave/internal-wave decomposition

“…While the forward angle Fraunhofer oscillations are readily understood in the nearside-farside picture in terms of an interference between f N and f F , the Airy minima, which are observed here around 60 • , 90 • , and 120 • in the farside contribution to the amplitude, can only be explained if one assumes [1,13,14] that two different ranges of angular momenta, < and > , contribute to f F (Fig. 1).…”

“…While we interpret the minima around 60 • and 90 • as being due to an interference between the barrierwave and internal-wave contributions to the scattering amplitude, these minima have repeatedly been interpreted in previous works (see, e.g., [1]) as resulting from an interference in the farside amplitude between the contributions of the two ranges of angular mo- menta < and > alluded to above. The contributions σ F,< and σ F,> of these two ranges to the farside cross section have sometimes been extracted in an approximate way using the so-called interpolatedenvelope technique [13,18]. These two contributions can be obtained in a more natural and more rigorous way by performing a nearside-farside decomposition of the barrier-wave and internal-wave amplitudes themselves; this decomposition is performed in an automatic way by replacing the Legendre polynomials by the functionsQ (−) andQ (+) in the partial wave series for the barrier-wave and internal-wave amplitudes.…”