Semiclassical calculation of heavy-ion scattering in the chaotic regime

Abstract

The semiclassical approach has proven to be a most valuable tool for the construction of the scattering matrix and accurate evaluation of cross sections in a large variety of heavy-ion collision problems. In its familiar implementation, however, its use is restricted to what is now known as the "regular regime", as it makes use of classical reaction functions that must be continuous and interpolable. In this paper we identify what version of the semiclassical formalisms may be especially suitable for extension into the chaotic regime that develops at energies close to the Coulomb barrier. We also show the crucial role of the absorptive part of the ion-ion potential to retain the usefulness of the semiclassical methods under conditions of irregularity.

Semiquantum approach for fast atom diffraction: Solving the rainbow divergence

“…Precisely, this IVR strategy makes it possible to avoid the classical rainbow divergence, incorporating an approximate description of classically forbidden transitions in terms of real-valued trajectories [25]. The IVR solution has been successfully applied to different branches, providing accurate transition probabilities for several atomic, molecular and nuclear processes [25,26,[29][30][31][32][33]. In most of these cases, IVR results are in excellent agreement with the corresponding full quantum values.…”

Dynamical effects as a window into van der Waals interactions in grazing-incidence fast He-atom diffraction from KCl(001)

“…The SIVR approximation is based on the well-known IVR approach [20] which, within a Feynman path integral formulation of quantum mechanics, introduces Van Vleck's approximation [21] for the quantum time-evolution operator, without the additional stationary phase approximation, of customary use in semiclassical methods. The IVR method provides results in excellent agreement with the full quantum values for a wide variety of atomic, molecular and nuclear processes [20,[22][23][24][25][26][27], which demostrates its ability to describe quantum effects in complex systems evolving over time.…”

Semiclassical initial value theory of rotationally inelastic scattering: Some remarks on the phase index in the interaction picture

“…In an illuminating analysis, McCurdy and Miller 66 showed within a planar model of atom-diatom inelastic collision that the semiclassical theory of molecular collision [42][43][44][45][46][47][48][49][50][51][52][53][54][55] not only reproduces the previous interference features, but also provides deep insight into their physical origin. The primary reason for this success is that, as previously stated, semiclassical methods assign probability amplitudes and phases to classical trajectories and make them interfere, respecting thereby the quantum principle of superposition.…”

“…These calculations may require quantum corrections to improve their accuracy, like the use of Wigner distributions, 14,30 one-dimensional tunneling probabilities, [31][32][33][34][35][36] Gaussian binning, 8,13 surface hopping, [37][38][39][40][41] etc., but contrary to semiclassical calculations, [42][43][44][45][46][47][48][49][50][51][52][53][54][55] they do not assign probability amplitudes and phases to classical paths. In this regard, the classical trajectory method mostly ignores the wave character of nuclear motions involved in molecular processes.…”

“…[57][58][59][60][61][62][63][64][65] This is likely due to major and somehow discouraging numerical difficulties encountered in the application of semiclassical scattering methods, especially when the dynamics involves trapped trajectories. 53 However, the processes under scrutiny in stereodynamical studies [57][58][59][60][61][62][63][64][65] involve a single rebound mechanism and hence, no trapping. For such type of encounters, at least two previous works by Miller 74 and Campolieti and Brumer 49 suggest that realistic (full-dimensional) semiclassical calculations should be feasible.…”