Loss of wave-packet coherence in ion-atom collisions

Abstract

The projectile beam coherence effects occurring in ion-atom collisions are analyzed on the basis of the recent theory of Karlovets et al. [Phys. Rev. A 92, 052703 (2015)] developed for the elastic scattering of wave packets of particles off a potential field. This theory is generalized to estimate the loss of coherence for inelastically scattered projectiles in ionizing collisions. The results obtained by the suggested model are compared with experimental data for the ionization of hydrogen atoms and molecules by 75-keV proton impact. Significantly improved agreement is observed between the theory and experiment. DOI: 10.1103/PhysRevA.93.032702 In a recent work Karlovets et al.[1] investigated theoretically the scattering of wave packets of nonrelativistic particles off a potential field. The authors derived a simple general expression that determines the number of scattering events for the case when the incident particle beam is a wave packet of arbitrary form but with its mean momentum strongly centered at a given value p i . Furthermore, they considered the example when the wave packet is scattered off randomly distributed potential centers. By averaging the number of events over the impact parameter between the potential center and the wave packet axis, they derived a formula for the effective cross section that reproduces the one obtained by previous authors (see, e.g., [2,3]where dσ /d | q i →q f is the differential cross section for the elastic scattering in an angle θ = arccos(q i ·q f ). Furthermore, by writing (k) = ⊥ (k ⊥ ) (k ), with strongly centered on p i , they obtainedKarlovets et al. carried out sample calculations for the case of electron impact, applying the Born approximation. They considered the collisions of a Gaussian wave packeton a Gaussian potential as well as on the hydrogen atom. Here σ ⊥ is the averaged transverse size of the wave packet. As a remarkable result, they found that the angular distributions of the effective cross section broaden with the decrease of σ ⊥ . [4] could control the coherence properties of the ion beam and thereby demonstrate the effect of the projectile coherence on the angular distribution of the scattered protons. The principle of the experiment is based on the van Cittert-Zernike theorem according to which the transverse coherence length r (the diameter of the area of coherence) of a source of waves at a distance L is of the order of λ/kα, where λ is the wavelength, α is the angular diameter of the source, and k is a dimensionless constant.Egodapitiya et al. used a well-collimated nearly monochromatic [< 1 eV full width at half maximum (FWHM)] proton beam that crossed a molecular hydrogen beam. The measured quantity was the doubly differential cross section (DDCS) for the ionization as a function of the scattering angle θ and the energy loss of the protons. The measurements were made at two coherence length values corresponding to two values of the distance between the target and the last aperture of the collimator, L = 6.5 and 50 cm. The diameter of t...

Theoretical investigation of the fully differential cross sections for single ionization of He in collisions with 75-keV protons

“…Applying the method of the authors of Ref. [40], good agreement with the experimental data for the 75-keV H + -H 2 collision was reported in [18]. Wave-packet effects for the projectile have been questioned for the case 100-MeV/amu C 6+ -He collision due to the very low transverse coherence length, and instead wave-packet effects related to the target are suggested for the explanation [8,41].…”

“…However, it should be noted that the numerical result presented for demonstrating the idea of the authors of Ref. [17] was based on incorrect estimation of the divergence for the projectile beam [5,18]. For atomic targets the size of the diffracting object is the typical impact parameter separation between the contributing processes, like first-and higher-order transition mechanisms [5].…”

Relativistic vortex electrons: Paraxial versus nonparaxial regimes

“…Depending on a problem, this may happen when the beam is focused to a spot of a size σ ⊥ comparable to a Bohr radius, a ≈ 0.053 nm, or to an electron's Compton wavelength, λ c = /mc ≈ 0.39 pm. As the vortex electrons have already been focused to a spot of σ ⊥ 0.1 nm ≈ 2a [3], a more realistic wave-packet approach beyond the paraxial approximation is needed, in particular, for proper study of the spin-orbit phenomena and for scattering problems in atomic and high-energy physics, especially when the quantum interference and coherence play a notable role [4][5][6]. The quantum interference of the incoming packets is of crucial importance -say, for potential applications in hadronic physics [7] -and the orthogonal Bessel states do not describe these effects.…”

Fully Differential Study of Capture with Vibrational Dissociation in p+H2 Collisions

“…In contrast, for η close to unity by now there is an extensive literature on experimental and theoretical studies [e.g. [15][16][17][18]20,26,27] supporting the interpretation that scattering cross sections can be significantly affected by the projectile coherence properties. In this regime, experimental studies now enter a phase in which such coherence effects are used as a tool to sensitively investigate the few-body reaction dynamics.…”

“…[15][16][17][18][19][20]). Experiments were performed for different transverse coherence lengths of the projectiles by placing a collimating slit at varying distances from the target.…”