Two-center interference in fast proton–H2-electron transfer and excitation processes

Abstract

We present experimental evidence for a strong dependence on the angle between the molecular axis of H 2 and the direction of the incoming projectile ͑p͒ in the cross section for transfer excitation in fast p-H 2 collisions. For collision energies of 1.0 and 1.3 MeV we find good agreement between the observed data and an analytical expression based on a two-atomic-center description using Brinkman-Kramers amplitudes. This clearly shows that the observed angular dependence is a result of quantum mechanical interference and not a trivial geometrical effect.Experimental indications and verifications of quantum mechanical interference effects continue to spur considerable interest and discussions, although such effects are wellknown consequences of the wave description of matter ͑which has been around for almost a century͒. One example of a recent discussion concerns the observation of interference effects in electron emission from randomly oriented H 2 molecules in fast charged-particle collision ͓1-7͔. In this Rapid Communication we report on collisions between fast protons and fixed-in-space H 2 where we observe strong interferences of electron-transfer amplitudes for the two centers leading to molecular-orientation dependences in the electron transfer cross section. In 1960 Tuan and Gerjuoy ͓8͔ formulated the problem of electron transfer in atom-molecule collisions in terms of a separated-atoms picture with interfering electron-transfer amplitudes. A similar description for scattering amplitudes was employed by Deb et al. ͓9͔ in 1988 considering the "two-slit" problem of high-velocity electron capture from an oriented hydrogen molecule for which the projectile has to pass close by one of the target nuclei ͓10͔. Shingal and Lin ͓11͔ used a semiclassical approach in combination with close-coupling electron transfer amplitudes to calculate strong variations in electron transfer cross sections as functions of the molecular orientations for 1 -500 keV. Later Wang, McGuire, and Rivarola ͓12͔ deduced an analytical expression, based on Brinkman-Kramers amplitudes ͓13͔, and valid for high energies ͑ജ1 MeV͒.Due to the very small electron-transfer cross sections at high energies ͓14͔, experiments are difficult and the only earlier investigation of the molecular orientation dependence was performed with O 8+ increasing the count rate by a large factor ͓15͔ in relation to the proton projectile case. However, using O 8+ instead of protons makes comparisons with model calculations that rely on small values of the projectile charge-to-velocity parameter Z p / v p , more difficult. Further-more capture to excited projectile states becomes important as the projectile charge is increased ͓16͔. In the present paper we have utilized the unique properties of the ion storage and cooler ring CRYRING with its internal gas-jet target to improve the luminosity by orders of magnitude compared to earlier studies ͑c.f. ͓17-20͔͒. This has allowed us to investigate two-center interference effects in electron-transfer for p H 2 with Z p = 1 and v...

Two-site double-core-hole states formed when fast protons capture electrons from aligned N2

“…We interpret this as a result of two contributions. First, the general contribution from the electron transfer process itself possibly through a similar projectile interference effects as observed earlier for hydrogen targets [15,17]. Second for the higher atomic target fragment charge states, there is an enhancement for orientations where the molecular axis is (close to) aligned with the projectile trajectory.…”

“…This surprising result would call for further experimental investigations before any conclusions can be made. In the p + H 2 case [15], the projectile-wave interference was nicely demonstrated by the variation of the position of the minimum with projectile velocity. In the case of p + N 2 core-electron capture a 2.0 Mev projectile kinetic energy would give δka ≈ 4.4 and a minimum in the orientation dependent cross section for θ ≈ 44…”

“…In earlier studies of transfer and excitation in p + H 2 collisions [15] a similar strong orientation dependence could be explained by the well-defined changes in projectile momentum (and thus deBroglie wavelength) that accompanies the electron capture in the vicinity of either target proton. For capture of a target electron from an initial state of gerade symmetry it was predicted [34,35] and later found [15,17] that constructive interference gives a maximum in the cross section for the transverse orientation of the molecular axis with respect to the incoming projectile direction. The same reasoning predicts that there should be minima due to destructive interferences at specific orientations (θ) given by the momentum gained by the projectile (≈ v P /2, where v P is the projectile velocity) when an electron is captured.…”

“…This was the first partly successful attempt to establish effects of two-slit projectile wave interference in fast electron-transfer collisions. Much later, similar effects were investigated in more detail by means of a COLTRIMS apparatus where strong interference effects were observed for electron-transfer reactions in H + + H 2 [15] and He 2+ + H 2 [16] collisions as variations in the total projectile neutralisation cross sections with molecular orientation. Further the two-slit interference was demonstrated more directly through measurement of markedly different projectile angular scattering distributions for different molecular orientations in the p + H 2 case [17].…”

Role of Projectile Coherence in Close Heavy Ion-Atom Collisions

“…At large projectile speeds capture is known to occur at much smaller b than ionization [32][33][34]. Therefore, with the right choice of ∆r we can realize ∆r < ∆b for pure single ionization and ∆r > ∆b for ionization accompanied by capture (transfer-ionization, TI) simultaneously in the same experiment.…”