Ultra-cold ion–atom collisions: near resonant charge exchange

Abstract

Abstract. Accurate calculations of the near resonant charge exchange crosssections in HD + , HT + and DT + at very low energies are presented. The charge exchange process between an ion and its parent atom is a near resonant process that becomes inelastic when two different isotopes are involved. We find that, at very low energies, the charge exchange cross-section follows Wigner's law for inelastic processes and becomes much larger than the cross-section for elastic collisions which tends to a finite limit. The efficiency of inelastic charge exchange increases as the mass difference between the two isotopes decreases. Contents

Quantization rule for highly excited vibrational states of H

“…This result differs from the values near �29 au as obtained in [27,28], but is very robust; it does not depend on which of the various reference potentials V tail (R) is chosen, and it does not require any assumptions concerning the p-H interaction at small distances.…”

“…The further entries in the last column in Table 3 show that the values predicted for the scattering length consistently lie in the range �30.5 to �31 au, regardless of which reference potential is chosen for V tail (R). This can be compared to the results of two sophisticated ab initio calculations for the full three-body ppe system [27,28]. In [27] the authors obtained a ¼ �29.3 au on the basis of the solution of the appropriate Faddeev equations.…”

“…In [27] the authors obtained a ¼ �29.3 au on the basis of the solution of the appropriate Faddeev equations. In [28] the authors obtained a ¼ �28.8 au from a calculation of elastic p-H scattering crosssections down to very low energies.…”

“…The consideration of relativistic corrections and QED Figure 3. Scattering length a according to (11) [27] and [28], respectively. (24) containing only then leading contributions to V pol and V ex [23], while the solid line includes all terms given by Damburg and Propin [24], see Equations (16), (17).…”

Quantum-defect theory for−1/r4-type interactions

“…Third, ion-atom and ion-molecule interactions are extremely sensitive to the short-range potential [32,33], due again to their large reduced mass [34]. With the exception of H + +H and its isotopic variations [35][36][37][38], this sensitive dependence makes most theoretical predictions based on ab initio potentials unreliable. QDT and related multichannel quantum-defect theory (MQDT), especially though their partial-wave insensitive formulations [28,39], offer a prospect to overcome this difficulty by reducing their description to very few parameters that can be determined with a few experimental data points [32,[40][41][42][43], without relying on the precise knowledge of the shortrange potential [33].…”