Proton-hydrogen collisions at low temperatures

Abstract

We study the proton-hydrogen collision in the energy range from 0 to 5 K where the hyperfine structure of the hydrogen atom becomes important. A proper multichannel treatment of the hyperfine structure is found to be crucial at cold temperatures compared to the elastic approximation traditionally used at higher temperatures. Both elastic and hyperfine-changing inelastic processes are investigated, using both the multichannel quantum-defect theory (MQDT) and the coupled-channel numerical method. Results from the two methods show excellent agreement with MQDT providing an efficient and basically analytic description of the proton-hydrogen interaction throughout this energy range. We also discuss the validity of the elastic approximation and its relation to other methods.

Near-threshold scaling of resonant inelastic collisions at ultralow temperatures

“…While some computational studies did observe the k −1 scaling [16,21,39] others reported that the ICS for atomic EE collisions approach a constant value [35,38,40,41], a highly unexpected observation that has, to our knowledge, remained unexplained. Several authors attributed the k 0 scaling to a deficiency of the elastic approximation [55][56][57], which effectively neglects the hyperfine structure of colliding atoms [19,38,39]. More recently, the constant near-threshold scaling of spin-exchange cross sections was claimed to be incorrect [39], further deepening the existing controversy surrounding the threshold behavior of EE collisions.…”

“…It is commonly believed that the inelastic ICSs scale as k −1 with the incident collision wavevector k in the limit k → 0 [53,54]. While some computational studies did observe the k −1 scaling [16,21,39] others reported that the ICS for atomic EE collisions approach a constant value [35,38,40,41], a highly unexpected observation that has, to our knowledge, remained unexplained. Several authors attributed the k 0 scaling to a deficiency of the elastic approximation [55][56][57], which effectively neglects the hyperfine structure of colliding atoms [19,38,39].…”

“…Spin-exchange collisions, in particular, play an important role in a wide array of research fields, ranging from spin-exchange optical pumping [14][15][16][17], cold chemistry [20,21,32], precision magnetometry [18], and astrophysics [37][38][39][40][41] to quantum many-body physics [22][23][24][25] and quantum information processing, where they are used to generate entangled states [42,43] and to operate quantum logic gates [44][45][46][47][48]. Recent experiments observed spin-exchange collisions of ultracold alkalimetal atoms [49,50], Förster resonant energy transfer in Rydberg atom collisions [28][29][30], and electric fieldinduced resonances in collisions of rotationally excited KRb molecules [7].…”

“…Several authors attributed the k 0 scaling to a deficiency of the elastic approximation [55][56][57], which effectively neglects the hyperfine structure of colliding atoms [19,38,39]. More recently, the constant near-threshold scaling of spin-exchange cross sections was claimed to be incorrect [39], further deepening the existing controversy surrounding the threshold behavior of EE collisions.…”

Multichannel quantum-defect theory for anisotropic interactions

“…Specifically, we expect, to the lowest order, approximately one parameter per potential energy curve (PEC) and a few parameters per potential energy surface (PES), with allowance for a few more coupling constants if there are multiple curves and/or surfaces that cross or interact strongly in the short range. For atom-atom interactions, this efficient parameterization is accomplished through a frame transformation [34,57], and has been fully demonstrated for alkali-alkali interactions in the context of isotropic MQDT [29,34,43,[115][116][117][118][119][120][121]. In MQDTA, the more general frame transformations of Ref.…”