Scattering of hydrogen atoms at low temperature

Abstract

A non-adiabatic model is employed to investigate the H-H scattering at low temperatures. Unlike molecular-orbital calculation technique, no separate calculations are required to obtain the potential energies of electrons in the field of hadrons. This model generates the non-adiabatic effective potential automatically. The coefficients of van der Waals and higherorder potentials are estimated in the present model and are found to be in very good agreement with the corresponding standard values. The s-wave singlet and triplet scattering lengths and thermal-average total triplet cross-section at 2 K are reported and compared with the existing theoretical and experimental predictions.Introduction. -One of the major motivating factors in the study of collisions of cold ground-state neutral atoms has been the quest to achieve Bose Einstein condensation (BEC). BEC of atoms is now being experimentally observed [1][2][3]. The positive scattering length of atom-atom scattering in triplet state at low energies is one of the conditions for the formation of stable BEC. Out of all atom-atom scattering, the H-H scattering system is the simplest system to be investigated theoretically and the most celebrated atomic-collision problem. BEC of hydrogen atoms was successfully detected in 1998 by Fried et al. [4]. During the last decade several theoretical groups have paid renewed attention to the problem of the scattering of hydrogen atoms using standard molecular-orbital (M-O) technique which is adiabatic in nature. All these models are actually based on Born-Oppenheimer (B-O) approximation in which coupling between the nuclear and the light particle motion is neglected. In atom-atom scattering low-energy scattering parameters are very sensitive to the potential employed. In these models B-O potentials are calculated at some discrete points of hadronic separation and these points are then fitted to the long-range potentials (van der Waals and higher-order interactions). The B-O potential employed for the H-H scattering system is systematically improved during the span of the last thirty years [5][6][7][8][9][10][11]. The effect of electron exchange in the asymptotic region is approximated via a local exchange potential of Herring and Flicker [12]. The s-wave singlet and triplet scattering parameters obtained by several theoreticians differ appreciably from each other (see [13,14] and the references therein). These investigations are considered as the first phase of calculations up to 1990. On the other hand, Hershcovitch [15]

Scattering properties of dark atoms and molecules

“…We find scattering lengths a s = 0.28 and a t = 1.37. These are in reasonable agreement with values found by other authors; for example, determinations of a t in the atomic physics literature range from 1.2 to 2 [23]. Our values agree with those of [24].…”

Low-energy universality and scaling of van der Waals forces

“…(17). Alternatively, and discarding the exceptional outliers for α 0 [24,25,26] (Li-Li,Na-Na), [27] (Cs-Cs), [28] (Na-Rb), [29] (Be-Be), [30] (Cs-Rb), [31] (Cr-Cr), [32] (Fr-Fr), [33,34,35,36] (H-H), [36] (He-He). The line corresponds to Eq.…”

Renormalization and Universality of Van der Waals forces

“…Thus, the short distance cut-off r c is a parameter for kR 6 ≫ 1 but becomes innocuous otherwise when r c ≪ R 6 implying that universality is robust. We show for a sample case in [37] (Li-Li,Na-Na), [38] (Na-Na), [39] (Cs-Cs), [40] (Cs-Cs), [41] (Na-Rb), [42] (Be-Be), [43] (Cs-Rb), [44] (Cr-Cr), [45] (Fr-Fr), [46] (H-H), [47] (H-H), [48] (H-H), [49] (H-H). Fig.…”