Three-body configuration space calculations with hard-core potentials

Abstract

We present a mathematically rigorous method suitable for solving three-body bound state and scattering problems when the inter-particle interaction is of a hard-core nature. The proposed method is a variant of the Boundary Condition Model and it has been employed to calculate the binding energies for a system consisting of three 4 He atoms. Two realistic He-He interactions of Aziz and collaborators, have been used for this purpose. The results obtained compare favorably with those previously obtained by other methods. We further used the model to calculate, for the first time, the ultra-low energy scattering phase shifts. This study revealed that our method is ideally suited for three-body molecular calculations where the practically hard-core of the inter-atomic potential gives rise to strong numerical inaccuracies that make calculations for these molecules cumbersome.LANL E-print physics/9612012.

Binding energies and scattering observables in the 4He3 atomic system

“…It is well known that the excited state of the 4 He trimer is an Efimov state [16,19,23,25,26]. The results obtained for its energy E (1) t , as well as the results found in the literature, are presented in Table III.…”

“…In this work we employ a hard-core version of the BCM [42,45] developed in [41,46] (for details see Ref. [23]). Therefore, in what follows we shall only outline the formalism and present its main characteristics.…”

“…[18] the characteristics of the He-He 2 scattering at zero energy were studied, while the recombination rate of the reaction (1 + 1 + 1 → 2 + 1) was estimated in [38]. Recently, the phase shifts of the He-He 2 elastic scattering and breakup amplitudes at ultra-low energies have also been calculated [23,39,40].…”

“…Second, the strong repulsion of the He-He interaction at short distances produces large numerical errors. In the present paper, which is an extension of our studies for 4 He 3 [23,25,26,39,40], we employed the mathematically rigorous three-body Boundary Condition Model (BCM) of Refs. [41,42] to the above-mentioned problems.…”

“…As compared to [23,25,26,39,40] we employ, in the present work, the refined He-He interatomic potentials LM2M2 by Aziz and Slaman [8], and TTY by Tang, Toennies, and Yiu [9]. Our numerical methods have been substantially improved, and this allowed us to use considerably larger grids achieving, thus, a better accuracy.…”