Ultralow energy scattering of a He atom off a He dimer

Abstract

We present a new, mathematically rigorous, method suitable for bound state and scattering processes calculations for various three atomic or molecular systems where the underlying forces are of a hard-core nature. We employed this method to calculate the binding energies and the ultra-low energy scattering phase shifts below as well as above the break-up threshold for the three He-atom system. The method is proved to be highly successful and suitable for solving the three-body bound state and scattering problem in configuration space and thus it paves the way to study various three-atomic systems, and to calculate important quantities such as the cross-sections, recombination rates etc.LANL E-print physics/9802016. Published in Phys. Rev. A., 1997, v. 56, No. 3, pp. 1686 The 4 He trimer is of interest in various areas of Physical Chemistry and Molecular Physics, in particular such as the behavior of atomic clusters under collisions and BoseEinstein condensation. Various theoretical and experimental works have been devoted in the past to study its ground state properties and in general the properties of the 4 He and other noble gas droplets. From the theoretical works we mention here those using Variational and Monte Carlo type methods [1][2][3][4][5], the Faddeev equations [6][7][8], and the hyperspherical approach [9][10][11]. From the experimental works we recall those of Refs. [12][13][14][15] where molecular clusters consisting of a small number of noble gas atoms were investigated.Despite the efforts made to solve the He-trimer problem various questions such as the existence of Efimov states and the study of scattering processes at ultra-low energies still have not been satisfactorily addressed. In particular for scattering processes there are no works which we are aware of apart from a recent study concerning recombination rates [16]. There are various reasons for this the main one being the fact that the three-body calculations * On leave of absence from the

Binding energies and scattering observables in the 4He3 atomic system

“…The value of c was fixed to be such that any further decrease of it did not appreciably influence the dimer binding energy ǫ d and the energy of the trimer ground state E (0) t . In our previous work [23,39,40] c was chosen as 0.7Å. In the present work, however, we choose c = 1.0Å.…”

“…The use of this method makes it possible to avoid writing the matrix on the hard drive of the computer. Besides, the matrix sweep method reduces the computer time required by almost one order of magnitude as compared to [23,39,40].…”

“…[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].…”

“…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.…”

“…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.…”