The 4 He3 bound states and the scattering of a 4 He atom off a 4 He dimer at ultra-low energies are investigated using a hard-core version of the Faddeev differential equations. Various realistic 4 He-4 He interactions were employed, amomg them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. The ground state and the excited (Efimov) state obtained are compared with other results. The scattering lengths and the atom-diatom phase shifts were calculated for center of mass energies up to 2.45 mK. It was found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results.

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.

We present our recent results on the scattering length of 4 He-4 He 2 collisions. These investigations are based on the hard-core version of the Faddeev differential equations. As compared to our previous calculations of the same quantity, a much more refined grid is employed, providing an improvement of about 10%. Our results are compared with other ab initio, and with model calculations.PACS numbers (2001)

We review the results obtained in the last four decades which demonstrate the Efimov nature of the 4 He three-atomic system.

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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

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We present a mathematically rigorous method for solving three-atomic bound state and scattering problems. The method is well suited for applications in systems where the inter-atomic interaction is of a hard-core nature. It has been employed to obtain the ground-and excited-state energies for the Helium trimer and to calculate, for the first time, the scattering phase shifts and wave-functions for the He atom-He dimer at ultra-low energies.LANL E-print physics/9709037; Published in Chem. Phys. Lett. 275 (1997), 168-172. The4 He triatomic system is of interest in various areas of physical chemistry and molecular physics. The study of the Helium dimer and trimer properties is the first step towards the understanding of the Helium liquid drops, superfluidity in 4 He films, finite pores [1] etc. Various theoretical and experimental works have been devoted in the past to study the ground state properties of the 4 He clusters. From the theoretical works we mention here those using Variational and Monte Carlo type methods [2][3][4][5][6], the Faddeev equations [7][8][9], and the hyperspherical approach [10][11][12]. From the experimental works we recall those of Refs. [13][14][15][16] where the Helium dimer and trimer clusters 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 still have not been satisfactorily addressed. In particular for scattering processes there are no works which we are aware of apart from a zero-energy calculation of Ref. [7] and a recent study [17] concerning recombination rates. There are various reasons for this, the main one being that the threebody calculations involved are extremely difficult to perform due to the practically hard-core * On leave of absence from the Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia 1 of the interatomic interaction which gives rise to strong numerical inaccuracies that make calculations cumbersome and unstable.In this work we employed a mathematically rigorous method based on a hard-core version [18,19] of the boundary-condition model to calculate the binding energies and the ultralow energy scattering phase shifts below as well as above the breakup threshold. Such an approach takes into account, from the beginning, the hard-core nature of the He-He interatomic interaction. We show that this method is highly successful and suitable for solving three-body bound state and scattering problems in configuration space when the two-body interactions have a hard-core.In the present investigation we consider that the 4 He 3 molecule has a total angular momentum L = 0. In this case one has to solve the following, two-dimensional, integrodifferential Faddeev equations [20]Here, x, y stand for the standard Jacobi variables and c, for the core range. The angular momentum l corresponds to a dimer subsystem and a complementary atom; for the S-state three-boson system l is even, l = 0, 2, 4, . . . . V (x) ...