T. K. Lim

A study of the Efimov states and binding energies of the helium trimer through the Faddeev‐coordinate–momentum approach

A thorough bound state analysis of the helium trimer is made using the Faddeev equations with form factors generated by a modified Kowalski–Feldman approach. The presence of Efimov states is manifested by each of the realistic potentials considered.

Mixed and fermionic helium trimers

The existence of mixed and fermionic helium trimers is investigated via the Faddeev–UPE method. Each three‐atom system is assumed to interact through phenomenological pairwise local potentials. The ground‐state binding energy of (4He)2–3He is evaluated to be about 0.000 002–0.0008 °K while (3He)2–4He is found to be unbound as is (3He)3.

The Ramsauer–Townsend effect in molecular systems of electron‐spin‐polarized hydrogen and helium and their isotopes

From arguments based on the De Boer quantum parameter and accurate phase shift calculations, we predict that the Ramsauer–Townsend effect occurs in numerous molecular systems involving electron‐spin‐polarized hydrogen and helium and their isotopes. Our work raises prospects of more precise determination of the two‐body potential parameters of these systems as well as exciting quantum behavior in their macroscopic states.

On the existence of bound helium trimers by the equivalent two‐body method

The binding energies of the 3,4He trimers are computed for a range of realistic interatomic potentials using the equivalent two‐body method of Bodmer and Ali. We find a 4He trimer bound with a binding energy of about 0.25°K and a 3He trimer which is but loosely bound. We also confirm that the Hall–Post–Stenschke method gives poor lower bounds to the energy and that (4He)3 is large, having a root mean square interparticle spacing of 23 A.

Faddeev–UPE theory and the three 4He‐atom system: Bound states and zero‐energy atom–diatom scattering

Faddeev–UPE theory is applied to the trimer bound states and atom–diatom scattering of 4He. (4He)3 has two bound states while the scattering length of 4He– (4He)2 is 207 A.

Effective‐range theory in two dimensions

A parametrization of low‐energy two‐dimensional quantum scattering is given which is in the tradition of familiar three‐dimensional effective‐range theory. A scattering length differing from previous treatments is introduced whose behavior reflects the repulsive or attractive nature of the interaction, and whether or not bound states are present. However its definition is subject to an unknown length parameter. An effective‐range parameter is also defined and together with the scattering length explains the nonexistence of the Efimov effect in two dimensions. It is also shown that the Ramsauer–Townsend effect exists in 2D. Application to the case of a square‐well potential reveals direct relationships between the unknown length parameter and the effective range to the actual range of the potential.

Faddeev-UPE theory and three 4He atoms interacting through realistic diatomic potentials

The first successful application of Faddeev-UPE theory to the binding energy of the ground state of three 4He atoms interacting through realistic intermolecular potentials is reported. (4He)3 is probably bound by about 0.1 K.

The role of vibrational excitations in collision‐induced dissociation using Faddeev–AGS theory

This paper examines the role of vibrational (and rotational) excitations in collision‐induced dissociation in atom–diatom reactions. We treat a model system of identical, bosonic hydrogen atoms and investigate the total H+H2→H+H+H cross section as functions of total center‐of‐mass (c.m.) energy and vibrational–rotational quantum numbers v, j. The investigations are based on Faddeev–AGS theory and both three‐dimensional (3D) and collinear (one‐dimensional, 1D) geometries are considered. We derive both low‐ and high‐energy relations between the total dissociation cross section, c.m. energy, and the vibrational–rotational wave functions, employing the single‐scattering approximation of Faddeev theory. We apply these relations to the spectrum of the Kolos–Wolniewicz potential, both in three dimensions and one dimension. For collisions with a fixed total c.m. energy, our investigations predict considerable vibrational enhancement of the total cross section in the low‐energy limit, with this enhancement much mo...

The quantum‐mechanical second virial coefficients of electron‐spin‐polarized atomic hydrogen and its admixtures with the isotopes of helium

The quantum‐mechanical second virial coefficient of electron‐spin‐polarized atomic hydrogen H↑ and the second cross virial coefficients of H↑–3He and H↑–4He have been calculated for a range of temperatures using a Lennard‐Jones 12‐6 potential in each case. Our results indicate that the exchange (spin and quantum statistics) contributions for H↑ drop rapidly with increasing temperature. The Boyle temperature for H↑ occurs at a reduced temperature T*B = 0.25. Those for H↑–3He and H↑–4He are at T*B = 0.53 and 0.74, respectively.

Heavy rare‐gas trimers and tetramers: Testing ground for few‐body techniques in chemical physics

The ground‐state energies of systems of three and four identical heavy rare‐gas atoms, treated as spinless bosons and assumed to interact via pairwise Morse potentials, are calculated using five different methods. Self‐bound trimers and tetramers are found in every case with upper and lower bound formulas yielding energies which are extremely close. For these near‐classical and massive systems, the Faddeev–UPE method is decidedly poor. On the other hand, the simple generalization of Bruch–Sawada’s upper bound is particularly effective. The plight of Faddeev–UPE here implies that great caution must be exercised in using the unitary pole expansion in chemical physics. ATMS is excellent and appears the method of choice for bound‐state problems.