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The Journal of Chemical Physics

Boson trimers with nonzero total angular momenta

Ludwig W. Bruch

Published Feb 1, 1999• 15 citations
Publisher

Abstract

The lowest energy states of van der Waals trimers of identical spinless bosons with one and two units of total angular momentum are examined. Parameters corresponding to He4 and para-H2 are treated and the relation of the results to level orderings for the rotation of rigid symmetric molecules is discussed. The 2+ rotational state of the para-H2 trimer is bound by 3 K relative to the dimer, while the rotational states of He34, if any, have binding energies of less than 1 mK relative to He24.

DOI
10.1063/1.477946

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The lowest energy states of van der Waals trimers of identical spinless bosons with one and two units of total angular momentum are examined. Parameters corresponding to He4 and para-H2 are treated and the relation of the results to level orderings for the rotation of rigid symmetric molecules is discussed. The 2+ rotational state of the para-H2 trimer is bound by 3 K relative to the dimer, while the rotational states of He34, if any, have binding energies of less than 1 mK relative to He24.
We discuss the bound states of weakly bound van der Waals trimers within the framework of hyperspherical coordinates. The wave function is expanded in terms of hyperspherical harmonics, which form a complete basis set in the angular variables. The resulting set of coupled second-order differential equations in the hyperradius is solved exactly. Our method gives a value for the zero-point energy of H+3 which is in excellent agreement with previous calculations. For (H2)3 and Ne3, however, our results show some discrepancy with earlier work.
When studying the structure formation and fragmentation of complex atomic and nuclear systems it is preferable to start with simple systems where all details can be explored. Some of the knowledge gained from studies of atomic dimers can be generalised to more complex systems. Adding a third atom to an atomic dimer gives a first chance to study how the binding between two atoms is affected by a third. Few-body physics is an intermediate area which helps us to understand some but not all phenomena in many-body physics.Very weakly bound, spatially very extended quantum systems with a wave function reaching far beyond the classical forbidden region and with low angular momentum are characterized as halo systems. These unusual quantum systems, first discovered in nuclear physics may also exist in systems of neutral atoms.Since the first clear theoretical prediction in 1977, of a halo system possessing an Efimov state, manifested in the excited state of the bosonic van der Waals helium trimer 42He3, small helium and different spin-polarised halo hydrogen clusters and their corresponding isotopologues have been intensively studied the last three decades.In the work presented here, the existence of the spin-polarized tritium trimer ground state, 31H3, is demonstrated, verifying earlier predictions, and the system's properties elucidated. Detailed analysis has found no found evidence for other bound states and shape resonances in this system. The properties of the halo helium trimers, 42He3 and 42He2-32He have been investigated. Earlier predictions concerning the ground state energies and structural properties of these systems are validated using our three-dimensional finite element method. In the last part of this work we present results on the bound states and structural properties of the van der Waals bosonic atomic trimers Ne3 and Ar3. We believe to be the first to find evidence of a possible shape resonance just above the three-body dissociation limit of the neon trimer.
We have searched for bound states of helium trimers with nonzero angular momenta. Including only pair interactions between helium atoms, we solved the Schrödinger equation in hyperspherical coordinates in the adiabatic approximation. From the resulting potential curves - which are mostly repulsive for nonzero angular momenta - we conclude that there are no bound rotational excited states in any of the isotopes of the helium trimer. The symmetry properties of the trimer wavefunctions in the body-fixed frame are also analysed.