Rotation±vibration interaction in 4 He trimers T. Gonz alez-Lezana a , D. Lopez a , S. Miret-Art es a , F.A. Gianturco b , G. Delgado-Barrio a , P. Villarreal a, * a Instituto de Matem aticas y F  õsica, Fundamental, Consejo Superior de Investigaciones Cient  õ®cas, Serrano, 123, 28006 Madrid, Spain b Department of Chemistry, The University of Rome, Citt  a Universitaria, I-00185 Rome, Italy Received 5 October 2000; in ®nal form 7 November 2000 Abstract An approximate treatment of the rotation±vibration interaction is considered in the helium trimer system to study the existence of bound states with non-zero J  1) total angular momentum and to elucidate its E®mov character. With the interaction used here, at least one bound state is found. In terms of a k-parameter modifying the strength of the two-body potential, the radial part of the wave function changes dramatically with tiny variations around the physical value k  1. High-resolution rotational Raman spectroscopy in a supersonic beam expansion is proposed as a feasible way of observing the bound state predicted. Ó 2001 Elsevier Science B.V. All rights reserved. 1. Introduction Quantum liquids and clusters are currently be- ing very actively investigated. In particular, helium clusters provide prototype systems which display unusual behaviors manifested in dierent phe- nomena such as, for example, atomic optics [1], cold atom scattering [2,3] Bose±Einstein conden- sation and super¯uidity [4]. Furthermore, in the kinetics of formation of small clusters from 4 He beams, dimers and trimers play a very important role in the dierent recombination mechanisms envisaged to lead to clusters of increasing size. Thus, a very precise knowledge of the partition functions for these small clusters is essential for a correct statistical description of formation dy- namics at low temperatures since the addition of a new bound state can represent a marked change in the partition function. As a consequence, the ex- istence of possible excited states of these clusters has recently lead to a very fruitful and enthusiastic debate in which the so-called E®mov states [5,6] are at the center of the dicussion. Very recently [7,8] helium trimer bound states have been calculated by us using a variational method described in terms of pair±atom coordi- nates and where the nuclear bound states are ex- panded over symmetrized products of distributed Gaussian functions for a total angular momentum J  0. With the two-body interaction potential that we used [9], only two bound states for the trimer with energies E v0 vib 0:1523 cm 1 and E v1 vib 1:24  10 3 cm 1 have been found. As we have further shown [7,8], the corresponding excited state of the boson system displays several characteristics of E®mov behavior. The dierent triangular con®gurations contributing to both bound trimer states have also been extracted from 16 February 2001 Chemical Physics Letters 335 2001) 105±110 www.elsevier.nl/locate/cplett * Corresponding author. Fax: 34-1-585-4894. E-mail address: pablo@fam88.ima.csic.es P. Villarreal). 0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII:S0009-261400)01423-8