**
Hyperspherical Calculations of He Trimer with Non-zero Angular Momenta
**

Teck G. Lee, B.D. Esry and C.D. Lin

Department of Physics, Kansas State University, Manhattan, Kansas 66506, U.S.A.

The properties of very weakly bound small He clusters have been examined
in a variety of theoretical and experimental studies. For helium
trimers, practically all theoretical calculations that have been carried
out dealt with states of zero total angular momentum. It is known that
there are two J=0 bound states for ^{4}He_{3}, and thus it has been
speculated whether there are possible J > 0 excited states.

Based on a simple rigid
rotor model, an estimate of the rotational energy using parameters from
the ^{4}He_{3} ground state suggests that a state with J=1
is close to being
bound. However, such a simple estimate can be grossly in error since
quantum statistics are not taken into account. In the present work, the
adiabatic hyperspherical method has been employed to investigate the
possible existence of bound states of triatomic helium molecules for
J>0. By including only the pair interactions between He atoms, we solved
the Schrodinger equation in hyperspherical coordinates within the
adiabatic approximation. The adiabatic channel functions are calculated
using B-spline functions in the body-frame of the molecule. From the
adiabatic hyperspherical potential curves we search for the existence of
bound states for J>0.

Figure 1 shows the adiabatic potential curves with respect to the
hyperradius. From these potential curves, except for J=0, the curves are
repulsive and therefore we conclude that no J > 0 bound states are
possible for the ^{4}He_{3} system. In figure 2, we show
potential curves for
the ^{4}He_{2}^{3}He system, and we found no bound states as well. It is
interesting to note the difference in the order of J^{π} curves in the two
systems. This difference is a result of quantum statistics. In figure 2,
^{4}He_{2}^{3}He has two bosons and one fermion,
hence the wave function needs to
be symmetric under the exchange of the two bosons only. For
^{4}He_{3} the
wave function must be symmetric under the interchange of any pair of He
atoms. This study clearly demonstrates that quantum symmetry governs the
order of these J^{π} curves for the diffuse molecular systems.

**Figures:**

**References:**

1. B. D. Esry, C. D. Lin and C. H. Greene, Phys. Rev. A. 54, 394 (1996).

2. W. Schöllkopf and J. P. Toennies, Science 226,1345 (1994).

3. L.W. Bruch, J. Chem. Phys. 110, 2410 (1999)

This work was supported by the
Chemical Sciences, Geosciences and Biosciences Division,

Office of Basic Energy Sciences,
Office of Science,
U.S. Department of Energy.

*Submitted to ICPEAC 2001, July 2001 in Santa Fe, NM.*

*This abstract is also available in
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