Variational description of the helium trimer using correlated hyperspherical harmonic basis functions

Abstract

A variational wave function constructed with correlated Hyperspherical Harmonic functions is used to describe the Helium trimer. This system is known to have a deep bound state. In addition, different potential models predict the existence of a shallow excited state that has been identified as an Efimov state. Using the Rayleigh-Ritz variational principle the energies and wave functions of both bound states have been obtained by solving a generalized eigenvalue problem. The introduction of a suitable correlation factor reduces considerably the dimension of the basis needed to accurately describe the structure of the system. The most recent helium-helium interactions have been investigated.

Imaging the structure of the trimer systems 4He3 and 3He4He2

“…For the case of the helium trimer this is different. In 4 He 3 there is apart from the ground state only one other predicted 18 Barletta and Kievsky 19 Gonzalez-Lezana et al 22 Paola et al 33 Blume et al 34 Figure 1 | Internuclear two-body distances. (a) Experimental distribution of the 4 He- 4 He distance of 4 He 3 and the 4 He- 3 He distances of 3 4 He- 4 He comparison with theoretical predictions.…”

“…Although there is theoretical consensus concerning the floppy nature of both the 4 He 3 and 3 He 4 He 2 molecules, the geometrical shape is a matter of extensive current debates. In the particular case of the 4 He 3 trimer some calculations suggest an equilateral triangular structure [18][19][20] , while others indicate a significant contribution of linear configurations 21,22 . It has also been recently suggested that this controversy is often mislead by drawing false conclusions from correctly calculated distributions 3 .…”

Adiabatic hyperspherical study of triatomic helium systems

“…Jeziorska et al [18] and Cencek et al [19] have recently developed not only a helium dimer potential, but also the retardation correction to the dimer potential and the nonadditive three-body term. Retarded potentials have been used previously [13,20] and were found to have clear impacts on the low-energy behavior of helium systems. Experimentally, the 4 He dimer has been observed by Luo et al.…”

The Three-Boson System at Next-to-Next-to-Leading Order

“…On the other hand, various "realistic" potentials have been developed (see, e.g. [22,23]) and have been employed for few-body calculations [17,18,19,20,21]. In need of a three-body observable to fix the value of our three-body parameter we will employ these calculations as our three-body input.…”

“…Since the atom-atom scattering length is a 2 = 104 +8 −18 Å while the typical van der Waal's forces between the Helium atoms have a range R ≈ 7Å, in this case the expansion parameter R/a 2 < ∼ 10%. The 4 He trimer, tetramer, and several larger 4 He clusters have been observed [15,16], but unfortunately there are no measurements of trimer binding energies, and so we use precise few-body calculations [17,18,19,20,21], based on quite complicated inter-atomic potentials [22,23], to provide the two input ratios for our EFT. We then compare the EFT's predictions with the corresponding results obtained in Refs.…”