Finite element investigation of the ground states of the helium trimers ⁴He₃ and ⁴He₂–³He

Abstract

A three-dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers 4 He 3 and 4 He 2 -3 He. Three different He-He interaction potentials of hard-core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated.

Universal short-range correlations in bosonic helium clusters

“…The 4 He trimer ground state energy using this potential has been calculated using several few-body techniques. Most results agree with B 3 ≈ 126.0(5) mK [20][21][22][23][24][25][26][27], while different values also exist [28,29].…”

The 4He Trimer as an Efimov System

“…The corresponding results for the TTY potential are shown in Table 2. The respective energies obtained for the LM2M2 potential are practically the same as for the TTY potential (see Table 3), that is, they are close to 126 mK for the ground state and close to 2.28 mK for the excited one [19,20,21,22,23,24,25,26,27,28,29,30,31]. For the 4 He trimer binding energies obtained with the SAPT potentials we refer to the calculations in [21,30,35,37].…”

Ultracold Few-Body Systems

“…The binding energies of three helium atoms have been calculated in many studies (Esry et al, 1996b;Nielsen et al, 1998;Lazauskas and Carbonell, 2006;Motovilov et al, 2001;Sandhas et al, 2004;Barletta and Kievsky, 2001;Lee et al, 2001;Kolganova et al, 2007;Salci et al, 2007;Bressanini et al, 2000;Suno and Esry, 2008). There are only two isotopologues that are bound: 4 He 3 has two bound states and 4 He 3 2 He has one bound state, all with the symmetry J = 0 + (Esry et al, 1996b;Nielsen et al, 1998).…”