Study of three-body Coulomb systems using a hyperspherical harmonics basis. I. Calculation of the ground state of the helium atom

Green function and scattering amplitudes in many-dimensional space

“…It is still much used by atomic physicists in spite of its large degeneracy, which prevents its application to more than three-body systems [18,27,28]. The ZB basis has no specific symmetry in an exchange of particles except for one pair.…”

“…Since our first application concerns atomic physics and the PH basis is not customary for such a kind of problems--atomic physicists rather use the ZB basis [6,18,27,28,363 or the S basis [30, 31, 34J--we shall discuss in more detail the properties of the PH basis in connection with the ZB basis and the Faddeev equations.…”

Universal angular probability distribution of three particles near zero-energy threshold

“…In the next section we shall discuss the two-particle case, this material would also be needed in the analysis of the three-particle case in Sec. 3. At the end of Sec.…”

“…where A 12 (k n ) := [H 0 + k 2 n ] −1 |v 12 |B 12 (k n ) and Z defined in [1] remain uniformly norm-bounded for all n, see Lemmas 6, 11 in [1]. The functionf (3) n is defined as followŝ…”

“…The detailed requirements on pair-potentials would be listed in Sec. 3. Suppose that for a converging sequence of coupling constants λ n → λ cr there exists a sequence of bound states ψ n ∈ D(H 0 ) such that H(λ n )ψ n = E n ψ n , where E n < 0, ψ n = 1 and E n → 0.…”