Two- and Three-particle States in a Nonrelativistic Four-fermion Model in the Fine-tuning Renormalization Scheme. Goldstone mode "against" extension theory

In a nonrelativistic contact four-fermion model we show that simple regularisation prescriptions together with a definite fine-tuning of the cut-off-parameter dependence of ``bare'' quantities give the exact solutions for the two-particle sector and Goldstone modes. Their correspondence with the self-adjoint extension into Pontryagin space is established leading to self-adjoint semi-bounded Hamiltonians in three-particle sectors as well. Renormalized Faddeev equations for the bound states with Fredholm properties are obtained and analysed.Comment: 23 pages, LaTeX, changed content, added references and two figures, to appear in the Few Body System

Tris(tetra­butyl­ammonium) hexa­kis­(tert-butane­thiol­ato-κS)hepta-μ3-chlorido-μ3-sulfido-hexa­molybdate dihydrate

The octa­hedral cluster core of the anion in the structure of the title compound, (C16H36N)3[Mo6(C4H9S)6(μ3-Cl)7(μ3-S)]·2H2O, has -3 site symmetry. Two μ3-Cl atoms fully occupy positions in the cluster core, while the remaining six positions are statistically occupied by Cl and S atoms in a 1:5 ratio. The fully occupied Cl-atom positions are located on sites with 3 symmetry, and the N atom of tetra­butyl­ammonium cation is located on a site with 2 symmetry. The structure contains also two disordered solvent water mol­ecules, one of which is located on a threefold rotation axis and the other in a general position, both with an occupancy of 0.25. The water mol­ecules are localized in cavities formed by the tetra­butyl­ammonium cations and the tert-butane­thiol­ate groups. The metal clusters are stacked in a cubic close packing arrangement along [001]