Binding three or four bosons without bound subsystems

Weakly bound three-body systems with no bound subsystems.

We investigate the domain of coupling constants which achieve binding for a 3-body system, while none of the 2-body subsystems is bound. We derive some general properties of the shape of the domain, and rigorous upper bounds on its size, using a Hall{Post decomposition of the Hamiltonian. Numerical illustrations are provided in the case of a Yukawa potential, using a simple variational method.

Extremal graphs without three-cycles or four-cycles

We derive bounds for f(v), the maximum number of edges in a graph on v vertices that contains neither three-cycles nor four-cycles. Also, we give the exact value of f(v) for all v up to 24 and constructive lower bounds for all v up to 200.

Bound States of Vector Bosons

Limits on the domain of coupling constants for binding N-body systems with no bound subsystems.

We study the domain of coupling constants for which a 3-body or 4-body system is bound while none of its subsystems is bound. Limits on the size of the domain are derived from a variant of the Hall–Post inequalities which relate N -body to (N −1)-body energies at given coupling. Possible applications to halo nuclei and hypernuclei are briefly outlined. 03.65.Ge, 21.45.+v, 21.80.+1, 21.60.Gx Typ...

Four-Body Bound State Calculations in Three-Dimensional Approach

The four-body bound state with two-body interactions is formulated in Three-Dimensional approach, a recently developed momentum space representation which greatly simplifies the numerical calculations of few-body systems without performing the partial wave decomposition. The obtained three-dimensional Faddeev-Yakubovsky integral equations are solved with two-body potentials. Results for four-bo...