A Faddeev Calculation of the α-Λ–Λ Bound State with a Three-Dimensional Treatment

Abstract

Without partial-wave decomposition we solve the Faddeev three-body equations to obtain the bound state of the α-Λ-Λ system. KEYWORDS: Double Λ Hyper-nucleus, Faddeev Calculation, No partial-wave decomposition Faddeev Equation with 3D treatmentWith recent improvements in super-computers, a method of directly solving a three-body problem has been developed without partial wave decomposition.[1] We have been able to calculate it using a realistic potential. It is well converged for the tritium nucleus. [2] The degrees of freedom by selecting coordinates fixed to the nucleus can be reduced to 3 (Bodyfixed frame). These degrees of freedom are the magnitudes of 2 Jacobi momenta ⃗ p, ⃗ q and an angle θ between these momenta.where ⃗ k i are intrinsic particle momenta and m i are masses. The wave function Φ consists of the Faddeev components ψ i (i = 1, 2, and 3);The components satisfy the Faddeev equationswhere ⃗ π i and ⃗ π ′ j are function of ⃗ q i and ⃗ q ′ j , and, ⃗ π ′′ i and ⃗ π ′′′ k are function of ⃗ q i and ⃗ q k ′′ , respectively, and t i and G 0 are the two-body t-matrix and the three-body free Green's function, respectively.