Application of contact interactions to Borromean halos

Abstract

Li and 6 He are described as three-body systems using different approaches. We compare our technique, based on a density-dependent, cutoff, contact interaction between the valence neutrons, with a Faddeev approach which is based on realistic interactions. The ground state properties of a weakly bound two-neutron halo are described fairly well once the contact interaction has been adjusted and calibrated to produce a realistic scattering length and effective range. ͓S0556-2813͑97͒01212-0͔

Strong dineutron correlation inHe8andC18

“…Before we do this, however, we first examine the applicability of the HFB method by applying it to the three-body model of 6 He nucleus [6,26]. This model has been solved exactly by diagonalizing the Hamiltonian matrix.…”

“…We use the same neutron-core potential, V nC , for 8 He as in Refs. [6,26], while we use the set D in Refs. [24,25] for the 18 C nucleus.…”

“…(3)) instead of the reduced mass, we multiply the factor (A − 1)/A · A C /(A C + 1), where A C is the mass number of the core nucleus, following the prescription given in Ref. [26]. The pairing interaction is given as…”

“…In Refs. [6,26], the center of mass motion is treated exactly by introducing the recoil kinetic energy of the core nucleus (see Ref. [14] for the derivation of the recoil term).…”

“…In Sec. III, we apply the method to 6 He, where the result of the exact diagonalization of the three-body (α+n+n) Hamiltonian has been obtained [6,26]. We compare the HFB result with the exact result, and discuss the applicability of the HFB method for the study of the spatial structure of valence neutrons.…”