Modeling of 6ΛHe hypernucleus within configuration space Faddeev approach

Abstract

The cluster 4 He + Λ + n model is applied to describe the 6 Λ He hypernucleus. The consideration is based on the configuration space Faddeev equations for a system of non-identical particles. A set of the pair potentials includes the OBE simulating (NSC97f) model for the Λn interaction and the phenomenological potentials for the αΛ and αn interactions. We calculated energies of spin (1 − ,2 − ) doublet. For the 2 − excitation energy, the obtained value is 0.18 MeV. The hyperon binding energy of the bound 1 − state is less than the experimental value, which may be an evidence for violation of the exact three-body cluster structure.

S wave resonance *

“…It is thus interesting to see if the existence of a resonance just below or above the threshold, as it has been found by the HAL QCD Collaboration [9] and low-energy effective field theory studies [10], may affect the position of the three-body S wave resonance found in Ref. [20]. For this purpose, we have now constructed separable potential models of the , , and amplitudes reproducing the behavior of the HAL QCD collaboration results [9].…”

“…[12], we developed a model in Ref. [20] of the three-body system, which allowed us to look for possible three-body resonances. Using separable two-body interactions fitted to the low-energy data of the Nijmegen S wave baryon-baryon Ξd ΞNN NN amplitudes [16][17][18], we found a resonance just below the threshold with a very small width of only 0.09 MeV.…”

“…We adopt the same convention as in Refs. [3,20], i.e., particles and are identical and particle is different in each three-body component. After the reduction for identical particles, the inhomogeneous integral equations appropriate for elastic scattering take the following form…”

“…( 14) and ( 15) of Ref. [20]. The scattering amplitude normalized as in the Argand diagram is given by…”

“…If the resonance lies below the threshold, as it was the case in Ref. [20], the contour rotation method allows to simultaneously consider both the momentum variables and the energy variable as complex, such that one can determine the position of the pole in the complex plane. However, if the resonance lies above the threshold, as in the present case, the contour rotation method works only if one takes the momentum variables as complex but leaves the energy variable real, such that one cannot determine the position of the pole in the complex plane.…”