ΛNNandΣNNsystems at threshold. II. The effect ofDwaves

Abstract

Using the two-body interactions obtained from a chiral constituent quark model, we study all N N and NN states with I = 0, 1, 2 and J = 1/2, 3/2 at threshold, taking into account all three-body configurations with S and D wave components. We constrain further the limits for the N spin-triplet scattering length a 1/2,1 . Using the hypertriton binding energy, we find a narrow interval for the possible values of the N spin-singlet scattering length a 1/2,0 . We find that the NN system has a quasibound state in the (I, J ) = (1, 1/2) channel very near threshold with a width of about 2.1 MeV.

Three-body resonances Λnn and ΛΛn

“…[24] overestimates the ΛΛ attraction and thus overbinds the hypernucleus 6 ΛΛ He. When we replaced it with a more realistic potential (27) of Ref.…”

“…[26], the ΛΛn hypercentral potential became pure repulsive, independent of the Table 1, and with the ΛΛ-potential of Ref. [24], that overbinds the hypernucleus 6 ΛΛ He.…”

“…Table 5 Complex resonance energies E 0 = E r − i 2 Γ for the system ΛΛn with the three choices of Λn-potential (see Table 1) and with the ΛΛ-potential of Ref. [24] that overbinds the hypernucleus 6 ΛΛ He Λn-potential…”

system

“…This cooperative effect of the attraction in the two-body subsystems when merged in few-baryon states was also made evident in the prediction of a ΣNN quasibound state in the (I)J P = (1)1/2 + channel very near threshold [20]. Such ΣNN quasibound state has been recently suggested in…”

“…Although by fitting the NΛ phase shifts, the coupling to the NΣ system has been included in an effective manner, it would also be interesting to unfold the effective ΛN interaction, separating the contribution from ΛN ↔ ΣN. As it has been discussed in the literature [7,8,20,[46][47][48] the hypertriton does not get bound by considering only NNΛ channels, but it is necessary to include also NNΣ channels. Similar considerations hold from the ΛΛ ↔ NΞ coupling, that is expected to play a minor role in this case, because the nucleon generated in the transition must occupy an excited p−shell, the lowest s−shell being forbidden by the Pauli principle [42,49].…”