Investigation of few body cluster systems is very important in nuclear physics. Problems appearing in few body systems can in principle be divided into two classes: bound state problems and scattering problems. The bound state problems are usually related to the spectroscopy of such systems while scattering problems describe their reactions. The main focus in the work is the scattering problem for systems consisting of two cluster systems. The single channel two body scattering problem is considered in the framework of different spin parity states for lithium isotopes.Scattering phase shifts on negative and positive parity states of 5 Li, 6 Li and 7 Li nuclei are calculated applying two-body 𝛼𝛼𝛼𝛼 + 𝑝𝑝𝑝𝑝, 𝛼𝛼𝛼𝛼 + 𝑑𝑑𝑑𝑑 and 𝛼𝛼𝛼𝛼 + 𝑡𝑡𝑡𝑡 systems and the complex scaling method. 6 Li and 7 Li are stable nuclei and their ground and low-lying excited states are considered in this work.In this study, we calculated scattering phase shifts of the negative parity 𝐽𝐽𝐽𝐽 𝜋𝜋𝜋𝜋 = 3/2 − and 𝐽𝐽𝐽𝐽 𝜋𝜋𝜋𝜋 = 1/2 − states for 𝑝𝑝𝑝𝑝 −wave of 5 Li, 𝐽𝐽𝐽𝐽 𝜋𝜋𝜋𝜋 = 7/2 − , 5/2 − , 3/2 − and 1/2 − states for 𝑝𝑝𝑝𝑝 − and 𝑓𝑓𝑓𝑓 −waves of 7 Li and the positive parity 𝐽𝐽𝐽𝐽 𝜋𝜋𝜋𝜋 = 1 + , 2 + , 3 + states for 𝑠𝑠𝑠𝑠 − and 𝑑𝑑𝑑𝑑 − waves of 6 Li.

The complex scaling method is one of the powerful tool in wide areas of physics, particularly in nuclear physics. In the first stage, its advantage was mainly pointed out for description of the resonance states in the composite systems. In the last decide, the usage of this method has increased not only to obtain information on resonance states but also to determine scattering quantities in the observables. To determine the presence of many resonant states at the wave is not easy and complex scaling method can be used to determine the obtain many resonant states. The simple schematic two-body model is applied for study of many resonant states. Applying the complex scaling method, we can easily obtain several resonance states even with a wide and a sharp decay widths simultaneously. In this work, one bound and five resonance states for J π = 0 + wave and one bound and four resonance states for J π = 1 − wave are reported.