We make a systematic study of Li isotopes (A=9,10,11) in the tensor optimized shell model for 9Li and treat the additional valence neutrons in the cluster model approach by taking into account the Pauli-blocking effect caused by the tensor and pairing correlations. We describe the tensor correlations in 9Li fully in the tensor-optimized shell model, where the variation of the size parameters of the single particle orbits is essential for getting strong tensor correlations. We have shown in our previous study that in $^{10,11}$Li the tensor and pairing correlations in 9Li are Pauli-blocked by additional valence neutrons, which make the p-shell configurations pushed up in energy. As a result, the $s^2$ valence neutron component increases to reveal the halo structure of 11Li and the inversion phenomenon of the single particle spectrum in 10Li arises. Following the previous study, we demonstrate the reliability of our framework by performing a detailed systematic analysis of the structures of $^{9,10,11}$Li, such as the charge radius, the spatial correlation of halo neutrons of 11Li and the electromagnetic properties of Li isotopes. The detailed effects of the Pauli-blocking on the spectroscopic properties of $^{10,11}$Li are also discussed. It is found that the blocking acts strongly for the 11Li ground state rather than for 10Li and for the dipole excited states of 11Li, which is mainly caused by the interplay between the tensor correlation in 9Li and the halo neutrons. The results obtained in these analyses clearly show that the inert core assumption of 9Li is not realistic to explain the anomalous structures observed in $^{10,11}$Li. For the dipole excitation spectrum of 11Li, the effect of the final state interactions is discussed in terms of the dipole strength function.
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