hi 

http://www.academia.edu/22213726/Level_shift_operator_and_second_order_perturbation_theory

You can give a look to this one

http://www.sciencedirect.com/science/article/pii/S0009261497006696

It explains the use of imaginary level shift in CASPT2 (to cure intruder states)

Best!

Thanks Osamah Nawfal Oudah and Riccardo Guareschi for your help. But the problem is that:

Let us suppose H(J) is the actual Hamiltonian and where J is the parameter. When J at some value say Jo has degenerate Eigen values of the Hamiltonian. If I introduce some perturbation to the system then how the Jo values shift.  How this shift is caught by the level shift operator? Or there is any other way to catch this shift?