Effective Operators in Time-Independent Approach
Keisuke Suzuki, R. Okamoto · Progress of Theoretical Physics · 1995
An effective operator Θeff is defined so that it operates in a restricted model space and gives the same matrix element as that of the original operator Θ between the corresponding true eigenstates. The Θeff is determined dependently on the model-space eigenstates, and therefore various types of Θeff are possible. General solutions for Θeff are derived in the time-independent and algebraic approach. These Θeff contain the usual non-Hermitian and Hermitian effective operators as special cases. The explicit expansion form for Θeff is given by extending the \hatQ-box formalism of Kuo et al. developed in the derivation of the effective interaction to the problem of constructing the effective operator.