Effective Operators in Time-Independent Approach

An effective operator e." is defined so that it operates in a restricted model space and gives the same matrix element as that of the original operator e between the corresponding true eigenstates. The Be" is determined dependently on the model-space eigenstates, and therefore various types of e." are possible. General solutions for e." are derived in the time-independent and algebraic approach. These eJerr contain the usual non-Hermitian and Hermitian effective operators as special cases. The explicit expansion form for Berr is given by extending the Q-box formalism of Kuo et al. developed in the derivation of the effective interaction to the problem of constructing the effective operator.