EFFECTIVE SUMMATION OVER INTERMEDIATE STATES IN DOUBLE-BETA DECAY

We consider two separate schemes for eliminating the explicit summation over states in the intermediate nucleus in double-beta decay. The first, known as the operator expansion method, has recently been applied in several calculations; we show in a variety of simple models that the method fails and isolate its weaknesses. We then describe an efficient technique for generating Green's function matrix elements, based on the Lanczos algorithm, and apply it to a full fp-shell calculation in 48Ca. The method efficiently generates an exact (to within machine accuracy) result while the operator expansion method is again inaccurate.