Constructing an Effective Neutrinoless Double-Beta Decay Operator in the Shell Model

We are developing a formalism to generate effective neutrinoless double-beta decay (0 nu beta beta) operators within the shell model. We use lighter nuclei (A = 8; 10) as a laboratory. We start with the A=6 system where the wavefunctions are generated using the No-Core Shell Model (NCSM) with the CD-Bonn potential in a relatively large space. Thereafter, both the 0 nu beta beta operator and the two-nucleon interaction are renormalized to the p-shell using the Lee-Suzuki transformation scheme. These renormalized p-shell operator and interaction are then used in the A = 8 system and compared with the 'full' result (in the large space). Here we present preliminary results for the He-8-Be-8 transition. Also worth mentioning is the fact that we are simultaneously evaluating other renormalization schemes.