*Review* **Double Beta Decay: A Shell Model Approach**

**Mihai Horoi**

Department of Physics, Central Michigan University, Mount Pleasant, MI 48859, USA; mihai.horoi@cmich.edu

**Abstract:** Studies of weak interaction in nuclei are important tools for testing different aspects of the fundamental symmetries of the Standard Model. Neutrinoless double beta decay offers an unique venue of investigating the possibility that neutrinos are Majorana fermions and that the lepton number conservation law is violated. Here, I use a shell model approach to calculate the nuclear matrix elements needed to extract the lepton-number-violating parameters of a few nuclei of experimental interest from the latest experimental lower limits of neutrinoless double beta decay half-lives. The analysis presented here could reveal valuable information regarding the dominant neutrinoless double beta decay mechanism if experimental half-life data become available for different isotopes. A complementary shell model analysis of the two-neutrino double beta decay nuclear matrix elements and half-lives is also presented.

**Keywords:** neutrino properties; double beta decay; nuclear shell model; many-body methods
