A Simplistic Analytical Approximation of the Three-Body Contribution to the Neutrinoless Double Beta Decay Transition Matrix Element in Ge-76 and Se-76
Undergraduate: James Wheeler
Faculty Advisor: Jonathan Engel
Department: Physics & Astronomy
In this project, we calculate the contribution of the three-body effects on the neutrinoless double beta decay transition matrix element between the ground states of 76Ge and 76Se within a 2-shell model space under the influence of a model Hamiltonian constructed from the isospin generators of SO(5) x SO(5) (one set of generators for each shell). The contribution is calculated via the construction of an effective operator acting in a single shell that reproduces exactly some relevant matrix elements of the full two-shell operator; once the effective operator is constructed, the desired matrix element is calculated for the effective operator between the projections of the ground states onto a single shell. While the constructed Hamiltonian is not particularly realistic, it is of the form necessary to admit analytically tractable solutions, and solutions in this model still provide insight into the problem of calculating this matrix element in general. Dr. Jonathan Engel has previously worked out the contribution of two-body effects within this same schema, and this project seeks to extend these results and ascertain the comparative significance of three-body effects, as similar calculations in the simpler SU(2) x SU(2) construction of the problem have found that three-body effects in that schema were non-negligible compared to the two-body contribution.