Abstract
We present a formalism for calculating nuclear matrix elements of double-$\ensuremath{\beta}$ decay within the framework of the microscopic interacting boson model. We calculate Fermi, Gamow-Teller, and tensor matrix elements in the decay of Ge-Se-Mo-Te-Xe-Nd-Sm and compare our results with those of the shell-model (SM) and of the quasiparticle random-phase approximation (QRPA). Our results are in agreement with QRPA. We discuss simple features of the matrix elements and give a formula that allows one to estimate matrix elements in terms of the number of valence proton and neutron pairs.
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