Double-beta-decay nuclear matrix elements in the QRPA framework

We review the recent work done by the Jyvaskyla-La Plata collaboration on the calculation of nuclear matrix elements for various modes of double-beta decays. Whenever helpful, we connect our recent work to the historical background in order to highlight the progress achieved in the field of double-beta decay. At the same time, we introduce some new concepts and ideas to treat e. g. possible backgrounds in Gamow-Teller strength functions generated in (p,n) and (n,p) reactions.