Title: General behavior of double beta decay amplitudes in the quasiparticle random phase approximation
Abstract: Simple formulas for the ${0}^{+}$\ensuremath{\rightarrow}${0}^{+}$ double beta decay matrix elements, as a function of the particle-particle strength ${\mathit{g}}^{\mathit{p}\mathit{p}}$, have been designed within the quasiparticle random phase approximation. The 2\ensuremath{\nu} amplitude is a bilinear function of ${\mathit{g}}^{\mathit{p}\mathit{p}}$, and all 0\ensuremath{\nu} moments behave as ratios of a linear function and the square root of another linear function of ${\mathit{g}}^{\mathit{p}\mathit{p}}$. It is suggested that these results are of general validity and that any modifications of the nuclear Hamiltonian or the configuration space cannot lead to a different functional dependence.