General behavior of double beta decay amplitudes in the quasiparticle random phase approximation

Simple formulas for the $0^{+}$→$0^{+}$ 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 2ν amplitude is a bilinear function of ${\mathit{g}}^{\mathit{p}\mathit{p}}$, and all 0ν 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.