A method to compute the QRPA

We introduce the finite amplitude method (FAM) for the QRPA. This method allows to build fully self consistent QRPA codes; since the FAM method is not limited to spherically symmetric systems it is helpful in the solution of the deformed QRPA problem where the construction of the matrices is a difficult task in itself. All that is needed to write a QRPA code with the FAM method is a HFB code; the residual fields ( $\delta h(\omega)$, $\delta h^{\dagger}(\omega)$, $\delta \Delta (\omega)$ and $\delta \Delta^{\dagger}(\omega)$), which usually are the difficult part to be calculated, are computed with a numerical derivation which requires the quasi-particle amplitudes previously obtained with the HFB code and the QRPA amplitudes. The FAM method is not involved in the diagonalization of the QRPA matrices, a task which can be solved via iterative methods (like the Conjugate Gradient Method).\\[4pt] [1] T. Nakatsukasa, T. Inakura and K. Yabana: Phys. \ Rev. \textbf{C 76} 024318 (2007)