We have presented a method to calculate accurate RPA response functions by using the iterative Arnoldi diagonalization related to the sum-rule conserving Lanczos method of Ref. [5]. We used strictly the same EDF for the ground state calculation and RPA excitations. We have showed how the Arnoldi method must be stabilized in order to apply it reliably to the RPA eigenvalue problem. The resulting electromagnetic strength functions are in good agreement with the standard RPA results and are obtained with numerical effort smaller by orders of magnitude.
Our method closely resembles the FAM of Nakatsukasa et al. [6,7], except that our iterative method is different and that we use the HO basis instead of the mesh in coordinate space. The FAM and our method both allow the existing EDF mean-field codes to be used for the calculation of the RPA or QRPA matrix-vector products. With minor modifications, mostly pertaining to the full implementation of the time-odd mean fields, these codes can easily be extended to RPA/QRPA. In particular, our future implementation of the deformed QRPA solution will be based on the code HFODD [25].
We also implemented the method to remove components of the spurious RPA modes from the calculated strength functions that keeps the physical excitations exactly orthogonal against the spurious excitations in any finite model space.
The smaller numerical effort of the iterative Arnoldi method, and the fact that in this method one does not have to calculate and store the RPA or QRPA matrices, allows our method to be applied to the calculation of electromagnetic and beta decay strengths and strength functions for deformed heavy nuclei. Work to extend our formalism and codes to deformed superfluid nuclei is in progress.
We are thankful to J. Terasaki for providing us with numerical values of the strength functions calculated in Ref. [17]. This work was supported by the Academy of Finland and University of Jyväskylä within the FIDIPRO program and by the Polish Ministry of Science and Higher Education under Contract No. N N 202 328234.