Low energy collective modes of deformed superfluid nuclei within the finite amplitude method
Background: The major challenge for nuclear theory is to describe and predict global properties and collective modes of atomic nuclei. Of particular interest is the response of the nucleus to a time-dependent external field that impacts the low-energy multipole and beta-decay strength. Purpose: We propose a method to compute low-lying collective modes in deformed nuclei within the finite amplitude method (FAM) based on the quasiparticle random-phase approximation (QRPA). By using the analytic property of the response function, we find the QRPA amplitudes by computing the residua of the FAM amplitudes by means of a contour integration around the QRPA poles in a complex frequency plane. Metho…
Isospin-invariant Skyrme energy-density-functional approach with axial symmetry
We develop the isospin-invariant Skyrme-EDF method by considering local densities in all possible isospin channels and proton-neutron (p-n) mixing terms as mandated by the isospin symmetry. The EDF employed has the most general form that depends quadratically on the isoscalar and isovector densities. We test and benchmark the resulting p-n EDF approach, and study the general properties of the new scheme by means of the cranking in the isospin space. We extend the existing axial DFT solver HFBTHO to the case of isospin-invariant EDF approach with all possible p-n mixing terms. Explicit expressions have been derived for all the densities and potentials that appear in the isospin representatio…
Finite amplitude method applied to giant dipole resonance in heavy rare-earth nuclei
Background: The quasiparticle random phase approximation (QRPA), within the framework of the nuclear density functional theory (DFT), has been a standard tool to access the collective excitations of the atomic nuclei. Recently, finite amplitude method (FAM) has been developed, in order to perform the QRPA calculations efficiently without any truncation on the two-quasiparticle model space. Purpose: We discuss the nuclear giant dipole resonance (GDR) in heavy rare-earth isotopes, for which the conventional matrix diagonalization of the QRPA is numerically demanding. A role of the Thomas-Reiche-Kuhn (TRK) sum rule enhancement factor, connected to the isovector effective mass, is also investig…
Complex-energy approach to sum rules within nuclear density functional theory
The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or EDF. But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute sum rules of the response that is adaptable to the optimization of the nuclear EDF an…
Multipole modes in deformed nuclei within the finite amplitude method
Background: To access selected excited states of nuclei, within the framework of nuclear density functional theory, the quasiparticle random phase approximation (QRPA) is commonly used. Purpose: We present a computationally efficient, fully self-consistent framework to compute the QRPA transition strength function of an arbitrary multipole operator in axially-deformed superfluid nuclei. Methods: The method is based on the finite amplitude method (FAM) QRPA, allowing fast iterative solution of QRPA equations. A numerical implementation of the FAM-QRPA solver module has been carried out for deformed nuclei. Results: The practical feasibility of the deformed FAM module has been demonstrated. I…