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. Methods: We use the superfluid nuclear density functional theory with Skyrme energy density functionals, FAM-QRPA approach, and the conventional matrix formulation of the QRPA (MQRPA). Results: We demonstrate that the complex-energy FAM-QRPA method reproduces low-lying collective states obtained within the conventional matrix formulation of the QRPA theory. Illustrative calculations are performed for the isoscalar monopole strength in deformed 24Mg and for low-lying K = 0 quadrupole vibrational modes of deformed Yb and Er isotopes. Conclusions: The proposed FAM-QRPA approach allows one to efficiently calculate low-lying collective modes in spherical and deformed nuclei throughout the entire nuclear landscape, including shape-vibrational excitations, pairing vibrational modes, and beta-decay rates.Comment: 9 pages, 2 figures, submitted to Phys. Rev.

Impact of nuclear mass uncertainties on the rr-process

Nuclear masses play a fundamental role in understanding how the heaviest elements in the Universe are created in the $r$-process. We predict $r$-process nucleosynthesis yields using neutron capture and photodissociation rates that are based on nuclear density functional theory. Using six Skyrme energy density functionals based on different optimization protocols, we determine for the first time systematic uncertainty bands -- related to mass modeling -- for $r$-process abundances in realistic astrophysical scenarios. We find that features of the underlying microphysics make an imprint on abundances especially in the vicinity of neutron shell closures: abundance peaks and troughs are reflected in trends of neutron separation energy. Further advances in nuclear theory and experiments, when linked to observations, will help in the understanding of astrophysical conditions in extreme $r$-process sites.Comment: 7 pages, 3 figure