We have developed a fully consistent framework for calculations in the Quasiparticle Random Phase Approximation (QRPA) with $NN$ interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions.
The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov (HFB) ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRG-evolved 3N interactions, we presently account for some 3N effects by means of a linearly density-dependent interaction, whose strength is adjusted to reproduce the charge radii of closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter $lambda$. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.
We examine the response of closed-shell nuclei using a correlated interaction, derived with the Unitary Correlation Operator Method (UCOM) from the Argonne V18 potential, in second RPA (SRPA) calculations. The same correlated two-body interaction is
used to derive the Hartree-Fock ground state and the SRPA equations. Our results show that the coupling of particle-hole states to higher-order configurations produces sizable effects compared with first-order RPA. A much improved description of the isovector dipole and isoscalar quadrupole resonances is obtained, thanks in part to the more fundamental treatment of the nucleon effective mass offered by SRPA. The present work suggests the prospect of describing giant resonance properties realistically and consistently within extended RPA theories. Self-consistency issues of the present SRPA method and residual three-body effects are pointed out.
Lately we have been tackling the problem of describing nuclear collective excitations starting from correlated realistic nucleon-nucleon (NN) interactions. The latter are constructed within the Unitary Correlation Operator Method (UCOM), starting fro
m realistic NN potentials. It has been concluded that first-order RPA with a two-body UCOM interaction is not capable, in general, of reproducing quantitatively the properties of giant resonances (GRs), due to missing higher-order configurations and long-range correlations as well as neglected three-body terms in the Hamiltonian. Here we report results on GRs obtained by employing a UCOM interaction based on the Argonne V18 potential in Second RPA (SRPA) calculations. The same interaction is used to describe the Hartree-Fock (HF) ground state and the residual interactions. We find that the inclusion of second-order configurations -- which effectively dress the underlying HF single-particle states with self-energy insertions -- produces sizable corrections. The effect appears essential for a realistic description of GRs when using the UCOM. We argue that effects of higher than second order should be negligible. Therefore, the UCOM-SRPA emerges as a promising tool for consistent calculations of collective states in closed-shell nuclei. This is an interesting development, given that SRPA can accommodate more physics than RPA (e.g., fragmentation). Remaining discrepancies due to the missing three-body terms and self-consistency issues of the present SRPA model are pointed out.
