Quasiparticle random-phase approximation with interactions from the Similarity Renormalization Group

Abstract

We have developed a fully consistent framework for calculations in the Quasiparticle Random Phase Approximation (QRPA) with N N 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 SRGevolved 3N interactions, we presently account for some 3N effects by means of a linearly densitydependent 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 λ. 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.

Local projections of low-momentum potentials

“…which has demonstrated momentum decoupling properties [13,[18][19][20][21][22][23][24][25][26]. We use the momentum decoupling scale λ = s 1/4 (in units where = c = m = 1 with nucleon mass m) to label the evolution.…”

Dipole response in neutron-rich nuclei within self-consistent approaches using realistic potentials

“…In a fully self-consistent (Q)RPA, the 1 − spurious state lies at zero excitation energy and collects the total strength induced by the CM. Numerically, it is very difficult to achieve a complete decoupling from the physical intrinsic states unless a huge configuration space is adopted [19]. In our space, the energy of the lowest 1 − (Q)RPA spurious state acquires a small imaginary component of the order ∼ 0.1 MeV.…”

“…[21,22], while V ρ is a corrective repulsive, density dependent, two-body potential with a coupling constant C ρ . This force, introduced to simulate a three-body contact force [26], improves the description of bulk properties in closed-shell nuclei [27] and yields more realistic single-particle spectra and multipole-nuclear responses [19,20]. We performed a HFB calculation in a configuration space which includes 13 harmonic oscillator major shells, up to the principal quantum number N max = 12.…”

“…We could therefore perform a systematic study of the dipole response in several chains of neutron rich isotopes [20]. As in [19], however, we found necessary to add a corrective density dependent piece in order to get single-particle spectra sufficiently compressed so as to reproduce the main peak of the experimental GDR. Using such a modified Hamiltonian, we obtained spectra qualitatively consistent with experiments for all light, medium mass and heavy isotopes [20].…”

“…Following an alternative route proposed recently [19], we carried out self-consistent calculations using directly realistic potentials derived from nucleon-nucleon (NN) forces. We have first adopted a V lowk potential derived from the CD-Bonn NN interaction to generate a HartreeFock-Bogoliubov (HFB) basis and, then, used such a basis to solve the eigenvalue equations in both (quasi-particle) Tamm-Dancoff ((Q)TDA) and random-phase approximations ((Q)RPA).…”