842 research outputs found
Giant Resonances using Correlated Realistic Interactions: The Case for Second RPA
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 from 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.Comment: 6 pages, incl. 1 figure; Proc. 26th Int. Workshop on Nuclear Theory,
June 2007, Rila mountains, Bulgari
Large-scale second RPA calculations with finite-range interactions
Second RPA (SRPA) calculations of nuclear response are performed and
analyzed. Unlike in most other SRPA applications, the ground state,
approximated by the Hartree-Fock (HF) ground state, and the residual couplings
are described by the same Hamiltonian and no arbitrary truncations are imposed
on the model space. Finite-range interactions are used and thus divergence
problems are not present. We employ a realistic interaction, derived from the
Argonne V18 potenial using the unitary correlation operator method (UCOM), as
well as the simple Brink-Boeker interaction. Representative results are
discussed, mainly on giant resonances and low-lying collective states. The
focus of the present work is not on the comparison with data, but rather on
technical and physical aspects of the method. We present how the large-scale
eigenvalue problem that SRPA entails can be treated, and demonstrate how the
method operates in producing self-energy corrections and fragmentation. The
so-called diagonal approximation is conditionally validated. Stability problems
are traced back to missing ground-state correlations.Comment: 13 pages, incl. 9 figures, 1 tabl
Crowd-sourcing with uncertain quality - an auction approach
This article addresses two important issues in crowd-sourcing: ex ante uncertainty about the quality and cost of different workers and strategic behaviour. We present a novel multi-dimensional auction that incentivises the workers to make partial enquiry into the task and to honestly report quality-cost estimates based on which the crowd-sourcer can choose the worker that offers the best value for money. The mechanism extends second score auction design to settings where the quality is uncertain and it provides incentives to both collect information and deliver desired qualities
Proton pygmy resonances: predictions for N=20 isotones
We study theoretically the low-energy electric-dipole response of N=20
isotones. We present results from a quasiparticle random-phase approximation
(QRPA) and a continuum random-phase approximation (CRPA), and we compare them
with results for the mirror Z=20 nuclei. According to our analysis, enhanced E1
strength is expected energetically well below the giant dipole resonance in the
proton-rich isotones. Large amounts of E1 strength in the asymmetric N=20
isotones are predicted, unlike their equally asymmetric Z=20 mirror nuclei,
pointing unambiguously to the role of structural effects such as loose binding.
A proton-skin oscillation could develop especially in 46Fe. The proper
description of non localized threshold transitions and the nucleon effective
mass in mean-field treatments may affect theoretical predictions. We call for
systematic theoretical investigations to quantify the role bulk-matter
properties, in anticipation of measurements of E1 transitions in proton-rich
nuclei.Comment: 10 pages, incl. 9 figures and 2 tables; v2: some rephrasing and
clarifications, corrected Fig.
The One-Body and Two-Body Density Matrices of Finite Nuclei and Center-of-Mass Correlations
A method is presented for the calculation of the one-body and two-body
density matrices and their Fourier transforms in momentum space, that is
consistent with the requirement for translational invariance, in the case of a
nucleus (a finite self-bound system). We restore translational invariance by
using the so-called fixed center-of-mass approximation for constructing an
intrinsic nuclear ground state wavefunction by starting from a
non-translationally invariant wavefunction and applying a projection
prescription. We discuss results for the one-body and two-body momentum
distributions of the 4He nucleus calculated with the Slater determinant of the
harmonic oscillator orbitals, as the initial non-translationally invariant
wavefunction. Effects of such an inclusion of CM correlations are found to be
quite important in the momentum distributions.Comment: 5 pages, incl. 2 figures; Proc. Int. Conf. on Frontiers in Nuclear
Structure, Astrophysics and Reactions (FINUSTAR), Kos, Greece, Sept.200
Quasiparticle Random Phase Approximation with Interactions from the Similarity Renormalization Group
We have developed a fully consistent framework for calculations in the
Quasiparticle Random Phase Approximation (QRPA) with 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 . 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.Comment: 18 pages, 17 figures, 3 tables (RevTeX 4.1), v2: fixed typos &
figures, as publishe
Giant Resonances based on Unitarily Transformed Two-Nucleon plus Phenomenological Three-Nucleon Interactions
We investigate giant resonances of spherical nuclei on the basis of the
Argonne V18 potential after unitary transformation within the Similarity
Renormalization Group or the Unitary Correlation Operator Method supplemented
by a phenomenological three-body contact interaction. Such Hamiltonians can
provide a good description of ground-state energies and radii within
Hartree-Fock plus low-order many-body perturbation theory. The standard Random
Phase Approximation is applied here to calculate the isoscalar monopole,
isovector dipole, and isoscalar quadrupole excitation modes of the 40Ca, 90Zr,
and 208Pb nuclei. Thanks to the inclusion of the three-nucleon interaction and
despite the minimal optimization effort, a reasonable agreement with
experimental centroid energies of all three modes has been achieved. The role
and scope of the Hartree-Fock reference state in RPA methods are discussed.Comment: v2: 11 pages, incl. 3 figures; extended discussion and outlook; to
appear in J.Phys.
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