337 research outputs found
The Unitary Correlation Operator Method from a Similarity Renormalization Group Perspective
We investigate how the Unitary Correlation Operator Method (UCOM), developed
to explicitly describe the strong short-range central and tensor correlations
present in the nuclear many-body system, relates to the Similarity
Renormalization Group (SRG), a method to band-diagonalize Hamiltonians by
continuous unitary transformations. We demonstrate how the structure of the
UCOM transformation, originally motivated from the physically intuitive picture
of correlations in coordinate space, arises naturally from the SRG flow
equation. Apart from formal considerations we show that the momentum space
matrix elements of the effective interactions obtained in both schemes agree
extremely well.Comment: 5 pages, 2 figures, using REVTEX4; v2: references adde
From nucleon-nucleon interaction matrix elements in momentum space to an operator representation
Starting from the matrix elements of the nucleon-nucleon interaction in
momentum space we present a method to derive an operator representation with a
minimal set of operators that is required to provide an optimal description of
the partial waves with low angular momentum. As a first application we use this
method to obtain an operator representation for the Argonne potential
transformed by means of the unitary correlation operator method and discuss the
necessity of including momentum dependent operators. The resulting operator
representation leads to the same results as the original momentum space matrix
elements when applied to the two-nucleon system and various light nuclei. For
applications in fermionic and antisymmetrized molecular dynamics, where an
operator representation of a soft but realistic effective interaction is
indispensable, a simplified version using a reduced set of operators is given
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
Nuclear Structure and Response based on Correlated Realistic NN Interactions
Starting from the Argonne V18 nucleon-nucleon (NN) interaction and using the
Unitary Correlation Operator Method, a correlated interaction v_UCOM has been
constructed, which is suitable for calculations within restricted Hilbert
spaces. In this work we employ the v_UCOM in Hartree-Fock, perturbation-theory
and RPA calculations and we study the ground-state properties of various
closed-shell nuclei, as well as some excited states. The present calculations
provide also important feedback for the optimization of the v_UCOM and valuable
information on its properties. The above scheme offers the prospect of ab
initio calculations in nuclei, regardless of their mass number. It can be used
in conjunction with other realistic NN interactions as well, and with various
many-body methods (Second RPA, QRPA, Shell Model, etc.).Comment: 3 pages, incl. 2 figures; Proc. Int. Conf. on Frontiers in Nuclear
Structure, Astrophysics and Reactions (FINUSTAR), Kos, Greece, Sept.200
Treatment of the Intrinsic Hamiltonian in Particle-Number Nonconserving Theories
We discuss the implications of using an intrinsic Hamiltonian in theories
without particle-number conservation, e.g., the Hartree-Fock-Bogoliubov
approximation, where the Hamiltonian's particle-number dependence leads to
discrepancies if one naively replaces the particle-number operator by its
expectation value. We develop a systematic expansion that fixes this problem
and leads to an a posteriori justification of the widely-used one- plus
two-body form of the intrinsic kinetic energy in nuclear self-consistent field
methods. The expansion's convergence properties as well as its practical
applications are discussed for several sample nuclei.Comment: 6 pages, 5 figure
Pairing in the Framework of the Unitary Correlation Operator Method (UCOM): Hartree-Fock-Bogoliubov Calculations
In this first in a series of articles, we apply effective interactions
derived by the Unitary Correlation Operator Method (UCOM) to the description of
open-shell nuclei, using a self-consistent Hartree-Fock-Bogoliubov framework to
account for pairing correlations. To disentangle the particle-hole and
particle-particle channels and assess the pairing properties of \VUCOM, we
consider hybrid calculations using the phenomenological Gogny D1S interaction
to derive the particle-hole mean field. In the main part of this article, we
perform calculations of the tin isotopic chain using \VUCOM in both the
particle-hole and particle-particle channels. We study the interplay of both
channels, and discuss the impact of non-central and non-local terms in
realistic interactions as well as the frequently used restriction of pairing
interactions to the partial wave. The treatment of the center-of-mass
motion and its effect on theoretical pairing gaps is assessed independently of
the used interactions.Comment: 14 pages, 10 figures, to appear in Phys. Rev. C, title modified
accordingl
Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Nucleon Interactions
We formulate the In-Medium Similarity Renormalization Group (IM-SRG) for
open-shell nuclei using a multi-reference formalism based on a generalized Wick
theorem introduced in quantum chemistry. The resulting multi-reference IM-SRG
(MR-IM-SRG) is used to perform the first ab initio study of even oxygen
isotopes with chiral NN and 3N Hamiltonians, from the proton to the neutron
drip lines. We obtain an excellent reproduction of experimental ground-state
energies with quantified uncertainties, which is validated by results from the
Importance-Truncated No-Core Shell Model and the Coupled Cluster method. The
agreement between conceptually different many-body approaches and experiment
highlights the predictive power of current chiral two- and three-nucleon
interactions, and establishes the MR-IM-SRG as a promising new tool for ab
initio calculations of medium-mass nuclei far from shell closures.Comment: 5 pages, 4 figures, v2 corresponding to published versio
Matrix Elements and Few-Body Calculations within the Unitary Correlation Operator Method
We employ the Unitary Correlation Operator Method (UCOM) to construct
correlated, low-momentum matrix elements of realistic nucleon-nucleon
interactions. The dominant short-range central and tensor correlations induced
by the interaction are included explicitly by an unitary transformation. Using
correlated momentum-space matrix elements of the Argonne V18 potential, we show
that the unitary transformation eliminates the strong off-diagonal
contributions caused by the short-range repulsion and the tensor interaction,
and leaves a correlated interaction dominated by low-momentum contributions. We
use correlated harmonic oscillator matrix elements as input for no-core shell
model calculations for few-nucleon systems. Compared to the bare interaction,
the convergence properties are dramatically improved. The bulk of the binding
energy can already be obtained in very small model spaces or even with a single
Slater determinant. Residual long-range correlations, not treated explicitly by
the unitary transformation, can easily be described in model spaces of moderate
size allowing for fast convergence. By varying the range of the tensor
correlator we are able to map out the Tjon line and can in turn constrain the
optimal correlator ranges.Comment: 16 pages, 9 figures, using REVTEX
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