xii nuclear physics workshop maria and pierre curie: nuclear structure physics and low-energy...
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XII Nuclear Physics Workshop Maria and Pierre Curie: Nuclear Structure Physics and Low-Energy Reactions, Sept. 21-25, Kazimierz Dolny, Poland
Self-Consistent Description of Collective Excitations
in the Unitary Correlation Operator Model
Self-Consistent Description of Collective Excitations
in the Unitary Correlation Operator Model
N. PaarN. Paar, P. Papakonstantinou, R. Roth, and H. Hergert, P. Papakonstantinou, R. Roth, and H. Hergert
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Realistic and Effective Nucleon-Nucleon Interactions
Realistic nucleon-nucleon interactions are determined from the phase-shift analysis of nucleon-nucleon scattering
Effective nucleon-nucleon interaction
strong repulsive core at small distances ~ 0.5 fm
Realistic nucleon-nucleon
interaction
Very large or infinite matrix elements of interaction (relative wave functions penetrate the core)
Very large or infinite matrix elements of interaction (relative wave functions penetrate the core)
AV18, central part (S,T)=(0,1)
4He
CC
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THE UNITARY CORRELATION OPERATOR METHOD
CORRELATED MANY-
BODY STATE
UNCORRELATED MANY-BODY
STATE
CORRELATED
OPERATOR
UNCORRELATED OPERATOR
Instead of correlated many-body states, the correlatedoperators are employed in nuclear structure models of finite nuclei
Short-range central and tensor correlations are included in the simple many body states via unitary transformation
R. Roth et al., Nucl. Phys. A 745, 3 (2004)H. Feldmeier et al., Nucl. Phys. A 632, 61 (1998)T. Neff et al., Nucl. Phys. A 713, 311 (2003)R. Roth et al., Phys. Rev. C 72, 034002 (2005)
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DEUTERON: MANIFESTATION OF CORRELATIONS
Spin-projected two-bodydensity of the deuteron for AV18 potential
Spin-projected two-bodydensity of the deuteron for AV18 potential
TWO-BODY DENSITY FULLY SUPPRESSED AT SMALL PARTICLE DISTANCES
ANGULAR DISTRIBUTIONDEPENDS STRONGLY ONRELATIVE SPIN ORIENTATION
CENTRAL CORRELATIONS TENSOR CORRELATIONS
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Argonne V18
Potential
VUCOM
Hartree-Fock
Random Phase
Approximation
Central Correlator Cr
Tensor Correlator CΩ
Fermionic
Molecular
Dynamics
No-core Shell Model
Two-Body Approximation
40
12
6
2
TW
O-N
UC
LEO
N S
YS
TEM
FIN
ITE N
UC
LEI
THE UNITARY CORRELATION OPERATOR METHOD
3-Nucleon Interactio
n
Correlation functions are constrained by the energy minimization in the two-body systemAdditional constraints necessary to restrict the ranges of the correlation functions
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CORRELATED REALISTIC NN INTERACTION - VUCOM
Closed operator expression for the correlated interactionVUCOM in two-body approximation
Correlated interaction and original NN-potential are phase shift equivalent by construction
Momentum-space matrix elements of the correlated interaction VUCOM are similar to low-momentum interaction Vlow-k
Central and tensor correlations are essential to obtain bound nuclear system
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CANCELLATION OF OMMITED 3-BODY CONTRIBUTIONS OF THE CLUSTER EXPANSION AND GENUINE 3-BODY FORCE
NO-CORE SHELL MODEL CALCULATIONS USING VUCOM POTENTIAL
R. Roth et al, nucl-th/0505080
WHAT IS OPTIMAL RANGE FOR THE TENSOR CORRELATOR?
VNN+V3N
Incr
easi
ng ra
nge
of
the
tens
or c
orre
lato
r
SELECT A CORRELATORWITH ENERGY CLOSE TO EXPERIMENTAL VALUE
SELECT A CORRELATORWITH ENERGY CLOSE TO EXPERIMENTAL VALUE
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Hartree-Fock Model Based on Correlated Realistic NN-potential
Nucleons are moving in an average single-particle potential
Expansion of the single-particle state in harmonic-oscillator basis
Matrix formulation of Hartree-Fock equations as a generalized eigenvalue problem
Restrictions on the maximal value of the major shell quantum number NMAX=12 and orbital angular momentum lMAX=8
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UCOM Hartree-Fock Single-Particle Spectra
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UCOM Hartree-Fock Binding Energies & Charge Radii
3-body interactionLong-range correlations
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Fully-self consistent RPA model: there is no mixing between the spurious 1-
state and excitation spectra
Vibration creation operator (1p-1h):
Equations of motion RPA
Low-amplitude collective oscillations
UCOM Random-Phase Approximation
VUCOMEXCITATIONENERGIES
&
Sum rules: Є=±3%
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UCOM-RPA Isoscalar Giant Monopole Resonance
Relativistic RPA (DD-ME1 interaction)
Various ranges of the UCOM tensor correlation functions
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UCOM-RPA Isovector Giant Dipole Resonance
Various ranges of the UCOM tensor correlation functions
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UCOM-RPA Giant Quadrupole Resonance
THE CORRELATED REALISTIC NN INTERACTION GENERATES THE LOW-LYING 2+ STATE AND GIANT QUADRUPOLE RESONANCE
THE CORRELATED REALISTIC NN INTERACTION GENERATES THE LOW-LYING 2+ STATE AND GIANT QUADRUPOLE RESONANCE
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UCOM-RPA Isoscalar Giant Quadrupole Resonance
Various ranges of the UCOM tensor correlation functions
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UCOM-RPA GROUND-STATE CORRELATIONS
Part of the missing long-range correlations in UCOM-Hartree-Fock model is reproduced by the RPA correlations
NMAX=12 & lMAX=8
Variation of the range of the tensor correlation function in (S=1,T=0) channel
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The unitary correlation operator model (UCOM) provides an effective interaction suitable for the nuclear structure models
UCOM Hartree-Fock model results with underbinding and small radii necessity for long-range correlations (recovered by RPA
& perturbation theory) and the three-body interaction
Fully self-consistent UCOM Random-Phase Approximation (RPA) is constructed in the UCOM Hartree-Fock single-nucleon basis
Correlated realistic NN interaction generates collective excitationmodes, however it overestimates IVGDR and ISGQR energies
SUMMARY
Damping, couplings of complex configurations, Second RPA
Optimization of the constraints for the ranges of correlators
Three-body interaction