jacek dobaczewski university of warsaw & university of jyväskylä
DESCRIPTION
Spectroscopic-quality energy density functional and how to get there. Jacek Dobaczewski University of Warsaw & University of Jyväskylä. Jyväskylä : Gillis Carlsson, Markus Kortelainen , Kazuhito Mizuyama, Jussi Toivanen Warsaw : Wojtek Satuła, Tomek Werner, - PowerPoint PPT PresentationTRANSCRIPT
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Jacek Dobaczewski
Jacek DobaczewskiUniversity of Warsaw & University of Jyväskylä
Spectroscopic-quality energy densityfunctional and how to get there
DFT-UNEDF WorkshopJoint Institute for Heavy Ion Research, ORNL,
Oak Ridge, TN-37831, USAJanuary 22, 2008
Jyväskylä: Gillis Carlsson, Markus Kortelainen, Kazuhito Mizuyama, Jussi ToivanenWarsaw: Wojtek Satuła, Tomek Werner, Maciek Zalewski
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Jacek Dobaczewski
Outline
1. The Matrix for SkP.2. Dependence of single-particle energies on
coupling constants.3. Fits of spin-orbit and tensor coupling
constants.4. Error analysis in mass fits.5. Extensions in density dependence and
stability conditions.6. Extensions to higher powers of
derivatives.7. Extensions to higher powers of densities.
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Jacek Dobaczewski
The bottom line
1. Spectroscopic-quality energy density functional correct description of positions and evolution of single-particle levels.
2. Single-particle levels correct description of one-particle separation energies with all polarization effects included.
3. Within the EDF method, shape and spin polarization effects in doubly-magic nuclei are relatively small – much smaller than deviations from data.
4. Dependence of total and single-particle energies on coupling constants is very linear.
5. No fits without error estimates and error propagation!
6. Extensions beyond the simple Skyrme functionals are mandatory.
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Jacek Dobaczewski
Skyrme binding energy, saturation
density incompressibility,
enhancement factor, isospin symmetry
energy at 0 and 0/2;
(6 parameters)
Effective Mass
Skyrme surface energy
Spin-orbit strength W0
Average pairing matrix
element
NM binding energy saturation density incompressibility,
enhancement factor, isospin symmetry
energy at 0 and 0/2;
(6 “observables”)
1
Binding energies of 16O and 208Pb
Binding energies of 120-132Sn
Average pairing gap
The Matrix – SkP caseThe Matrix – SkP case
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Jacek Dobaczewski
Nuclear Energy Density Functional
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Jacek Dobaczewski
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Jacek Dobaczewski
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Jacek Dobaczewski
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Jacek Dobaczewski
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Jacek Dobaczewski
-0,0015
-0,0010
-0,0005
0,0000
0 2 4 6R(fm)
0,00
0,05
0,10
0 2 4 6
(de
nsit
y)/
C0
(a) kinetic
(b) particle
(c) spin-orbit
(a)
(c)
(b)
dens
ity
SLy540Ca
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Jacek Dobaczewski
-0,1
0,0
0,1
0,2
0,3
0,4
0 2 4 6 8
-60
-40
-20
0
20
0 2 4 6 8
R(fm)
(po
tent
ial)
/C
0
(a) kinetic
(b) central
(c) spin-orbit
(a)
(c)
(b)
pote
ntia
l
SLy540Ca
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Jacek Dobaczewski
Mass, shape, and spin polarization effects
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Jacek Dobaczewski
Polarization effects for spin-orbit
splitting
Fits of C0J, C0
J , and C1
J
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Jacek Dobaczewski
Shell gaps
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Jacek Dobaczewski
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Jacek Dobaczewski
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Jacek Dobaczewski
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Jacek Dobaczewski
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Jacek Dobaczewski
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Jacek Dobaczewski
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