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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 Satula, Tomek Werner,
Maciek Zalewski
DFT-UNEDF Workshop Joint Institute for Heavy Ion
Research, ORNL, Oak Ridge, TN-37831, USA January
22, 2008
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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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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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The Matrix SkP case
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) ?
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Binding energies of 16O and 208Pb ?
Binding energies of 120-132Sn ?
Average pairing gap ?
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Nuclear Energy Density Functional
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(b) central
(a)
(c)
potential
?
(b)
(a) kinetic
?(potential)/?C0
40Ca
SLy5
(c) spin-orbit
R(fm)
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Mass, shape, and spin polarization effects
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Polarization effects for spin-orbit splitting
Fits of C0?J, C0J , and C1J
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Shell gaps
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