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

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.

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.

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

Jacek Dobaczewski

Nuclear Energy Density Functional

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

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

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

Jacek Dobaczewski

Mass, shape, and spin polarization effects

Jacek Dobaczewski

Polarization effects for spin-orbit

splitting

Fits of C0J, C0

J , and C1

J

Jacek Dobaczewski

Shell gaps

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

Jacek Dobaczewski

=1/6

Jacek Dobaczewski

=1/4

Jacek Dobaczewski

=1/6