Jacek Dobaczewski University of Warsaw & University of Jyväskylä

1. 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, Maciek Zalewski DFT-UNEDF Workshop Joint Institute for Heavy Ion Research, ORNL, Oak Ridge, TN-37831, USA January 22, 2008

2. Outline • The Matrix for SkP. • Dependence of single-particle energies on coupling constants. • Fits of spin-orbit and tensor coupling constants. • Error analysis in mass fits. • Extensions in density dependence and stability conditions. • Extensions to higher powers of derivatives. • Extensions to higher powers of densities.

3. The bottom line • Spectroscopic-quality energy density functional  correct description of positions and evolution of single-particle levels. • Single-particle levels  correct description of one-particle separation energies with all polarization effects included. • Within the EDF method, shape and spin polarization effects in doubly-magic nuclei are relatively small – much smaller than deviations from data. • Dependence of total and single-particle energies on coupling constants is very linear. • No fits without error estimates and error propagation! • Extensions beyond the simple Skyrme functionals are mandatory.

4. The Matrix – SkP case

5. Nuclear Energy Density Functional

10. (c) spin-orbit  (density)/C0 (b) particle 40Ca SLy5 (b) (a) density (a) kinetic (c) R(fm)

11. (b) central (a) (c) potential  (b) (a) kinetic (potential)/C0 40Ca SLy5 (c) spin-orbit R(fm)

12. Mass, shape, and spin polarization effects

13. Polarization effects for spin-orbit splitting Fits of C0J, C0J , and C1J

14. Shell gaps

22. =1/6

23. =1/4

24. =1/6