Energy density optimization: UNEDF2
ARIS 2014

ARIS 2014, Jun 6, 2014

Skyrme energy density
ρ 2τΔρ∇JJ 2H even(r)=C
ρ+Cρ
τ+CρΔρ+Cρ
∇⋅J+Ctt tt t tttttttt JtρρργCt = Ct0 + C tD ρ0 , t=0,1
Skyrme EDF is constructed frombilinear terms of density matrices andtheir derivatives up to the 2nd order● Each term multiplied by a constantcoupling constant(except density dependent Cρ)● Volume part of the ED can beparameterized with infinite nuclearmatter parameters● Coupling constants adjusted toexperimental input●From G. Bertsch et al, SciDAC Review 6 42 (2007)

ARIS 2014, Jun 6, 2014

Energy density optimization: UNEDF0 and UNEDF1
UNEDF0 dataset

UNEDF0: M. K., T. Lesinski, J. Moré, W. Nazarewicz, J.
Sarich, N. Schunck, M. V. Stoitsov, S. Wild, PRC 82,024313 (2010)
UNEDF1: M. K., J. McDonnell, W. Nazarewicz, P.-G.
Reinhard, J. Sarich, N. Schunck, M. V. Stoitsov, S. Wild,PRC 85, 024304 (2012)

Experimental data:●44 deformed b.e.
●28 spherical b.e.
●28 rms radii●8 oes energies●Optimization of Skyrme-like ED with respect of
12 parameters at deformed HFB levelNMNMNM

NM−1

 c , E / A , K , a sym , L sym , M s
C 0   , C 1   , V n0 , V 0p , C 0 ∇ J ,C 1∇ J

UNEDF1 was the first parameterization which
was systematically optimized at the deformed
HFB level for fission studies● UNEDF1 included data on 4 fission isomers
states (226U, 238U, 240Pu, 242Cm)●ARIS 2014, Jun 6, 2014

UNEDF0 and UNEDF1: Performance

ARIS 2014, Jun 6, 2014

Energy density optimization: UNEDF2●Optimization of Skyrme-like ED with respect of
14 parameters at deformed HFB level: Tensorterms now included
NM−1ρc , E NM / A , K NM , aNM,L,M
symsyms
ρ Δρ
ρΔ ρnpρ∇ Jρ∇JC 0 ,C 1 , V 0 ,V 0 , C 0 , C1 ,C J0 , C1J●UNEDF2: M.K., J. McDonnell, W. Nazarewicz, E. Olsen,P.-G. Reinhard, J. Sarich, N. Schunck, S.M. Wild, D.
Davesne, J. Erler, A. Pastore, Phys. Rev. C 89 054314(2014)

Single particle energies included in theoptimization. These are handled with blocked
HFB calculations
UNEDF2 binding energies

ARIS 2014, Jun 6, 2014

UNEDF2: Global properties
RMS deviations of various observables●Generally, UNEDF2 gives no or only marginal improvement over to UNEDF1⇒ Novel EDF developments required to improve precision (see Jacek's talk)

ARIS 2014, Jun 6, 2014

Sensitivity analysis
UNEDF2 correlation matrix

With UNEDF0,1 and 2, a complete
sensitivity analysis was done for theobtained minimum● Standard deviations and correlations ofoptimized EDF parameters● Crucial information when addressing
predictive power.
power E.g propagation ofthe error.
●Impact of a datapoint to obtained parameterization●Sensitivity analysis shows that UNEDF2 fully
constrained with the data
⇒ Major improvements not possible in
the Skyrme-EDF framework

ARIS 2014, Jun 6, 2014

Conclusions and outlook

UNEDF0, 1 and 2 presents a optimization scheme of Skyrme-like EDF, which includes
progressively more experimental data.
● Many UNEDF2 properties sligthly worse than with more specialiced UNEDF0 or
UNEDF1. UNEDF2 is the best all-around Skyrme EDF● Sensitivity analysis shows that further major improvements for UNEDF2 are unlikely● Generally, limits of the Skyrme-like EDF models have been reached: Novel EDFs
required to improve precision. This conclusion is also supported by several other studies.
●Possible future directions: EDFs with higher order derivatives, DME-based functionals,regularized higher-order functionals.
● Future EDF optimizations schemes should include sensitivity analysis to assess thepredictive power of the model●ARIS 2014, Jun 6, 2014

Backup slides

UNEDF parameters

ARIS 2014, Jun 6, 2014

UNEDF2 parameters

ARIS 2014, Jun 6, 2014

UNEDF properties

ARIS 2014, Jun 6, 2014