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NN+NNNinterac+ons
DensityMatrixExpansion
Input
EnergyDensityFunc+onal
Observables
• Directcomparisonwithexperiment
• Pseudo-dataforreac+onsandastrophysics
Densitydependentinterac+ons
Fit-observables• experiment• pseudodata
Op+miza+on
DFTvaria+onalprincipleHF,HFB(self-consistency)
Symmetrybreaking
Symmetryrestora+onMul+-referenceDFT(GCM)TimedependentDFT(TDHFB)
Nuclear Density Functional Theory and Extensions
• two fermi liquids • self-bound • superfluid (ph and pp channels) • self-consistent mean-fields • broken-symmetry generalized product states
Technology to calculate observables Global properties
Spectroscopy DFT Solvers
Functional form Functional optimization
Estimation of theoretical errors
Mean-Field Theory ⇒ Density Functional Theory
• mean-field ⇒ one-body densities
• zero-range ⇒ local densities
• finite-range ⇒ gradient terms
• particle-hole and pairing channels
• Has been extremely successful. A broken-symmetry generalized product state does surprisingly good job for nuclei.
Nuclear DFT • two fermi liquids • self-bound • superfluid
Degrees of freedom: nucleonic densities
• Constrained by microscopic theory: ab-initio functionals provide quasi-data! • Not all terms are equally important. Usually ~12 terms considered • Some terms probe specific experimental data • Pairing functional poorly determined. Usually 1-2 terms active. • Becomes very simple in limiting cases (e.g., unitary limit) • Can be extended into multi-reference DFT (GCM) and projected DFT
Nuclear Energy Density Functional
p-h density p-p density (pairing functional)
isoscalar (T=0) density
€
ρ0 = ρn + ρp( )
isovector (T=1) density
€
ρ1 = ρn − ρp( )
+isoscalar and isovector densities: spin, current, spin-current tensor, kinetic, and kinetic-spin
+ pairing densities
E =�H(r)d3r
Expansion in densities and their derivatives
Mass table
Goriely, Chamel, Pearson: HFB-17 Phys. Rev. Lett. 102, 152503 (2009)
δm=0.581 MeV
Cwiok et al., Nature, 433, 705 (2005)
BE differences
Examples: Nuclear Density Functional Theory
Traditional (limited) functionals provide quantitative description
0 40 80 120 160 200 240 280
neutron number
0
40
80
120
prot
on n
umbe
r two-proton drip line
two-neutron drip line
232 240 248 256neutron number
prot
on n
umbe
r
90
110
100
Z=50
Z=82
Z=20
N=50
N=82
N=126
N=20
N=184
drip line
SV-min
known nucleistable nuclei
N=28
Z=28
230 244
N=258
Nuclear Landscape 2012
S2n = 2 MeV
How many protons and neutrons can be bound in a nucleus?
Skyrme-DFT:6,900±500systLiterature: 5,000-12,000
288 ~3,000
Erleretal.Nature486,509(2012)
Asymptotic freedom ?
from B. Sherrill
DFTFRIB
current
Quantified Nuclear Landscape
SmallandLarge-AmplitudeCollec+veMo+on• New-genera+oncomputa+onalframeworksdeveloped
• Time-dependentDFTanditsextensions• Collec+veSchrödingerEqua+on• Quasi-par+cleRPA• Projec+ontechniques
• AppliedtoHIfusion,fission,coexistencephenomenaShapecoexistence
Hinohara et al. PRC 84, 061302(R) (2011)
Fusion cross section
45 50 55 60 65Ec.m. (MeV)
10-4
10-3
10-2
10-1
100
101
102
σfu
sion (m
b)
Ec.m. = 55 MeV, TDDFT Experiment
48Ca+238U
R. Keser et al., PRC 85, 044606 (2012)
48Ca+48Ca
also: Tsunoda et al. Phys. Rev. C 89, 031301(R) (2014); HPCI
NuclearFission
Sadhukhan et al. Phys. Rev. C 90 061304(R) (2014) and arXiv:1510.08003 30 70
0
10
20
30
40
50
5
7753
95
57
75
39
11
-3
-9-15
-21
911
-27
3
qI
240Pu
100 150 200 250 300 350 4000
10
20
30
40
50
qII
Q30(b3/2 )
Q20 (b)
dynamic
static
Q22(b)
Spontaneousfissionyields
50 60
0.1
1
10
120 140 160
0.1
1
10
cha
rge
yiel
d (%
)
fragment charge
mas
s yi
eld
(%)
fragment mass
240Pu
http://science.energy.gov/ascr/highlights/2015/ascr-2015-08-a/
Quest for understanding the neutron-rich matter on Earth and in the Cosmos
Data Crustal structures in neutron stars
0.8 0.9 1.1 1.21.0R(1.4 M )/R.
_
R skin
(208 Pb
)/Rsk
in
_
0.8
0.9
1.1
1.2
1.0
0.032% 0.057%
0.075%
The covariance ellipsoid for the neutron skin Rskin in 208Pb and the radius of a 1.4M⊙ neutron star. The mean values are: R(1.4M⊙ )=10 km and Rskin= 0.17 fm.
ISNET:Enhancingtheinterac+onbetweennuclearexperimentandtheorythroughinforma+onandsta+s+cs
JPGFocusIssue:hHp://iopscience.iop.org/0954-3899/page/ISNETAround35papers(includingnuclearstructure,reac+ons,nuclearastrophysics,mediumenergyphysics,sta+s+calmethods…andfission…)
“Rememberthatallmodelsarewrong;theprac+calques+onishowwrongdotheyhavetobetonotbeuseful”(E.P.Box)
Errores+matesoftheore+calmodels:aguideJ.Phys.G41074001(2014)
Informa+onContentofNewMeasurementsJ.McDonnelletal.Phys.Rev.LeH.114,122501(2015)
• DevelopedaBayesianframeworktoquantifyandpropagatestatisticaluncertaintiesofEDFs.
• ShowedthatnewprecisemassmeasurementsdonotimposesufficientconstraintstoleadtosignificantchangesinthecurrentDFTmodels(modelsarenotpreciseenough)
Bivariatemarginalestimatesoftheposteriordistributionforthe12-dimensionalDFTUNEDF1parameterization.
1teraflop=1012 flops 1peta=1015 flops (today) 1exa=1018 flops (next 10 years)
Tremendous opportunities for nuclear theory!
Theoretical Tools and Connections to Computational Science
33.9 pflops
November 2015
3,120,000 cores
http://top500.org
Future: large multi-institutional efforts involving strong coupling between physics, computer science, and applied math
“High performance computing provides answers to questions that neither experiment nor analytic theory can address; hence, it becomes a third leg supporting the field of nuclear physics.” (NAC Decadal Study Report)
HighPerformanceCompu+ngandNuclearTheory