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