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Technology to calculate observables• Global properties• SpectroscopyDFT SolversFunctional formFunctional optimizationEstimation of theoretical errors

Using the Functionals Towards Spectroscopic-Quality NEDF

DFT ApplicationsWitold Nazarewicz (Tennessee)

DOE UNEDF Review, April 2008

UTK/ORNL (Nazarewicz, Schunck, Stoitsov)MSU (Brown), UW (Bertsch),Texas Commerce (Bertulani)ANL (Moré, Sarich)Warsaw, Jyväskylä (Dobaczewski)

UTK/ORNL (Nazarewicz, Schunck, Stoitsov)UW (Bulgac)ANL (Moré, Norris, Sarich)ORNL (Fann, Shelton, Roche)Warsaw (Dobaczewski, Magierski)UTK (Pei)

UTK/ORNL (Nazarewicz)ANL (Moré, Norris, Sarich)Bruyeres (Goutte)Lublin (Baran, Staszczak)

UNEDF PhysicsUNEDF CS/AMUNEDF Foreign CollaboratorOutside UNEDF

• Constrained by microscopic theory: ab-initio functionals (cf. talks by Carlson and Furnstahl)

• 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)

pairingfunctional

Construction of the functionalPerlinska et al., Phys. Rev. C 69, 014316 (2004)

Most general second order expansion in densities and their derivatives(cf. talk by Bertsch for definitions of densities and currents)

p-h density p-p density

Nuclear DFT: works well for differences

• Global DFT mass calculations: HFB mass formula: m~700keV

Stoitsov et al., PRL 98, 132502 (2007)

Bimodal fission in nuclear DFT

http://orph02.phy.ornl.gov/workshops/lacm08/unedf.html

41 participants

see http://orph02.phy.ornl.gov/workshops/lacm08/UNEDF/database.html

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Example:Example: Large Scale Mass Table Calculations Large Scale Mass Table CalculationsScience scales with processors

The SkM* mass table contains 2525 even-even nucleiThe SkM* mass table contains 2525 even-even nuclei A single processor calculates each nucleus 3 times (prolate, oblate, spherical) A single processor calculates each nucleus 3 times (prolate, oblate, spherical)

and records all nuclear characteristics and candidates for blocked calculations and records all nuclear characteristics and candidates for blocked calculations in the neighborsin the neighbors

Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration)Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration)

9,210 nuclei9,210 nuclei 599,265 configurations599,265 configurations Using 3,000 processors - about 25 CPU hoursUsing 3,000 processors - about 25 CPU hours

Even-Even NucleiEven-Even Nuclei

All NucleiAll Nuclei

M. Stoitsov

HFB+LN mass table, HFBTHO

Number of processors > number of nuclei!

Jaguar Cray XT4 at ORNL

INCITE awardDean et al. 17.5M hours

INCITE awardDean et al. 17.5M hours

Example: Broyden Mixing

Collaborative effort: UTK/ORNL, UW, ANL

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Example:Example: Mass Table eXplorer ( Mass Table eXplorer (http://mtex.110mb.com/http://mtex.110mb.com/) (tools for data analysis/processing)(tools for data analysis/processing)

• Solid microscopic foundation link to ab-initio approaches limits obeyed (e.g., unitary regime)

• Unique opportunities provided by coupling to CS/AM• Comprehensive phenomenology probing crucial parts of the

functional different observables probing different physics

• Stringent optimization protocol providing not only the coupling constants but also their uncertainties (theoretical errors)

• Unprecedented international effort• Unique experimental data available (in particular: far from

stability; link to FRIB science)

Conclusion: we can deliver a well theoretically founded EDF, of spectroscopic quality, for structure and reactions, based on as much as possible ab initio input at this point in time

Why us?There is a zoo of nuclear functionals on the market. What makes us believe we can make a breakthrough?

Backup

Building blocks: Nuclear Local Densities and Currents

€

ρ0

r r ( ) = ρ 0

r r ,

r r ( ) = ρ

r r στ ;

r r στ( )

στ

∑ isoscalar (T=0) density

€

ρ0 = ρ n + ρ p( )

€

ρ1

r r ( ) = ρ1

r r ,

r r ( ) = ρ

r r στ ;

r r στ( )

στ

∑ τ isovector (T=1) density

€

ρ1 = ρ n − ρ p( )

€

vs 1

r r ( ) = ρ

r r στ ;

r r σ 'τ( )

σσ 'τ

∑ σ σ 'σ τ isovector spin density

€

vs 0

r r ( ) = ρ

r r στ ;

r r σ 'τ( )

σσ 'τ

∑ σ σ 'σ isoscalar spin density

€

rj T

r r ( ) =

i

2

r ∇'−

r ∇( )ρT

r r ,

r r '( ) r

r '=r r

€

tJ T

r r ( ) =

i

2

r ∇'−

r ∇( )⊗

v s T

r r ,

r r '( ) r

r '=r r

€

τT

r r ( ) =

r ∇ ⋅

r ∇'ρT

r r ,

r r '( ) r

r '=r r

€

rT T

r r ( ) =

r ∇ ⋅

r ∇'

r s T

r r ,

r r '( ) r

r '=r r

current density

spin-current tensor density

kinetic density

kinetic spin density

+ analogous p-p densities and currents

Can dynamics be incorporated directly into the functional?Example: Local Density Functional Theory for Superfluid Fermionic Systems: The

Unitary Gas, Aurel Bulgac, Phys. Rev. A 76, 040502 (2007)

See also:

Density-functional theory for fermions in the unitary regimeT. PapenbrockPhys. Rev. A72, 041603 (2005)

Density functional theory for fermionsclose to the unitary regime A. Bhattacharyya and T. PapenbrockPhys. Rev. A 74, 041602(R) (2006)

One-quasiparticle States

Deformed States

Collaborative effort: UTK/ORNL, UW, ANL

ES

D(t

he.)

-ES

D(e

xp.)

[M

eV]

Physics/Computer Science PartnershipsFann+, More+, Roche+

Examples:

• Optimization techniques for petascale nuclear structure DFT codes

• Solving large-scale systems of nonlinear equations• Evaluation of performance and scalability in DFT calculations• Evaluation of derivative-free methods for noisy, nonlinear

problems• 3-D adaptive multi-resolution method for atomic nuclei

(Madness)