No Core CI Calculations for light nuclear systems · INT Extreme Computing workshop, June 2011 No Core CI Calculations for light nuclear systems Pieter Maris [email protected] Iowa

INT Extreme Computing workshop, June 2011

No Core CI Calculationsfor light nuclear systems

Pieter [email protected]

Iowa State University

SciDAC project – UNEDFspokespersons: Rusty Lusk (ANL), Witek Nazarewicz (ORNL/UT)http://www.unedf.org

PetaApps awardPIs: Jerry Draayer (LSU), Umit Catalyurek (OSU)Masha Sosonkina, James Vary (ISU)

INCITE award – Computational Nuclear StructurePI: James Vary (ISU)

NERSC CPU time

INT Extreme Computing, June 7 2011 – p.1/43

SciDAC/UNEDF – Uniform description of nuclear structure

Universal Nuclear EnergyDensity Functional thatspans the entire mass tablebased on ab initio calculations

Greens Function MonteCarlo (Pieper et al, ANL)

No-Core ConfigurationInteraction calculations

Coupled Cluster(Papenbrock et al, ORNL)

http://www.unedf.org

spokespersons:R. Lusk (ANL)W. Nazarewicz (ORNL/UT)

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Configuration Interaction Methods

Expand wave function in basis states |Ψ〉 =∑

ai|ψi〉

Express Hamiltonian in basis 〈ψj |H|ψi〉 = Hij

Diagonalize Hamiltonian matrix Hij

Complete basis −→ exact result

caveat: complete basis is infinite dimensional

In practicetruncate basisstudy behavior of observables as function of truncation

Computational challenge

construct large (1010 × 1010) sparse symmetric real matrix Hij

use Lanczos algorithmto obtain lowest eigenvalues & eigenvectors


Many-Body Basis Space


ai|ψi〉

Many-Body basis states |ψi〉

Slater Determinants of single-particle states |φ〉

|ψ〉 = |φ1〉 ⊗ . . .⊗ |φA〉

single-particle basis stateseigenstates of SU(2) operatorsL

2, S2, J

2 = (L + S)2, and Jz

w. quantum numbers |φ〉 = |n, l, s, j,m〉

radial wavefunctions:Harmonic Oscillator

M -scheme: many-body basis states eigenstates of Jz

Jz|ψ〉 = M |ψ〉 =A

∑

i=1

mi|ψ〉

Alternatives: LS-scheme, Total-J-scheme, Symplectic basis, . . .


Truncation Schemes

Nmax truncationtruncation on the total numberof H.O. oscillator quantaabove minimal configurationfor that nucleus

NMIN=0

NMAX=6

configuration

“6h!” configuration for 6Li

allows for exact seperationof Center-of-Mass motionand intrinsic motion

Alternative truncation schemesFCI – Full ConfigurationInteraction – truncation onsingle-particle basis only

100 1 k 10 k 100 k 1 M 10 M 100 M

basis space dimension

-32

-30

-28

-26

-24

-22

-20

grou

nd s

tate

ene

rgy

4He, FCI truncation4He, N

max truncation

6Li, FCI truncation6Li, N

max truncation

4He, NCFC result6Li, NCFC result

Importance Sampling, Monte Carlo Sampling, Symplectic, . . .


Intermezzo: Center-of-Mass excitations

Use single-particle coordinates, not relative (Jacobi) coordinatesstraightforward to extend to many particleshave to seperate Center-of-Mass motion from intrinsic motion

Add Lagrange multiplier to Hamiltonian

Hrel −→ Hrel + ΛCM

(

HH.O.CM −

3

2~ω

)

with Hrel = Trel + Vrel the relative Hamiltonianseperates CM excitations from CM ground state |ΦCM 〉

Center-of-Mass wave function factorizes forH.O. basis functions in combination with Nmax truncation

|Ψtotal〉 = |φ1〉 ⊗ . . .⊗ |φA〉

= |ΦCenter-of-Mass〉 ⊗ |Ψintrinsic〉

whereHrel|Ψj, intrinsic〉 = Ej|Ψj, intrinsic〉




ai|ψi〉


H = Trel + ΛCM

(

HH.O.CM −

3

2~ω

)

+∑

i<j

Vij +∑

i<j<k

Vijk + . . .

Pick your favorite potentialArgonne potentials: AV8, AV18(plus Illinois NNN interactions)Bonn potentialsChiral NN interactions (plus chiral NNN interactions). . .JISP16 (phenomenological NN potential). . .




ai|ψi〉


large sparse symmetric matrix

Obtain lowest eigenvaluesusing Lanczos algorithm

Eigenvalues:bound state spectrumEigenvectors:nuclear wavefunctions

Use wavefunctions to calculate observables

Challenge: eliminate dependence on basis space truncation


CI calculation – convergence


ai|ψi〉


Diagonalize sparse real symmetric matrix Hij

Variational: for any finite truncation of the basis space,eigenvalue is an upper bound for the ground state energy

Smooth approach to asymptotic valuewith increasing basis space=⇒ extrapolation

to infinite basis

Convergence: independence ofbasis space parameters

different methods(NCFC, CC, GFMC, DME, . . . )

using the same interactionshould give same resultswithin numerical errors

-16

-12

-8

-4

0

bind

ing

ener

gy p

er n

ucle

on [

MeV

]

No-Core Full ConfigurationCoupled Cluster Singles Doubles

SRG evolved N3LO 2-body interactions

8He

16O

40Ca

λ = 1.5

λ = 2.5

λ = 2.5

λ = 1.5

λ = 1.5

λ = 2.5

PRELIMINARY


Intermezzo: Extrapolation Techniques

Challenge: achieve numerical convergence for no-core Full Configuationcalculations using finite model space calculations

Perform a series of calculations with increasing Nmax truncation(while keeping everything else fixed)

Extrapolate to infinite model space −→ exact resultsbinding energy: exponential in Nmax

ENbinding = E∞binding + a1 exp(−a2Nmax)

use 3 or 4 consecutive Nmax values to determine E∞binding

use ~ω and Nmax dependenceto estimate numerical error bars

Maris, Shirokov, Vary, Phys. Rev. C79, 014308 (2009)

need at least Nmax = 8 for meaningfull extrapolations


Intermezzo: Extrapolation Techniques

Challenge: achieve numerical convergence for no-core Full Configuationcalculations using finite model space calculations

Perform a series of calculations with increasing Nmax truncation(while keeping everything else fixed)

Extrapolate to infinite model space −→ exact results

0 5 10 15 20 25 30 35 40 45hw

-30

-25

-20

grou

nd s

tate

ene

rgy

Nmax

= 4N

max= 6

Nmax

= 8N

max= 10

Nmax

= 12N

max= 14

extrapolatedN

max= 16

extrapolatedα D thresholdexpt.

6Li JISP16

0 4 8 12 16N

max

-32

-31

-30

-29

-28variational upperboundextrapolation at fixed hwα D thresholdexpt.

6Li JISP16


CI calculations – main challenges

0 2 4 6 8 10 12 14N

max

100

101

102

103

104

105

106

107

108

109

1010

M-s

chem

e ba

sis

spac

e di

men

sion

4He6Li8Be10B12C16O19F23Na27Al

0 2 4 6 8 10N

max

100

103

106

109

1012

1015

num

ber

of n

onze

ro m

atri

x el

emen

ts

16O, dimension2-body interactions3-body interactions4-body interactionsA-body interactions

Single most important computational issue:exponential increase of dimensionality with increasing H.O. levels

Additional computational issue:sparseness of matrix / number of nonzero matrix elements


High-performance computing

Hardwareindividual desk- and lap-topslocal linux clustersNERSC (DOE)

10,000,000 CPU hours for ISU collaborationLeadership Computing Facilities (DOE)INCITE award – Computational Nuclear Structure (PI: J. Vary, ISU)

28,000,000 CPU hours on Cray XT5 at ORNL15,000,000 CPU hours on IBM BlueGene/P at ANL

grand challenge award at Livermore (Jurgenson, Navratil, Ormand)

applied for CPU time at NCSA (NSF) – Blue Waters (IBM)

SoftwareLanczos algorithm – iterative methodto find lowest eigenvalues and eigenvectors of sparse matriximplemented in Many Fermion Dynamics

parallel F90/MPI/OpenMP CI code for nuclear physics


MFDn – 2-dimensional distribution of matrix

Real symmetric matrix: store only lower (or upper) triangle

Store Lanczos vectors distributed over all processors

In principle, we can deal with arbitrary large vectorseven if we cannot store an entire vector on a single processor

largest dimension: 8 billion, 32 GB / vector in single precision


MFDn – load-balancing

Lexico-graphical enumeration of basis states on d procs

Round-robin distribution of basis states over d procs

Almost perfect load balancing

However, no (apparent) structure in sparse matrixmulti-level blocking scheme to locate nonzero’s (Sternberg 2008)

Under development: distribute groupds of basis states over d procsin order to retain part of the natural structure of the matrix


Strong force between nucleons

Strong interaction in principle calculable from QCD

Use chiral perturbation theory to obtain effective A-bodyinteraction from QCD Entem and Machleidt, Phys. Rev. C68, 041001 (2003)

controlled power series expansionin Q/Λχ with Λχ ∼ 1 GeVnatural hierarchyfor many-body forces

VNN ≫ VNNN ≫ VNNNN

in principleno free parameters

in practice a fewundetermined parameters

renormalization necessaryLee–Suzuki–OkamotoSimilarity Renormalization Group +... +... +...

+...

2N Force 3N Force 4N Force

Q0LO

Q2NLO

Q3NNLO

Q4N LO3


Similarity Renormalization Group – NN interaction

SRG evolution Bogner, Furnstahl, Perry, PRC 75 (2007) 061001

drives interaction towards band-diagonal structureSRG shifts strength between 2-body and many-body forces

Initial chiral EFT Hamiltonianpower-counting hierarchy A-body forces

VNN ≫ VNNN ≫ VNNNN

key issue: preserve hierarchy of many-body forces


Improve convergence rate by applying SRG to N3LO

−30

−25

−20

−15

Gro

und-

Stat

e E

nerg

y [M

eV]

20 25 30 35 40h⁄ Ω [MeV]

−30

−25

−20

Nmax

= 2N

max = 4

Nmax

= 6N

max = 8

Nmax

= 10

Nmax

= 12

10 15 20 25 30h⁄ Ω [MeV]

4He

N3LO (500 MeV)

λ = 3.0 fm−1

λ = 2.0 fm−1

λ = 1.5 fm−1

Bogner, Furnstahl, Maris, Perry, Schwenk, Vary, NPA801, 21 (2008), arXiv:0708.3754


Effect of three-body forces

0 2 4 6 8 10 12 14N

max cut

λ = 1.0 fm−1

λ = 1.2 fm−1

λ = 1.5 fm−1

λ = 1.8 fm−1

λ = 2.0 fm−1

λ = 2.2 fm−1

0 2 4 6 8 10 12 14N

max cut

0 2 4 6 8 10 12 14N

max cut

−34−33−32−31−30−29−28−27−26−25−24−23−22−21−20

Gro

und-

Stat

e E

nerg

y [M

eV]

NA3max

= 40

NA2max

= 300

NN+NNNNN+NNN-induced

6Li

h- Ω = 20 MeV

NN-only

(Jurgenson, Navratil, Furnstahl, PRC83, 034301 (2011), arXiv:1011.4085)

Induced 3NF significantly reduce dependence on SRG parameter

N2LO 3NFbinding energy in agreement with experimentmay need induced 4NF?

Calculations for A = 7 to 12 in progress (LLNL)


Do we really need 3-body interactions?

0

2

4

6

8

E (

MeV

)

NN NN + NNN Exp JISP16chiral eff. interaction

3+

1+

0+

1+

2+

3+

2+2+

4+

2+10

BSpectrum of 10B

with chiral 2- and3-body forcesat Nmax = 6

nonlocal 2-bodyinteraction JISP16at Nmax = 8

Vary, Maris, Negoita, Navratil, Gueorguiev, Ormand, Nogga, Shirokov, and Stoica,in “Exotic Nuclei and Nuclear/Particle Astrophysic (II)”, AIP Conf. Proc. 972, 49 (2008);N3LO+3NF from Navratil, Gueorguiev, Vary, Ormand, and Nogga, PRL 99, 042501 (2007);

for JISP16 see Shirokov, Vary, Mazur, Weber, PLB 644, 33 (2007)


Phenomeological NN interaction: JISP16

A.M. Shirokov, J.P. Vary, A.I. Mazur, T.A. Weber, PLB 644, 33 (2007)

J-matrix Inverse Scattering Potential tuned up to 16O

finite rank seperable potential in H.O. representation

fitted to available NN scattering data

use unitary transformations to tune off-shell interaction tobinding energy of 3He

low-lying spectrum of 6Li (JISP6, precursor to JISP16)

binding energy of 16O

good fit to a range of light nuclear properties

very soft potential compared to other NN potentials

nonlocal potential (by construction)

details available at

http://nuclear.physics.iastate.edu/


Ground state energy Be-isotopes with JISP16

6 8 10 12 14total number of nucleons A

-70

-60

-50

-40

-30

grou

nd s

tate

ene

rgy

[M

eV]

variational boundNCFC w. JISP16experiment

Be isotopes

Nmax

= 12

Nmax

= 14

Nmax

= 10

Nmax

= 8


7Be – Ground state properties

0 5 10 15 20 25 30 35 40basis space frequency hω (MeV)

-38

-36

-34

-32

-30

bind

ing

ener

gy (

MeV

)

Nmax

= 6N

max = 8

Nmax

= 10N

max = 12

extrapolatedN

max = 14

extrapolated4He +

3He

experiment

7Be

JISP16

0 5 10 15 20 25 30 35 40basis space frequency hω (MeV)

1.5

2.0

2.5

3.0

prot

on r

ms

radi

us (

fm)

Nmax

= 6N

max = 8

Nmax

= 10N

max = 12

Nmax

= 14

7Be JISP16

Binding energy converges monotonically,with optimal H.O. freuqency around ~ω = 20 MeV to 25 MeV

Ground state about 0.7 MeV underbound with JISP16

Proton point radius does not converge monotonically


7Be – Excited states

0 expt. 10 15 20 25 30 35 40hω (MeV)

0

4

8

12

exci

tatio

n en

ergy

(M

eV)

Nm

= 10N

m = 12

Nm

= 14

7/2

5/2

7/2

5/2

3/2

1/2

JISP167Be

0 expt. 10 15 20 25 30 35 40hω (MeV)

-1

0

1

2

3

4

Mag

netic

mom

ent JISP16

7Be

5/2

5/2

1/2

7/2

3/2 (g.s.)

Excitation energy of narrow statesconverge rapidlyagree with experiments

Broad resonances depend ~ω

Magnetic momentswell converged

2-body currents neededfor agreement with data(meson-exchange currents)


7Be – Proton density

Intrinsic density – center-of-mass motion taken outw. Cockrell, PhD student ISU

0 1 2 3 4r (fm)

0

0.05

0.1

prot

on d

ensi

ty ρ

(r)

Nm

= 2N

m = 6

Nm

= 10N

m = 14

JISP167Be

hω = 12.5 MeV

hω = 20.0 MeV

0 2 4 6r (fm)

10-5

10-4

10-3

10-2

10-1

prot

on d

ensi

ty ρ

(r)

Nm

= 2N

m = 6

Nm

= 10N

m = 14

fit: a exp(-b r)

JISP167Be

hω = 12.5 MeV

hω = 20.0 MeV

Slow build up of asymptotic tail of wavefunction

Proton density appears to converge more rapidly at ~ω = 12.5 MeVthan at 20 MeV because long-range part of wavefunction is betterrepresented with smaller H.O. parameter


7Be – Proton radius

0 2 4 6r (fm)

0

0.2

0.4

0.6

0.8

r4ρ(

r)

Nm

= 2N

m = 6

Nm

= 10N

m = 14

JISP167Be

hω = 12.5 MeV

hω = 20.0 MeV

0 4 8 12 16N

max

2.0

2.2

2.4

2.6

2.8

3.0

prot

on p

oint

RM

S ra

dius

(fm

)

hω = 8.0 MeVhω = 9.0 MeVhω = 10.0 MeVhω = 12.5 MeVhω = 15.0 MeVhω = 17.5 MeVhω = 20.0 MeV

7Be

JISP16

Calculation one-body observables 〈i|O|j〉 ∼∫

O(r) r2 ρij(r) dr

RMS radius: O(r) = r2

Slow convergence of RMS radius due toslow build up of asymptotic tail

Ground state RMS radius in agreement with data


7Be – Quadrupole moment

4 8 12 16N

max

-8

-7

-6

-5

-4

-3

-2

-1

0

quad

rupo

le m

omen

t

hω = 8.0 MeVhω = 9.0 MeVhω = 10.0 MeVhω = 12.5 MeVhω = 15.0 MeVhω = 17.5 MeVhω = 20.0 MeV

7Be JISP16

Ground state quadrupole moment in agreement with data

Optimal basis space around ~ω = 10 MeV to 12 MeV

Similar slow convergence for E2 transitions


7Be – Rotational band

E2 observables suggest rotational structure for 3

2, 1

2, 7

2, 5

2states

0 5 10 15 20 25 30 35 40hω (MeV)

-10

-8

-6

-4

-2

0

Qua

drup

ole

mom

ent

JISP16

7Be

rotational band?

3/2

5/2

7/2

5/2

0 10 20 30 40basis space frequency hω (MeV)

10-1

100

101

102

B(E

2) t

o g.

s. 3

/2-

JISP167Be1/2

-

5/2-

5/2-

7/2-

rotational band?

Q(J) =3

4− J(J + 1)

(J + 1)(2J + 3)Q

1

2

0

B(E2; i→ f) =5

16π

(

Q1

2

0

)2(

Ji,1

2; 2, 0

∣

∣

∣Jf ,

1

2

)2


8Be – Spectrum positive parity

0 5 10 15 20 25 30 35 40hω (MeV)

0

5

10

15

20

exci

tatio

n en

ergy

(M

eV)

dotted: Nmax

= 8 solid: Nmax

= 12

2

4

13

2

4

JISP168Be

Pairs of isospin 0 and 1states with J = 2, 1, and 3

Evidence of continuumstates (J = 0 and 2)at Nmax = 12

Rotational band

expt. calc rotor

E4/E2 3.75 3.40 3.33

Ground state above 2α threshold: radius not converged

Quadrupole moments 2+ and 4+ not converged, nor B(E2)’s,but in qualitative agreement with rotational structure


Results with JISP16 for 12C

0 5 10 15 20 25 30 35 40

-100

-90

-80

-70

Nmax

= 2

Nmax

= 4

Nmax

= 6

Nmax

= 8

extrapolatedN

max=10

extrapolatedexpt.

Calculations for Nmax = 10 underway (D = 8 billion)using 100,000 cores on JaguarPF (ORNL) under INCITE award


Spectrum of 12C with JISP16 – work in progress

0 10 20 30 40basis space hω (MeV)

0

5

10

15

20

25

exci

tatio

n en

ergy

(M

eV)

spectrum 12C with JISP16 at Nmax = 8 (solid) and 10 (crosses)

(2+, 0)

(1+, 0)

(1+, 1)

(2+, 1)

(0+, 0)

(2+, 0)

(0+, 0)

(4+, 0)

so-called Hoyle state missing

(0+, 1)

Pos. parity states in agreement with data, except for Hoyle state

Electromagnetic transitions in progressrotational 2+ and 4+ states, significantly enhanced B(E2)optimal basis ~ω for Q and B(E2) around ~ω = 12.5 MeV

Neutrino and pion scattering calculations in progressINT Extreme Computing, June 7 2011 – p.30/43

Density of 12C with JISP16

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Radius (fm)

Den

sity

(fm

− 3)Carbon 12 Proton Densities

Pieper GFMCNmax 8, hw=12.5, JISP16Experimental Data

GFMC: AV18 + IL7, on BlueGene/P using 131,072 cores (INCITE)“More scalability, Less pain”, Lusk, Pieper, and Butler, SciDAC review 17, 30 (2010)

JISP16 density at Nmax = 8, ~ω = 12.5 MeVINT Extreme Computing, June 7 2011 – p.31/43

Scientific Discovery – unstable nucleus 14F

Maris, Shirokov, Vary, arXiv:0911.2281 [nucl-th], Phys. Rev. C81, 021301(R) (2010)

0 2 4 6 8Nmax

0

5

10

Exc

itat

ion

ener

gy (

MeV

)

Extrapolation B Exp.2

-

1-(?)

3-(?)

2-

4-

??

1-0-

2-5

-

14F

1-

14B

3-

3-

2-

4-(?)

4-

2-

2-3

-

2-

3-

1-

5-

2-

4-

2-

1-

1-3

-

3-

4-

2-

1-0-

dimension 2 · 109

# nonzero m.e. 2 · 1012

runtime 2 to 3 hours on7,626 quad-core nodeson Jaguar (XT4)(INCITE 2009)

Predicted ground state energy: 72 ± 4 MeV (unstable)

Mirror nucleus 14B: 86 ± 4 MeV agrees with experiment 85.423 MeV


Predictions for 14F confirmed by experiments at Texas A&M

NCFC predictions (JISP16) in

close agreement with experiment

TAMU Cyclotron Institute

Experiment published: Aug. 3, 2010 Theory published PRC: Feb. 4, 2010


Petascale Early Science – Ab initio structure of Carbon-14

0 4 8basis space truncation N

max

103

106

109

1012

1015

dimension# nonzero’s NN# nonzero’s NNN# matrix elements

14C (Z= 6, N= 8)

0 4 8basis space truncation N

max

103

106

109

1012

1015

dimension# nonzero’s NN# nonzero’s NNN# matrix elements

14N (Z= 7, N= 7)

Chiral effective 2-body plus 3-body interactions at Nmax = 8

Basis space dimension 1.1 billion

Number of nonzero m.e. 39 trillion

Memory to store matrix (CRF) 320 TB

Total memory on JaguarPF 300 TB

ran on JaguarPF (XT5) using up to 36k 8GB processors (216k cores)after additional code-development for partial “reconstruct-on-the-fly”


Ab initio structure of Carbon-14 and Nitrogen-14

Maris, Vary, Navratil, Ormand, Nam, Dean, arXiv:1101.5124 [nucl-th]

2 4 6 8 expt 8 6 4 20

5

10

15

20ex

cita

tion

ener

gy (

MeV

)(3

+,0)

(1+,1)

(2+,1)

(2+,0)

(0+,1)

(1+,0)

N3LON3LO + 3NF

chiral 2-body plus 3-body forces (left) and 2-body forces only (right)


Origin of the anomalously long life-time of 14C

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

GT

mat

rix

elem

ent

no 3NF forceswith 3NF forces (c

D= -0.2)

with 3NF forces (cD

= -2.0)

s p sd pf sdg pfh sdgi pfhj sdgik pfhjl

shell

-0.1

0

0.1

0.2

0.3

0.2924

near-completecancellationsbetweendominantcontributionswithin p-shell

very sensitiveto details

Maris, Vary, Navratil,

Ormand, Nam, Dean,

arXiv:1101.5124 [nucl-th]


Neutrons in a trap: Why

Validate ab-initio DFT approachesagainst microscopic ab-initio calculations

compare Density Matrix Expansionand ab-initio NCFC calculations

using the same interactioncalculating the same observables for the same systems

Construct Universal Nuclear Energy Density Fuctionalconsistent with ab-initio calculations

Theoretical ’laboratory’ to exploreproperties of different nuclear interactionseffect of density and gradienton nuclear properties for different interactions

Model for neutron-rich systemsin particular those with closed shell protons (Oxygen, Calcium)

Essential in order to make meaningful comparison with other methods:quantify dependence on basis space truncation parameters


Validating ab-initio DME/DFT calculations

Bogner, Furnstahl, Kortelainen, Maris, Stoistov, Vary, in preparation

Simple model for interactionMinnesota potential

Ab-initio NCFC calculations for neutrons in H.O. potentialincluding numerical error estimates on all ’observables’

DFT using same NN interaction as NCFCHartree–FockDensity Matrix Expansion, Hartree–FockDensity Matrix Expansion, Brueckner–Hartree–Fock

DFT fit to NCFC results

Comparison for 8, 14, and 20 neutronstotal and internal energy per neutronrms radiusform factor F (q)


Minnesota potential – Total energy vs. radius

2.0 2.5 3.0radius [fm]

0.85

0.9

0.95

Eto

t/(N

4/3 hΩ

) NCFCHFPSABHFfit

2.0 2.5 3.0radius [fm]

0.8

0.85

0.9

Eto

t/(N

4/3 hΩ

) Minnesota potential

N = 8

N = 20

Neither HFnor DME/PSA HFin agreement with NCFC

DME BHF close to NCFCresults oftenwithin error estimates

Fit with volume termand surface term canreproduce NCFC data

Bogner, Kortelainen, Furnstahl, Stoistov, Vary, PM, work in progress


Internal energy vs. radius

2.0 2.5 3.0radius [fm]

0.4

0.42

0.44

Ein

t/(N

4/3 hΩ

)

NCFCHFPSABHFfit

2.0 2.5 3.0radius [fm]

0.38

0.4

0.42

Ein

t/(N

4/3 hΩ

)

N = 8

N = 20 Neither HFnor DME/PSA HFwithin variational bound

DME BHF close to NCFCresults oftenwithin error estimatesand within bounds

Fit with volume termand surface term canreproduce NCFC data

Variational upper bound on combination Eint + 1

2N mΩ2r2


Minnesota potential – density

0 1 2 3 4 5r [fm]

0

0.02

0.04

0.06

0.08

0.1

ρ [f

m−3

]

NCFCPSABHFfit

NN-only

Minnesota potential

N = 8hΩ = 10 MeV

0 1 2 3 4r [fm]

0

0.1

0.2

0.3

ρ [f

m−3

]

NCFCPSABHFfit

NN-only

Minnesota potential

N = 20

hΩ = 15 MeV

Agreement between DME/DFT calculations and NCFC

Density profile dominated by H.O. external fieldmodefied by NN interaction

Bogner, Kortelainen, Furnstahl, Stoistov, Vary, PM, work in progress


Eint vs. radius – more realistic potentials

1.5 2 2.5 3 3.5 4radius [fm]

0

10

20

30

40E

int/ A

[M

eV]

8 neutrons, JISP168 n, N3LO

SRG[λ=1.5]

20 neutrons, JISP1620 n, N3LO

SRG[λ=1.5]

neutron droplets in external fields

Results virtually identical for N3LO(λ = 1.5) and JISP16despite different results for nuclei (e.g. 186 vs. 144 MeV for 16O)presented at JUSTIPEN–EFES–Hokudai–UNEDF workshop, 2008, Hokkaido, Japan


Conclusions

MFDn: Scalable and load-balanced CI code for nuclear structurenew version under development, has run on 200k+ coreson Jaguar (ORNL) enabling largest model-space calculations

Significant benefits from collaboration between nuclear physicists,applied mathematicians, and computer scientists

JISP16, nonlocal phenomenological 2-body interactiongood description of light nuclei (more than just energies!)rapid convergence

prediction of new isotope, 14F

Understanding of the anomalously large lifetime of 14C

Validation of DFT/DME calculations (in progress)

Main challenge: construction and diagonalizationof extremely large (D > 1 billion) sparse matrices

Future developments: Taming the scale explosion


Documents

No Core CI Calculations for light nuclear systems · INT Extreme Computing workshop, June 2011 No Core CI Calculations for light nuclear systems Pieter Maris [email protected] Iowa