Lawrence Livermore National Laboratory

Ab initio reactions of nucleons on light nuclei

LLNL-PRES-410642

Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551

This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344

Petr Navratil (LLNL)Collaborators: Sofia Quaglioni (LLNL), Robert Roth (TU Darmstadt)

UNEDF SCIDAC meeting, Pack Forest, WA, 6/22/2009

4LLNL-PRES--410642

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The ab initio NCSM/RGM in a snapshot

Ansatz:

Non-local integro-differential coupled-channel equations:

Hamiltonian kernel Norm kernel

Many-body Schrödinger equation:

eigenstates of H(A-a) and H(a)

in the ab initio

NCSM basis

either bare interaction or NCSM effective interaction

Fully implemented for nucleon-nucleus basis. Work on deuteron-nucleus basis under way.

8LLNL-PRES-405596

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NCSM/RGM ab initio calculation of n-3H and p-3He phase shifts

NCSM/RGM calculations with n+3H(g.s.) and p+3He(g.s.), respectively.

Benchmark with Alt, Grassberger and Sandhas (AGS) results [PRC75, 014005(2007)]

• What is missing? - n+3H(ex), 2n+d, p-3He(ex), 2p+d configurations

The omission of three-nucleon partial waves with 1/2 < J ≤ 5/2 leads to effects of comparable magnitude on the AGS results. Need to include target excited states!

EFT N3LO NN potential: convergence reached with two-body effective interaction

3He

p

3H

n

9LLNL-PRES--410642

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n-4He & p-4He phase shifts from accurate NN interactions

4He states: g.s.,

Reasonable

agreement with

experiment for 2S1/2 ,

2P1/2, 2D3/2 channels

Coulomb under control

n-4He and p-4He phase shifts

Insufficient spin-orbit strength: 2P3/2 underestimated NNN needed

CD-Bonn the best description of 2S1/2 phase shifts

Insufficient spin-orbit strength: 2P3/2 underestimated NNN needed

CD-Bonn the best description of 2S1/2 phase shifts

10LLNL-PRES--410642

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First ever ab initio calculation of Ay in for a A=5

system. Strict test of inter-nucleon interactions.

n+4He differential cross section and analyzing power

Neutron energy of 17 MeV

• beyond low-lying resonances

Polarized neutron experiment at Karlsruhe

NCSM/RGM calculations

• n+4He(g.s,0+0)

• SRG-evolved N3LO NN potential

Good agreement for angular distribution

Differences for analyzing power

• Ay puzzle for A=5?

4He

n

11LLNL-PRES--410642

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NCSM/RGM ab initio calculation of n+7Li scattering 7Li

Full NCSM up to Nmax=10 (12 possible)

IT-NCSM up to Nmax=18

Convergence of both ground and excited states

8Li• NCSM predicts unobserved low-lying 0+ and 2+ states

• NCSM/RGM with 7Li 3/2- and 1/2- bound states included

• Up to Nmax=14 so far (hΩ=20 MeV used)

Moderate changes from Nmax=6 to Nmax=14

• Bound states 2+ state bound by 1.07 MeV (expt 2.03 MeV)

1+ state bound by 0.18 MeV (expt 1.05 MeV)

7Li

n

PRC 73, 065801 (2006)

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NCSM/RGM ab initio calculation of n+7Li scattering

7Li 3/2- and 1/2- bound states included

SRG-N3LO NN interaction with Λ=2.02 fm-1

• Up to Nmax=14 so far (hΩ=20 MeV used)

• Moderate changes from Nmax=6 to Nmax=14

• 2+ and 1+ states bound

• Other states unbound

S-wave scattering lengthExpt: a01=0.87(7) fm a02=-3.63(5) fm

Calc: a01=1.31 fm a02=-0.18 fm

7Li

n

Qualitative agreement with experiment. Calculated broad 1+ resonance, predicted narrow 0+ resonance. The 3+ resonance not seen when 7Li 7/2- state not included.

13LLNL-PRES--410642

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NCSM/RGM ab initio calculation of n+7Li scattering

7Li 3/2-, 1/2- and 7/2- states included

Result for Nmax=8 shown

2+ and 1+ states bound (slightly more)

0+ and 1+ resonances not affected

3+ and 2+ resonances appear

Improvement of S-wave scattering length

S-wave scattering lengthExpt: a01=0.87(7) fm a02=-3.63(5) fm

Calc: a01=0.73 fm a02=-1.42 fm

7Li

n

Good match of bound states and narrow resonances with the 8Li NCSM result. Predicted narrow 0+ and 2+ resonance. Seen at recent p+7Be FSU experiment.

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Nucleon-12C scattering with SRG-N3LO NN potential

12C • Full NCSM up to Nmax=8• IT NCSM up to Nmax=18(!)

Perfect agreement for both the 0+ ground- and 2+ excited state up to Nmax=8

Convergence of the IT-NCSM

h=24 MeV used

13N, 13C within the NCSM• 1/2+ state too high by ~ 6 MeV

13N, 13C within the NCSM/RGM• up Nmax=16 with 12C g.s. and 2+ included• 13C:

1/2- bound by 5.34 MeV (expt 4.95 MeV)

3/2- bound by 2.23 MeV (expt 1.27 MeV)

1/2+ bound by 0.03 MeV (expt 1.86 MeV)

Excitation energy 5.31 MeV (expt 3.09 MeV)

Excitation energy of the 1/2+ state drops by 4 MeV when n-12C long-range correlations included Excitation energy of the 1/2+ state drops by 4 MeV when n-12C long-range correlations included

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p-12C scattering with SRG-N3LO NN potential

Experiments with a polarized proton target under way

NCSM/RGM up Nmax=16

• 12C g.s. and 2+ included• 1/2- state bound by 2.9 MeV

13N ground state

• Other states unbound• 1/2+ resonance at ~1.2 MeV• 5/2+ resonance• Good stability: Moderate changes

from Nmax=6 to Nmax=16

• Minimal difference between Nmax=14 and Nmax=16

Qualitative agreement with experimentQualitative agreement with experiment

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The deuteron projectile: Norm kernel

2(A-2)

(A-2) (2)

+ (A-2)(A-3)/2

(A-2)

(2)

€

SDψ μ1

(A−2) a+aψν 1

(A−2)

SD

€

SDψ μ1

(A−2) a+a+ a a ψν 1

(A−2)

SD

(1,…,A-2)

(A-1,A)

(1,…,A-2)

(A-1,A)

€

1− 2(A − 2) ˆ P A−2,A−1 + 12 (A − 2)(A − 3) ˆ P A−2,A

ˆ P A−3,A−1

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The deuteron projectile: Hamiltonian kernel(A-2)

(2)

(1,…,A-2)

(A-1,A)

(1,…,A-2)

(A-1,A)

€

2(A − 2)VA−1,A−2(1− PA−1,A−2) − 2(A − 2)VA ,A−2ˆ P A−2,A−1

−2(A − 2)(A − 3)VA ,A−3(1− ˆ P A ,A−3) ˆ P A−2,A−1

−2(A − 2)(A − 3)VA−1,A−3ˆ P A−2,A−1

+(A − 2)(A − 3)(A − 4)VA−1,A−4ˆ P A−2,A

ˆ P A−3,A−1

€

SDψ μ1

(A−2) a+aψν 1

(A−2)

SD

€

SDψ μ1

(A−2) a+a+ aa ψν 1

(A−2)

SD

€

SDψ μ1

(A−2) a+a+a+ a aa ψν 1

(A−2)

SD

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d- scattering: Progress so far

Norm kernel coded Hamiltonian kernel partially coded

• Term with three-body density in progress

Convergence reached for d- norm kernel (physics - Pauli principle)

1+

S-wave dominated

2+

D-wave dominated

1-

P-wave dominated

28LLNL-PRES--410642

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Toward the first ab initio description of the Deuterium-Tritium fusion

Solve the many-body Schrödinger equation in the Hilbert space spanned by the RGM basis states:

Progress so far: Norm kernels calculated

29LLNL-PRES--410642

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FY09 accomplishments

Development of ab initio many-body reaction theory by merging the NCSM and the RGM (P. Navratil and S. Quaglioni)• Results with NN potentials used by UNEDF collaboration

n-7Li with SRG-N3LO using the importance-truncated NCSM p-12C with SRG-N3LO using the importance-truncated NCSM n-16O with SRG-N3LO using the importance-truncated NCSM Collaboration with R. Roth (TU Darmstadt)

Deuteron-nucleus scattering under development Development of the TRDENS transition density code

Distribution of two-body density structure over groups of processors

Similarity-renormalization-group evolution of NN+NNN interactions Collaboration with D. Furnstahl (OSU) and E. Jurgenson (OSU)

A=14 nuclei with chiral EFT NN+NNN up to Nmax=8• Transformation of NNN to SD basis up to Nmax=8 Collaboration with J. Vary, P. Maris, H. Nam, E. Ormand and D. Dean

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Publications relevant to UNEDF in 2008/2009

E. D. Jurgenson, P. Navratil, and R. J. Furnstahl, Evolution of nuclear many-body forces with the similarity renormalization group, arXiv:0905.1873 [nucl-th], submitted to Phys. Rev. Lett.

I. Stetcu, S. Quaglioni, J.L. Friar, A.C. Hayes, and P. Navratil, Electric Dipole Polarizabilities of Hydrogen and Helium Isotopes, Phys. Rev. C 79, 064001 (2009)

P. Navratil, S. Quaglioni, I. Stetcu and B. R. Barrett, Recent developments in no-core shell-model calculations, J. of Phys. G 36 (2009) 083101, invited topical review.

S. Quaglioni, P. Navratil, Ab initio many-body calculations of nucleon-nucleus scattering, Phys. Rev. C 79, 044606 (2009)

C. Forssen, E. Caurier, P. Navratil, Charge radii and electromagnetic moments of Li and Be isotopes from the ab initio no-core shell model, arXiv:0901.0453 [nucl-th], Phys. Rev. C 79, 021303(R) (2009)

D. Gazit, S. Quaglioni, P. Navratil, Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory, arXiv:0812.4444 [nucl-th], submitted to Phys. Rev. Lett.

S. Quaglioni, P. Navratil, Ab initio many-body calculations of n-3H, n-4He, p-3He,4He, and n-10Be scattering, PHYSICAL REVIEW LETTERS 101, 092501 (2008)

R. Roth, P. Navratil, Comment on "Ab initio Study of Ca-40 with an Importance-Truncated No-Core Shell Model'' – Reply, PHYSICAL REVIEW LETTERS 101, 119202 (2008)

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Future plan

The rest of Year 3• Complete n-7Li calculations• Begin n-8He investigation• Continue work on deuteron-nucleus formalism (supported by LDRD)

Year 4• n-8He, n-9Li calculations• Development of 3H and 3He – nucleus formalism (supported by LDRD)• Development of the coupling of NCSM/RGM and NCSM NCSMC• Similarity-renormalization-group evolution of NN+NNN interactions

Application to p-shell nuclei (supported by DOE/SC/NP)

• Further development of importance-truncation NCSM scheme Year 5

• High profile science: Capture reactions - 3He(,)7Be

Computational challenges:• n-body density (n>2) calculations

Distribution of structure allocation, parallelization