Ab initio Coupled Cluster Calculations of Nuclei: Status and Outlook

Gaute Hagen

and

UNEDF: J. Holt (UT), T. Papenbrock (UT/ORNL) CS support: H. A. Nam (ORNL) External collaborators: D. J. Dean (ORNL), M. Hjorth-Jensen

(Oslo), G. Baardsen (Oslo), G. Jansen (Oslo), O. Jensen (Bergen), T. Lesinski (Seattle) 1. Status and main accomplishments since last meeting 2. Status regarding high-performance computing 3. Roadmap for remainder of year 5 and outlook

Annual UNEDF collaboration meeting

East Lansing, MI, June 19-24 2011 Research partly funded by the US Department of Energy

Personnel UNEDF collaborators: G. Hagen, J. Holt, T. Papenbrock, T. Lesinski (UW) CS support: Hai Ah Nam (ORNL) Development of coupled-cluster method with relevance for UNEDF (by

students supervised by M. Hjorth-Jensen and G. Hagen) • Øyvind Jensen (student at University of Bergen – Graduated July 2011; one nucleon overlap functions and spectroscopic factors in J-coupled scheme) • Gustav Jansen (student at University of Oslo; closed shell ± 2 nucleons) • Gustav Baardsen (student at University of Oslo; coupled-cluster theory for infinite nuclear matter)

Publication Summary

Published / accepted since July 2010

1.

Quenching of spectroscopic factors for proton removal in oxygen isotopes, Ø. Jensen, G. Hagen, M. Hjorth-

2.

3.

Jensen, B. Alex Brown, and A. Gade, Phys. Rev. Lett., in press (2011), arXiv:1104.1552

Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions

, G. Hagen, T. Papenbrock, D. J. Dean, and M. Hjorth-Jensen, Phys. Rev. C 82, 034330 (2010).

Fermionic-Bosonic Couplings in a Weakly-Deformed Odd-Mass Nucleus, 93Nb

, J. N. Orce, J. D. Holt, A.

4.

5.

6.

Linnemann, C. J. McKay, et al. Phys. Rev. C 82, 044317 (2010)

Computation of spectroscopic factors with the coupled-cluster method

, O. Jensen, G. Hagen, T. Papenbrock, D. J. Dean, and J. S. Vaagen, Phys. Rev. C 82, 014310 (2010).

Closed-shell properties of 24 O with ab initio coupled-cluster theory

, Ø. Jensen, G. Hagen, M. Hjorth-Jensen, and J. S. Vaagen, Phys. Rev. C(R), 83, 021305 (2011).

Towards open-shell nuclei with coupled-cluster theory

, G. R. Jansen, M. Hjorth-Jensen, G. Hagen, and T. Papenbrock Phys. Rev. C 83, 054306 (2011)

Submitted articles

1.

Ab initio computation of circular quantum dots

, M. Pedersen Lohne, G. Hagen, M. Hjorth-Jensen, S. Kvaal, and F. Pederiva, Phys. Rev. B (2011) submitted, arXiv:1009.4833v1.

2.

3.

Three-Body Forces and Shell Structure in Calcium Isotopes

, J. D. Holt, T. Otsuka, A. Schwenk, and T. Suzuki arXiv:1009.5984, submitted to Phys. Rev. Lett.

Chiral Three-Nucleon Forces and Bound Excited States in Neutron-Rich Oxygen Isotopes

, J. D. Holt, A. Schwenk, T. Otsuka, and T. Suzuki,Submitted to Phys. Rev. C

4.

Role of many-body processes and three-nucleon forces in nuclear pairing

, J. D. Holt, J. Menendez, and A. Schwenk, Submitted to Phys. Rev. C

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Talks

“Coupled-cluster approach to medium-mass and neutron-rich nuclei”, Nuclear Structure 2010 (NS2010), Clark-Kerr Campus, U. C. Berkeley, CA, August 8th – August 13th, 2010. (GH) “Coupled-cluster approach to medium-mass and neutron-rich nuclei”, Frontiers In NUclear STructure, Astrophysics and Reactions (FINUSTAR 3), Rhodes, Greece, August 23 to August 27, 2010. (GH) “Probing the driplines with ab ‐ initio Coupled ‐ Cluster theory”, ECT Workshop on Limits of existence of Light nuclei, ECT, Trento, Italy, October 25, 2010. (GH) “The nuclear many-body problem”, Second Uio-MSU-ORNL-UT School on Topics in Nuclear Physics: Many-Body Theory, Connections to Experiment and Nuclear Astrophysics (five lectures), January 3-7, 2011, Michigan State University. (GH) “Towards ab initio structure and reactions in neutron rich nuclei with coupled ‐ cluster theory”, ECT workshop on Effective theories and the nuclear many-body problem, ECT, Trento, Italy, March 7-11, 2011. (GH) “Towards ab initio structure and reactions in neutron rich nuclei with coupled ‐ cluster theory”, invited seminar talk at CEA, CEA, Saclay, May 13, 2011. (GH) “Towards a unified description of nuclear structure and reactions with coupled-cluster theory”, FUSTIPEN Topical Meeting «Structure and reactions at the drip lines», May 24-25, 2011, GANIL, Caen, France. (GH) “Ab initio calculations of weakly bound nuclei”, The first International Conference on Advances in Radioactive Isotope Science (ARIS - 2011), Leuven, Belgium, June 1, 2011. (GH) "Nuclear structure at the neutron drip-line", Gordon Research Conferences, Intersections Between Structure and Reactions: Pushing the Frontiers of Nuclear Science, Colby-Sawyer College, New London, June 14 th 2011. (GH) “Ab initio Coupled Cluster Calculations of Nuclei: Status and Outlook”, annual UNEDF meeting, Henry Center, East Lansing, June 20 th , 2011. “Model independent computation of atomic nuclei: status and perspectives,” “The INT at 20 years: The Future of Nuclear Physics and its Intersections,” Seattle, WA, July 1-2, 2010. (TP) “Ab initio nuclear structure calculations,” EMMI workshop “Strongly coupled systems,” GSI, Darmstadt, Germany, November 15-17, 2010. (TP) “Frontiers in nuclear structure theory,” Physics Colloquium, Technische Universität Darmstadt, Darmstadt, Germany, December 3, 2010. (TP) “Toward model-independent nuclear structure computations,” Physics seminar, Universität Frankfurt, Frankfurt, Germany, February 24, 2011. (TP) “Model-independent approaches to nuclear structure,” Annual NuSTAR meeting, GSI, Darmstadt, Germany, March 2-4, 2011. (TP) “Model-independent nuclear structure computations,” HISKP Colloquium, Universität Bonn, Bonn, Germany, May 12 2011 (TP) “Toward model-independent nuclear structure computations,” ECT* workshop on “Nuclear many-body open quantum systems,” Trento, Italy, June 7 2011. (TP) “Three-Nucleon Forces for Neutron-Rich, Medium-Mass Nuclei”, International Nuclear Physics Conference Vancouver, BC, Canada; July 4, 2010 (JH) “Three-Nucleon Forces for Medium Mass Nuclei Towards the Driplines“, Pan-American Advanced Studies Institute on Rare Isotopes Joao Pessoa, Brazil; August 1, 2010 (JH) “Three-Nucleon Forces and the Evolution of Nuclear Structure Towards the Driplines”, ECT* Workshop: “The Limits of Existence of Light Nuclei” Trento, Italy; October 27, 2010 (JH) “Three-Nucleon Forces and the Evolution of Nuclear Structure in Exotic Nuclei”, Nuclear Theory / EMMI Seminar; Technical University Darmstadt, Darmstadt, Germany; November 29, 2010.(JH) “Exploring Neutron-Rich Exotic Nuclei with Three-Nucleon Forces”, Nuclear Physics Seminar Instituto de Fisica Teorica Universidad Autonoma de Madrid, Madrid, Spain; February 2, 2011 (JH) “Three-Body Forces and Shell Structure in Exotic Nuclei”, ECT* Workshop: “Effective Theories and The Nuclear Many-Body Problem” Trento, Italy; March 7, 2011 (JH) “Three-Nucleon Forces and the Evolution of Nuclear Structure in Exotic Nuclei”, The Fifth LACM-EFES-JUSTIPEN Workshop Oak Ridge, TN; March 17, 2011. (JH)

Main accomplishments since last meeting

Science:

1. Long article on nuclear structure with NN interactions from chiral EFT 2. Quenching of spectroscopic factors for proton removal in neutron oxygen isotopes (Phys. Rev. Lett. 2011). 3. Computation of one-nucleon overlap functions for nuclear reactions and scattering (unpublished) 4. Computation of intrinsic densities with application to oxygen isotopes (unpublished) 5. Towards open shell nuclei with CCM extension to A ± 2: 18 O and 26 F 6. Coupled-cluster theory for nuclear matter. Implemented exact Pauli operator and HF + MBPT(2). 7. Constraining EDFs from ab-initio CC theory (See J. Holt’s talk)

Computing / algorithm developments:

1. Implementation of J-coupled code for computing one-nucleon overlaps and spectroscopic factors 2. Implementation of two-particle attached EOM-CCSD in J-coupled scheme.

Saturation of N

3

LO (NN only) in medium mass nuclei

Benchmarks in light nuclei:

Coupled-cluster meets few-body benchmarks for 4 He. Recent IT-NCSM and UMOA calculations of 16 O agree with CCM. R. Roth et al, arXiv:1105.3173 (2011) Fujii et al, PRL 103, 182501(2009) G. Hagen, T. Papenbrock, D. J. Dean, M.

Hjorth-Jensen, Phys. Rev. C 82, 034330 (2010).

Overlap functions and spectroscopic factors

Microscopic definition of Spectroscopic Factors (SF):

Elastic scattering, capture and transfer of a nucleon on/to a target nucleus with mass A is given by the overlap function The norm of the overlap functions defines the spectroscopic factor:

Asymptotic properties of the one-nucleon overlap function:

Outside the range of the interaction the overlap function is proportional to a single-particle wave function.

Quenching of SFs for proton removal in the oxygens

• SF is a useful tool to study the role correlations toward the dripline.

• We find a significant quenching of the SFs due to enhanced correlations coming from coupling to the scattering continuum.

Ø. Jensen, G. Hagen and M. Hjorth-Jensen, Phys. Rev. C(R) 83, 021305 (2011) Ø. Jensen, G. Hagen, Hjorth-Jensen, Brown, Gade, in press Phys. Rev. Lett. (2011) arXiv:1104.1552

For threshold effects in SFs see N. Michel et al Phys. Rev. C(R) 75, 031301 (2007)

Asymptotic normalization coefficients

Overlap function for a bound A + 1 nucleus:

We use an SRG evolved interaction with cutoff 2.66 fm-1. The CCSD ground state energy for 16 O in N = 11 major shells is 140.52 MeV.

One neutron overlap functions for the bound J = 1/2+ state in 17 O with the ground state of 16 O. For 17 O we get E(1/2+) = -3.83 MeV.

Elastic scattering of neutrons on 16O with CCM (Preliminary

)

Overlap functions provides a simple and intuitive picture of reactions

Left figure: One neutron overlap functions for various J = 1=2+ scattering states in 17O using SRG evolved interaction with cutoff = 2.66fm-1 Right figure: By matching the known asymptotic form of the overlap functions to scattering solutions we can extract low-energy elastic scattering phase shifts.

Intrinsic densities from microscopic CCM

Computing intrinsic densities

The one-body density matrix for the A and A-1 nuclei are computed in the coupled-cluster formalism and the local laboratory density is CC wave function factorizes and the CoM wave function is a Gaussian with fixed width (G. Hagen et al Phys. Rev. Lett. 103, 062503 (2009)) We can get the internal density by a deconvolution of the local laboratory density (B. G. Giraud, Phys. Rev. C 77, 014311 (2008))

Matter and charge radii in the

21,22,23,24

O isotopes

Binding energies of 21,22,23,24 O with respect to the ground state of 21 O.

Point matter and charge radii for computed from intrinsic densities For the nucleon-nucleon (NN) interaction we used the SRG evolved N3LO nucleon-nucleon interaction with momentum cutoffs = 3.6, 3.8, 4.0fm-1.

Matter and charge radii in the

21,22,23,24

O isotopes

Binding energies of 21,22,23,24 O with respect to the ground state of 21 O.

Point matter and charge radii for computed from intrinsic densities For the nucleon-nucleon (NN) interaction we used the SRG evolved N3LO nucleon-nucleon interaction with momentum cutoffs = 3.6, 3.8, 4.0fm-1.

Going beyond closed-shell nuclei. Low-lying states in

18

O and

26

F (Preliminary)

Two-particle attached coupled-cluster works very well for low-lying states in open-shell nuclei like 18 O and 26 F.

Our results for 26 F seem to suggest a more compressed spectrum as compared to USDA/USDB calculations. G. Jansen, M. Hjorth-Jensen, G. Hagen, T. Papenbrock, Phys. Rev. C 83, 054306 (2011).

Low-lying states in neutron rich Potassium isotopes

Proton separation energies 40,48,52,54,60 Ca.

Low lying states in Potassium isotopes calculated using PA/PR EOMCCSD with “bare" chiral interactions. Model space consists of 15 major harmonic oscillator shells with fixed oscillator frequency hw = 30MeV.

Coupled-cluster theory for nuclear matter (Preliminary)

Implemented exact Pauli operator in relative-center of mass coordinates Implemented Hartree-Fock and MBPT(2) for nuclear matter in relative and Center-of-mass coordinates. Code has been validated and verified using Argonne-V18 and vlow-k. Particle-particle and hole-hole ladders are in progress. Particle-hole channels will be implemented using exact and angle average Pauli operator

Proposed work

Progress for years 4-5

Status

Interface with DFT: response of energy and density to external potentials Spectroscopic factors in J-coupled scheme with continuum coupling Computing intrinsic ground state densities See J. Holts talk Completed oxygen isotopes Completed : 21-24 O Lorentz integral transform (w/ Sonia Bacca and Nir Barnea) Role of three-nucleon forces in medium-mass nuclei (w/A. Schwenk and S. Bacca) Coupled-cluster approach to nuclear matter (w/ Gustav Baardsen UiO) In progress In progress In progress Project is reasonably well on track

Computational status

Data organization

• Interaction spread across processors • cluster amplitudes stored locally • oxygen-16 in 20 shells ~ 1500 processor hours per model space • oxygen-28 with continuum: total cost of about 100,000 CPU hours on Jaguar.

Challenge

• Number of j-coupled matrix elements of interactions fluctuate strongly for given sets of quantum numbers • load balancing non-trivial: Calculation of estimated computational cost  distribution of data • scaling (load-balancing) up to few thousand processors • Working on optimizing code with OpenMP.

Future plans (remainder of year 5 and outlook

) 1. Interface with DFT, and toward ab initio reactions 1. Compute phaseshifts for elastic scattering of neutrons on selected closed shell nuclei using one-nucleon overlap functions. 2. Constraining EDFs from ab-initio coupled-cluster theory 3. Develop spherical EOM-CCSD code for general spin and compute dipole response function using Lorentz integral transform.

2. Role of three-nucleon forces in medium-mass nuclei Outlook / SciDAC-3 ? 1. Ab initio computation of 48 Ca with 3NF as possible highlight 2. Validation and verification of nuclear forces from Chiral EFT with uncertainty quantification. 3. Exploring Magic Numbers at the extreme using nuclear coupled-cluster 4. One- and two-nucleon overlap functions from coupled-cluster theory 5. Time dependent coupled-cluster approach to reactions 6. Nuclear matter (PhD student Gustav Baardsen from UiO)