• Introduction
• General principles
• Today: quantitative theory;
predictive capability
• Challenges for tomorrow
• Summary
Computational nuclear structure in the eve of exascale
Witek Nazarewicz (MSU/FRIB)
Symposium on Quarks to Universe in Computational Science (QUCS 2015) Nara, November 4-8, 2015
ORNL Creative Media
The Nuclear Landscape and the Big Questions (NAS report)
• Where do nuclei and elements come from?
• How are nuclei organized?
• What are practical and scientific uses of nuclei?
BOTTOM LINE
Revolution due to major advances in accelerator technology, experimental
techniques, analytic theory, and computing.
This has led to a shift from phenomenological picture to nuclear theory grounded in the
Standard Model. Today, we are constructing
a roadmap that will lead to a predictive theory
of nuclei.
Rooting nuclei in QCD
QCD
LQCD predictions for magnetic moments A<4
Beane et al., PRL113, 252001 (2014); NPLQCD
F. Nunes
Nuclear Force from Lattice QCD
Inoue et al. PRL 111, 112503 (2013); HALQCD/HPCI
How to explain the nuclear landscape from the bottom up? Theory revolution
R e so lu tio n
Coupled cluster description of binding energies and radii
A. Ekstrom et al., PRC 91, 051301 (2015)
45 50 55 60 65
Ec.m. (MeV) 10-4
10-3 10-2 10-1 100 101 102
s fusion (mb)
Ec.m. = 55 MeV, TDDFT Experiment
Fusion cross sections from TDDFT
R. Keser et al., PRC 85, 044606 (2012)
48
Ca+
48Ca
Who could have predicted this 20 years ago?
4 Ab-initio approach to reactions(p+4He)
Hupin et al. PRC 90, 061601 (2014)
DFT CI ab initio LQCD
Geometric Algebraic
Magnetic moments of light nuclei from QMC with two-body corrents
Pastore et al., PRC 113, 035503 (2013)
dim ens ion of th e pr oble m
How to explain the nuclear landscape from the bottom up? Theory roadmap
Theory of nuclei is demanding
in pu t
open channels
d yn am
ic s
• New insights
• Data on exotic nuclei crucial o long isotopic chains
o low-energy reaction thresholds
o large neutron-to-proton asymmetries
• High performance computing o algorithmic developments o benchmarking and
validation
o uncertainty quantification
• Quality input: garbage in,
garbage out!
Illustrative physics examples
1980 1990 2000 2010 2020
Year
0 10 20 30 40 50 60
A
Progress in ab-initio calculations
In the early decades, the progress was approximately linear in A because the computing power, which increased exponentially according to Moore’s law, was applied to exponentially expensive numerical algorithms. In recent years, new- generation algorithms, which exhibit polynomial scaling in A, have greatly
increased the reach.
The nuclear A-body problem
G. Hagen et al., Nature Physics (2015)
0 1 2 3 4 q ( f m - 1)
1 0- 4 1 0- 3 1 0- 2 1 0- 1 1 00
|F(q)|
e x p r1 b r1 b + 2 b
0 2 4
r ( f m ) 0 . 0 0
0 . 0 4 0 . 0 8 r ch (r)
Results - Longitudinal form factor
• Experimental data are well reproduced by theory over the whole range of
momentum transfers;
• Two-body terms become appreciable only for q > 3 fm−1, where they interfere destructively with the one- body contributions bringing theory into closer
agreement with experiment.
Monday, June 24, 13
Lovato et al., Phys. Rev. Lett. 111, 092501 (2013). Quantum Monte Carlo
12 C structure: Ground-state and Hoyle-state
In 1954, Hoyle postulated that a7.65 MeV carbon state. This state plays a crucial role in the hydrogen burning of stars heavier than our sun and in the production of carbon and other elements necessary for life.
Epelbaum et al., Phys. Rev. Lett. 109, 252501 (2012). Lattice EFT
12 C
~ 0p
8
0
2
4439
7366
7654
0
8 Be +
11
C +n
11
B +p
18721
15957
The frontier: neutron-rich calcium isotopes
where ab-initio and DFT meet…
Unique dataneutron number
Extrapolations are tough
Nuclear Forces from χEFT
derived 2000 derived 2002
derived 2003 derived 2011 N2LO
N3LO NLO
LO
NN NNN
+...
+...
+... +...
optimized simultaneously 2014
A. Ekström et al.
PRC 91, 051301(R) (2015)
Consistency with known data
Prediction of weak charge f.f.
CREX
G. Hagen et al., Nature Physics (2015); doi:10.1038/nphys3529
ORNL, University of Tennessee, Michigan
State University, Chalmers University of
Technology, TRIUMF, Hebrew University,
Technical University Darmstadt, University
of Oslo, University of Trento
Microscopic valence-space Shell Model
Coupled Cluster Effective Interaction (valence cluster expansion)
Jansen et al. , Phys. Rev. Lett. 113, 142502 (2014)
In-medium SRG Effective Interaction
Bogner et al. Phys. Rev. Lett. 113, 142501 (2014)
MBPT IM-SRG
NN+3N-ind IM-SRG
NN+3N-full Expt.
0 1 2 3 4 5 6 7 8
Energy (MeV)
0+ 2+
2+ 2+
0+ 0+
(2+) 2+
2+
(0+) 0+
0+ 4+
4+ (4+)
4+ 2+
0+
2+
0+ 3+
3+ 3+
3+
0+
22
O
Deformed sd-shell nuclei from first principles, Jansen et al. arXiv:1511.00757
Large-scale configuration interaction (shell model)
Photoabsorption cross section
E1 strength in
88Sr
Dimension of CI Hilbert space: 10 36
can do kan-calculation!
Model space: 3 major shells: pf - sdg – pfh (0h
11/2,1f
7/2, 2p
3/2) Electric dipole transitions in medium-mass nuclei in Monte
Carlo shell model (HPCI)
Togashi, Otsuka, Shimizu, Utsuno…
Novel approach based on
MCSM
Small and Large-Amplitude Collective Motion
• New-generation computational frameworks developed
• Time-dependent DFT and its extensions
• Collective Schrödinger Equation
• Quasi-particle RPA
• Projection techniques
• Applied to HI fusion, fission, coexistence phenomena Shape coexistence
Hinohara et al. PRC 84, 061302(R) (2011)
Fusion cross section
45 50 55 60 65
Ec.m. (MeV) 10-4
10-3 10-2 10-1 100 101 102
s fusion (mb)
Ec.m. = 55 MeV, TDDFT Experiment
48
Ca+
238U
R. Keser et al., PRC 85, 044606 (2012) 48
Ca+
48Ca
also: Tsunoda et al. Phys. Rev. C 89, 031301(R) (2014); HPCI
Nuclear Fission
Sadhukhan et al. Phys. Rev. C 90 061304(R) (2014) and arXiv:1510.08003 3 0 7 0
0 1 0 2 0 3 0 4 0 5 0
5
7 7
3 9 5
5
57
7 5
9 3 1 1
- 3 - 9- 1 5
- 2 1
1 19
- 2 7
3
q
I2 4 0
P u
1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 00 1 0 2 0 3 0 4 0 5 0
q
I IQ 30(b3/2 )
Q 2 0 ( b )
d y n a m ic
st at ic
Q 22(b)
Spontaneous fission yields
5 0 6 0
0 . 1 1 1 0
1 2 0 1 4 0 1 6 0
0 . 1 1 1 0
charge yield (%)
f r a g m e n t c h a r g e
mass yield (%)
f r a g m e n t m a s s
2 4 0
P u
http://science.energy.gov/ascr/highlights/2015/ascr-2015-08-a/
Ab initio calculations of ANCs and widths
Applications of Complex Scaling with realistic nuclear interactions
A suite of powerful approaches developed to open nuclear systems:
• Real-energy continuum shell model
• Complex-energy continuum shell model
• Complex scaline
• Ab-initio extensions
Impact of open channels on structural properties
Nollett, PRC 6, 044330 (2012)
Evaluation of the elastic scattering
3P
0phase-shifts using Complex Scaled chiral N
3LO and N
2LO
optinteractions.
Papadimitriou and Vary, PRC(R) 91, 021001 (2015)
Quest for understanding the neutron-rich matter on Earth and in the Cosmos
Crustal structures in neutron stars Data
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.
The limits: Skyrme-DFT Benchmark 2012
0 40 80 120 160 200 240 280
neutron number
0 40 80 120
pr ot on n um be r
tw o- p r oto n d r ip line
t w o - n e u t r o n d r i p li n e
232 240 248 256
n e u t r o n n u m b e r
proton number
90 110
100 Z=50
Z=82
Z=20
N=50
N=82
N=126
N=20
N=184
d r i p l i n e S V - m i n
k n o w n n u c l e i s t a b l e n u c l e i
N=28 Z=28
230 244
N=258
Nuclear Landscape 2012
S 2 n = 2 M e V
288
~3,000
Erler et al, Nature 486, 509 (2012)
A.V. Afanasjev, et al. Phys. Lett. B (2013)
Current 0nbb predictions
“There is generally significant variation among different calculations of the nuclear matrix elements for a given isotope. For consideration of future experiments and their projected sensitivity it would be very desirable to reduce the uncertainty in these nuclear matrix elements.” (Neutrinoless Double Beta Decay NSAC Report 2014)
Fundamental symmetry tests
Nuclear Theory for
Double-Beta Decay and Fundamental Symmetries (DBD Collaboration)
Engel (UNC), PI
Participating Institutions:
CMU, CWM, ISU, MSU,
LANL, LLNL, SDSU, UCB,
UMass, UNC, UTK
Prospects
Experimental context: some thoughts…
• Beam time and cycles are difficult to get and expensive.
• What is the information content of measured observables?
• Are estimated errors of measured observables meaningful?
• What experimental data are crucial for better constraining current nuclear models?
• Theoretical models are often applied to entirely new nuclear systems and conditions that are not accessible to experiment.
New technologies are essential for providing predictive capability, to estimate uncertainties, and to assess
extrapolations
A paradigm shift is needed to enhance the coupling
between theory and experiment
ISNET: Enhancing the interaction between nuclear experiment and theory through information and statistics
JPG Focus Issue: http://iopscience.iop.org/0954-3899/page/ISNET Around 35 papers (including LQCD, nuclear structure, reactions, nuclear astrophysics, medium energy physics, statistical methods…) ECT* ISNET-3 meeting Nov. 16-20 on “Information and statistics in nuclear experiment and theory”
“Remember that all models are
wrong; the practical question is
how wrong do they have to be
to not be useful” (E.P. Box)
Information Content of New Measurements
J. McDonnell et al. Phys. Rev. Lett. 114, 122501 (2015)
• Developed a Bayesian framework to quantify and propagate
statistical uncertainties of EDFs.
• Showed that new precise mass measurements do not impose sufficient constraints to lead to significant changes in the current DFT models (models are not
precise enough)
• Perfect for HPC!
Bivariate marginal estimates of the posterior distribution for the 12-dimensional DFT UNEDF
1parameterization.
We can quantify the statement:
“New data will provide stringent constraints on theory”
computingnuclei.org
Collaborations within NUCLEI
• Multiple direct partnerships formed. This eliminated the traditional difficulties of
PHY–CS/AM collaborative projects
• Increased collaboration across domains
• Many initially unanticipated blue-blue and blue-red links
• Worked well in UNEDF, continuing to work well in NUCLEI
• Collaborations have
deepened and expanded
See computingnuclei.org for more info on code performance,
scalability, porting, etc.
Electromagnetic and neutral-weak response of
4He and
12C
References: A. Lovato et al.
Phys. Rev. C 91, 062501 (2015)
Euclidean neutral-weak transverse response functions of 12C at q = 570 MeV. Two-body currents increase the one-body response in both the quasielastic and threshold regions.
Impact
• The calculations of the Euclidean electromagnetic response function of 12C can be used to predict the results of the latest electron-12C scattering experiment of JLab.
• Accurate calculations of electroweak response functions are relevant to neutrino-nucleus scattering experiment (MiniBoone) and to understand the mechanism of supernovae explosions.
Accomplishments
• Development of an algorithm to compute the Euclidean response functions within Green’s function Monte Carlo.
• Using Maximum Entropy techniques it is now possible to obtain the electromagnetic response of 4He from the Euclidean response.
• Two-body currents and nuclear correlations have to be accounted for in order to get good agreement with experimental data.
Objectives
• Compute the electromagnetic response functions of 4He and 12C for which accurate experimental data are available.
• Within the same formalism, study the neutral-current and charged-current response functions, fundamental ingredients for describing neutrino-12C scattering.
• Investigate the energy dependence of the two-body meson-exchange currents contributions.
Electromagnetic transverse response functions of
4He at q = 600 MeV obtained from the corresponding Euclidean response by using Maximum Entropy techniques.
Impact Objectives
• Predict properties of neutron-rich systems which relate to exotic nuclei and nuclear astrophysics
• Determine how well high-precision phenomenological strong interactions compare with effective field theory based on QCD
• Produce accurate predictions with quantified uncertainties
Improve nuclear energy density functionals used in extensive applications such as fission calculations
Demonstrate the predictive power of ab initio nuclear theory for exotic nuclei with quantified uncertainties
Guide future experiments at DOE-sponsored rare isotope production facilities
1. Provides results for next generation nuclear energy density functionals
2. Demonstrates that the role of three-nucleon (3N)
interactions in extreme neutron systems is
significantly weaker than predicted from high-
precision phenomemological interactions
Accomplishments
Ab initio Extreme Neutron Matter
Comparison of ground state energies of systems with N neutrons trapped in a harmonic oscillator with strength 10 MeV. Solid red
diamonds and blue dots signify new results with two-nucleon (NN) plus three-nucleon (3N) interactions derived from chiral effective field theory related to QCD. Inset displays the ratio of NN+3N to NN alone for the different interactions. Note that with increasing N, the chiral
predictions lie between results from different high-precision
phenomenological interactions, i.e.
between AV8’+UIX and AV8’+IL7.
References: H. Potter, S. Fischer, P. Maris, J.P. Vary, S. Binder, A. Calci, J. Langhammer and R.Roth, Phys. Lett. B739, 445 (2014);
P. Maris, J.P. Vary, S. Gandolfi, J. Carlson, S.C. Pieper, Phys. Rev. C87, 054318 (2013); Contact: [email protected]
From hypernuclei to hypermatter: the role of three-body forces
References: D. Lonardoni et al. PRC 89, 014314 (2014); PRL 114, 092301 (2015)
Hyperon separation energy. The inclusion of three-body hyperon-nucleon forces provides a good description of the ground state physics of Λ-hypernuclei over a wide mass range.
Impact
• Extension of ab-initio calculations to the strange nuclear sector.
• Provide the directions for future theoretical investigation and for the next generation of terrestrial hypernuclear experiments.
• New hints for the solution of the so-called hyperon
puzzle: connection between the theory of baryon-baryon interaction and astrophysical observations.
Accomplishments
•
Development of quantum Monte Carlo methods to explore nuclear systems with hyperons.
•
Improvement of existing realistic hyperon-nucleon Hamiltonians.
•
Point out the need of additional hypernuclear experimental input and further theoretical studies.
Objectives
• Study the ground state properties of Λ-hypernuclei over a wide mass range (3 A 91).
• Investigate the effect of the presence of hyperons in the inner core of neutron stars.
• Calculate the equation of state of pure neutron matter in presence of Λ hyperons by using realistic nucleon-
nucleon and hyperon-nucleon forces.
Mass radius relation. Different models of three-body hyperon-nucleon force predict dramatically different results on the maximum mass of neutron stars.
MADNESS-HFB: adaptive multi-resolution 3D DFT solver
Impact Objectives
• Complex many-body systems, such as fissioning nuclei, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies.
• To describe such systems, we introduce an adaptive
pseudospectral method for solving self-consistent equations of nuclear DFT in three dimensions. The numerical method is based on the multi-resolution and harmonic analysis
techniques with a multi-wavelet basis.
• The application of state-of-the-art parallel programming techniques include sophisticated
object-oriented templates which parse the high-level code into distributed parallel tasks with a multi- thread task queue scheduler for each multi-core node.
• Provides benchmark for future model developments.
• The new adaptive multi-resolution solver MADNESS-HFB is benchmarked against a two- dimensional coordinate-space solver based on the B-spline technique and a three-dimensional solver based on the harmonic-oscillator basis expansion.
• The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary
constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory.
• This paper has been chosen by the Editors of Physical Review C as Editors Suggestion.
Accomplishments
Pedagogical illustration of adaptive representations in MADNESS-HFB. (a) The modulus squared of the single-neutron wave function corresponding to the single-particle energy of
−5.214 MeV obtained in MADNESS-HF calculations for
110Mo, and (b) the corresponding spectral refinement structure.
Reference: J.C. Pei et al., Phys. Rev. C 90, 024317 (2014)
Newly discovered helical defects in nuclear pasta impact radio and X-ray obs. of neutron stars and provide model of an
important biological structure. MD simulations can provide insight into self-assembly of
structures, arrangement of multiple ramps, and dependence of structures on interactions.
Use large scale GPU computing to perform detailed molecular dynamics (MD) simulations of neutron star crust, including complex nuclear pasta phases, to determine possible structures.
Impact:
Objective :
Fig. 1: (Left) Endoplasmic reticulum (ER) is a structure present in cells where proteins are synthesized with the help of the large surface areas. (Middle) 3D electron micrograph of stacked ER sheets in secretory salivary gland cells of mice [2]. (Right) MD simulation of nuclear pasta involving 75,000 nucleons at a density of 0.05 fm-3 that shows very similar flat layers connected by a helical ramp [1].
MD simulations with 50,000 to 400,000 nucleons find new layered structure connected by helical ramps.
Accomplishments:
“Parking Garage” Structures in Biophysics and Astrophysics
References: [1] Phys. Rev. Lett. 114, 031102 (2015) [2] Cell 154, 285 (2013)
Contact: C. J. Horowitz, [email protected]
NUCLEI/UNEDF*Leadership3class*compu9ng*
!
Significant*accomplishments*in*NUCLEI/UNEDF,**
achieved*through*leadership3class*compu9ng*
"Ab#ini&o(calcula9ons*of*C312*
" Understanding*the*long*life9me*of*C314*
"Ab#ini&o(calcula9ons*of*Ca354*
" Improved*energy3density*func9onals*
" Quan9fying*the*limits*of*nuclear*existence*
!
SciDAC*collabora9ons*between*applied*
mathema9cians,*computer*scien9sts,*and*nuclear*
physicists*lead*to*efficient*u9liza9on*of*leadership3class*
compu9ng*resources*for*nuclear*physics*problems*
!
Typically,*>*60%*of*the*compu9ng*resources*are*
used*at*leadership3class*scale*(u9liza9on*@*OLCF)*
H.*Nam,*[email protected]/J.*Vary,*[email protected]*
• We recommend new investments in
computational nuclear theory that exploit the U.S. leadership in high-performance computing. These investments include a timely enhancement of the nuclear
physics contribution to the Scientific
Discovery through Advanced Computing program and complementary efforts as well as the deployment of the necessary capacity computing.
• We recommend the establishment of a national FRIB theory alliance. This alliance will enhance the field through the national FRIB theory fellow program and tenure-track bridge positions at
universities and national laboratories across the U.S.
• We recommend the expansion of the successful Topical Collaborations initiative to a steady-state level of five Topical Collaborations, each selected by a competitive peer-review process.
Theory Initiative
Advances in theory underpin the goal that we truly understand how nuclei and
strongly interacting matter in all its forms behave and can predict their behavior in new settings. To meet the challenges and realize the full scientific potential of current and future experiments, we require new investments in theoretical and
computational nuclear physics.
Double - Beta Double - Beta
Coupled cluster + LS Gaute, Coupled cluster + LS
Gaute,
IMSRG Scott IMSRG
Scott
NCSM?
James NCSM?
James
Shell model calculations
Shell model calculations
NuShellX Mihai
NuShellX Mihai
BIGSTICK Calvin, Wick
BIGSTICK Calvin, Wick
DFT DFT Ab Initio
Ab Initio
QMC Joe, Stefano
QMC Joe, Stefano
GCM, Jon GCM, Jon Effective interactions, ops
Multi-reference states
QRPA Witek, Jon
QRPA Witek, Jon
SRG Sofia, (Jon?)
SRG Sofia, (Jon?) Evolved ops
Exotic Mechanisms
Exotic Mechanisms
Short range ops Michael, Vincenzo
Short range ops Michael, Vincenzo
Effective ops
EDMs EDMs
Diamag.
atoms Diamag.
atoms
Nucleon Nucleon
Lattice Kostas, Andre
Lattice Kostas, Andre
Lattice Vincenzo et al?
Lattice Vincenzo et al?
Other EM operators Michael, Wick Other EM operators
Michael, Wick New mutlipole ops
V
PTfrom substructure
V
PTfrom substructure
EFT
Michael, Vincenzo EFT
Michael, Vincenzo Allow
connection with new physics Light ions
