• Introduction
• General principles
• Examples: quantitative nuclear theory;
predictive capability
• Initiatives
• Challenges
• Summary
Theory of Nuclei and Their Reactions
Witek Nazarewicz (MSU/ORNL)
Joint DNP Town Meetings on Nuclear Structure and Nuclear Astrophysics Texas A&M, August 21-23, 2014
Thanks for the input!
SCIENCE AND SOCIETY RELY ON OUR UNDERSTANDING OF THE ATOMIC NUCLEUS AND THE GRAND
NUCLEAR LANDSCAPE
TIMESCALE
➥ from QCD transition (color singlets formed; 10ms after Big Bang) till today (13.8 billion years later) DISTANCE SCALE
➥ from 10-15 m (proton’s radius) to 12 km (neutron star radius)
The Nuclear Landscape and the Big Questions (NAS report)
• How did visible matter come into being and how does it evolve? (origin of nuclei and atoms)
• How does subatomic matter organize itself and what phenomena emerge? (self-organization)
• Are the fundamental interactions that are basic to the structure of matter fully understood?
• How can the knowledge and technological progress
provided by nuclear physics best be used to benefit society?
The challenge and the prospect: physics of nuclei directly from QCD
R es ol ut io n
scale separation
DFT
collective models
CI
ab initio LQCD
quark models
E ffe ct iv e F ie ld T h eo ry
Theory of nuclei is demanding
input open ch
annels
dyn
am
ics
Great recent progress
• New ideas
• 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 o large-scale computations
Illustrative physics examples
More excellent examples in the experimental overview
Janssens
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 rch (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
Lattice EFT Green’s Function Monte Carlo
Anomalous Long Lifetime of 14C
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
GT matrix element
N3LO NN only N3LO + 3NF (cD= -0.2) N3LO + 3NF (cD= -2.0)
s p sd pf sdg pfh sdgi pfhj sdgik pfhjl
configuration space
-0.1 0 0.1 0.2 0.3
0.29
Ab-initio frontier: quantitative predictions
12C ground state and Hoyle state
The frontier: medium-mass nuclei
Microscopic valence-space Shell Model
Coupled Cluster Effective
Interaction
(valence cluster expansion)
In-medium SRG
Effective Interaction
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+
22O
0 40 80 120 160 200 240 280
neutron number
0 40 80 120
proton number tw o- p r oto n
d r ip line
t w o- n e u t r o n d r i p l i 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
Nuclear Density Functional Theory: Large-Scale Surveys The challenge: Universal Energy Density Functional
Asymptotic freedom ?
from B. Sherrill
DFT FRIB
current
Small and Large-Amplitude Collective Motion
• New-generation computational frameworks developed
• Time-dependent DFT and its extensions
• Adiabatic approaches rooted in Collective Schrödinger Equation
• Quasi-particle RPA
• Projection techniques
• Applied to HI fusion, fission, coexistence phenomena, collective strength, superfluid modes
0 . 5 1 . 0
1 . 5 2 . 0 2 . 5
3 . 0 3 . 5
4 . 5 4 . 0 5 . 0
3 . 5
5 . 5
6 . 0 3 . 0
2 . 5 6 . 5
2 . 0
1 . 5 7 . 0
1 . 0
4 . 5 4 . 5
7 . 5
0 . 5 4 . 0
4 . 0
4 0 6 0 8 0 1 0 0
0 4 8
1 2 d y n a m i c
Q 22(b)
Q 2 0( b )
s t a t i c
ground
state saddle pre-scission
Vortex dynamics in superfluid condensates Spontaneous fission
Heavy Ion fusion
4
FIG. 4: (Color online) Vibrational wave functions squared
K |Φα I K(β, γ)|2 of the 0+1, 2+1, 0+2 and 2+2,3 states in
30− 34Mg. Contour lines are drawn at every eighth part of the maximum value.
tern of the K = 02bands in30Mg and32Mg, noticed above, can be seen more drastically in the inter-band E 2 transition properties. In the lower panel of Fig. 3, we plot the ratio B (E 2; 0+2 → 2+1)/ B (E 2;0+1 → 2+2,3) of the inter-band transition strengths between the K = 01
and K = 02bands. If the K = 01and K = 02 bands are composed of only the K = 0 component and the in- trinsic structures in the (β, γ) plane are the same within the band members, this ratio should be one. T hese ra- tios for34Mg and36Mg are close to one, indicating that the change of the intrinsic structure between the 0+and 2+states is small. In contrast, the ratios for30Mg and
32Mg are larger than 10, indicating a remarkable change in the shape-fluctuation properties between the 0+ and 2+states belonging to the K = 01and K = 02bands.
Figure 4 shows the vibrational wave functions squared
K |ΦαI K(β, γ)|2. Let us first examine the character changeof the ground state from30Mg to34Mg. In30Mg, the vibrational wave function of the ground 0+1 state is distributed around the spherical shape. In32Mg, it is re- markably extended to the prolately deformed region. In
34Mg, it is distributed around the prolate shape. From the behavior of the vibrational wave functions, one can concludethat shapefluctuation in the ground 0+1 state is largest in32Mg. To understand the microscopic mecha- nism of this changefrom30Mg to34Mg, it is necessary to
takeinto account not only theproperties of thecollective potential in the β direction but also its curvature in the γ direction and the collective kinetic energy (collective masses). T his point will be discussed in our forthcoming full-length paper. As suggested from the behavior of the inter-band B (E 2) ratio, the vibrational wave functions of the 2+1 state are noticeably different from those of the 0+1 state in30Mg and32Mg, while they are similar in the case of34Mg. Next, let us examine the vibrational wave functions of the 0+2 and 2+2,3states in30−34Mg. It is im- mediately seen that they exhibit onenodein the β direc- tion. T his is their common feature. In30Mg and32Mg, one bump is seen in the spherical to weakly-deformed region, while the other bump is located in the prolately deformed region around β = 0.3−0.4. In34Mg, the node is located near the peak of the vibrational wave function of the 0+1 state, suggesting that they have β-vibrational properties.
0 0.5
|FaIK(b,g)|2
(a) 01+
30Mg
32Mg
34Mg
0 0.5
0 0.1 0.2 0.3 0.4 0.5 0.6
|FaIK(b,g)|2
b (g=0.5o) (c) 02+
0 10 20
P(b)
(b) 01+
0 0.1 0.2 0.3 0.4 0.5 0.60 10 20
P(b)
b (d) 02+
FIG. 5: (Color online) (a) Vibrational wave functions squared, |Φα ,I = 0,K =0(β, γ = 0.5◦)|2, of the 0+1 states in
30− 34Mg. T heir values along the γ = 0.5◦ line are plotted as functions of β. (b) Probability densities integrated over γ, P (β) ≡ dγ|Φα ,I =0,K =0(β, γ)|2|G(β, γ)|1/ 2, of the 0+1 states in30− 34Mg, plotted as functions of β. (c) Same as (a) but for the 0+2 states. (d) Same as (b) but for the 0+2 states.
To further reveal the nature of the ground and excited 0+states, it is important to examinenot only their vibra- tional wave functions but also their probability density distributions. Since the 5D collective space is a curved space, the normalization condition for the vibrational wave functions is given by
K
|ΦαI K(β, γ)|2|G(β, γ)|1/ 2dβdγ = 1 (5)
with the volume element
|G(β, γ)|1/ 2dβdγ = 2β4 W(β, γ)R(β, γ) sin3γdβdγ, (6)
Shape coexistence
Isospin mixing
E1 strength
Fusion cross section SF lifetimes
8 9 10 11 12 13 14 15 R (km)
0 1 2
M (Msolar)
2r
04r
01.4 1.97(4)
NN
3r
05r
00 . 3 0 f m 0 . 1 5 f m
r
0 NN+NNN
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⊙ )
=12 km and Rskin= 0.17 fm.
From nuclei to neutron stars (a multiscale problem)
Major uncertainty: density dependence of the symmetry energy. Depends on T=3/2 three-nucleon forces
Reddy
Atomic Nuclei: Many-Body Open Quantum Systems
• Facts: (i) nuclear structure is impacted by couplings to reaction and decay channels;
(ii) reaction dynamics is
impacted by nuclear structure
• Challenge: clustering, alpha decay, and fission still remain major challenges for theory
• Answer: unified picture of structure and reactions
45Fe
Ab initio calculations of ANCs and widths Ab initio calculations of nuclear spectra (CC, NCSM/RGM, NCGSM)
Di-neutron correlations in CS/GSM
A suite of powerful approaches developed to open nuclear systems:
• Real-energy continuum shell model
• Complex-energy continuum shell model
• Ab-initio extensions
Profound interdisciplinary connections:
• resonance trapping and super-radiance
• threshold anomalies and channel coupling effects
• spectral fluctuations and statistics of resonances
• clusterization
• spatially extended halos and Efimov states
Impact of open channels on structural properties
Ab initio reaction theory
Microscopic reaction theory
Near-term prospects:
• High-fidelity simulations with NN+NNN for composite projectiles and exotic nuclei
• Nuclear reactions with microscopic optical potentials
• Description of direct, semi-direct, pre- equilibrium, and compound processes
Quality input: nonlocal dispersive optical potential
Proton-recoil cross section [b/sr]
Direct reaction theory
Fundamental symmetry tests and neutrino physics
• Superallowed Fermi 0
+→0
+b-decays
• Neutrinoless double-beta decays
• Schiff moment for EDM
• Neutrino-nucleus scattering
“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)
Current 0nbb predictions
Prospects
Scientific method: our paradigm
The theory-experiment cycle is repeated, continually testing and modifying the theory, until the theory describes experimental
observations. Then the theory is considered a scientific law.
Yin and yang can be thought of as complementary (rather than opposing) forces that interact to form a dynamic system in which the whole is greater than the assembled parts.
Experimental context: some thoughts…
• Beam time and cycles are difficult to get and expensive.
Experiment keeps theory honest. Theory could help by being more involved in assessing the impact of planned runs and projects.
• 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?
• New technologies are essential for providing predictive capability, to estimate uncertainties, and to assess extrapolations
• Theoretical models are often applied to entirely new nuclear systems and conditions that are not accessible to experiment
A paradigm shift is needed to enhance the coupling
between theory and experiment
-1 0 1 2 3 4 5 6
s2 (10-3 fm2 )
200 204 208 212 216 220 224
A
remaining
left bars: UNEDF0 right bars: SV-min
asym L
CrDr
rskin
1
Quality control through Uncertainty Quantification
but…
…EFT framework is designed for model
independence and systematic improvement of approximations. This has a potential of
enriching the experiment-theory feedback
analytic theory su
percom
puting
experim ent
Future: large multi-institutional efforts involving strong coupling between physics, computer science, and applied math
“High performance computing provides answers to
questions that neither
experiment nor analytic theory can address; hence, it
becomes a third leg
supporting the field of nuclear physics.” (NAC Decadal
Study Report) Carlson
High Performance Computing and Nuclear Theory
⇒ New Initiative: FRIB Theory Center
It will enhance the national low-energy nuclear physics effort by:
• Delivering excellent research in theory relevant to the big science questions;
• Serving as a focal point for stimulating continuous interactions between theory and experiment;
• Rejuvenating the field by creating (bridge/joint) permanent positions in FRIB theory across the country;
• Attracting young talent through the national FRIB theory fellow program;
• Strengthening theory in areas of most need;
• Fostering interdisciplinary collaborations and build scientific bridges to wider theory communities;
• Coordinating a sustainable educational program in advanced; low-energy nuclear theory (TALENT!!!);
• Coordinating international initiatives in theory of rare isotopes. Building on success of J/F/C-USTIPEN.
Theory needs FRIB; FRIB needs Theory
• Describe the lightest nuclei in terms of lattice QCD
• Develop first-principles framework for light, medium-mass nuclei, and nuclear matter from 0.1 to twice the saturation density
• Develop predictive and quantified nuclear energy density functional rooted in first- principles theory
• Unify the fields of nuclear structure and reactions: we must free ourselves from limitations imposed by (physical) boundary conditions
• Achieve a comprehensive description of direct, semi-direct, pre-equilibrium, and compound processes for a variety of reactions
• Provide the microscopic underpinning of observed, and new, (partial-) dynamical symmetries and simple patterns
• Develop predictive microscopic model of fusion and fission that will provide the missing data for astrophysics, nuclear security, and energy research
• Carry out predictive and quantified calculations of nuclear matrix elements for fundamental symmetry tests in nuclei and for neutrino physics. Explore the role of correlations and currents.
Develop and utilize tools of uncertainty quantification
Enhance the coupling between theory and experiment
Take the full advantage of high performance computing
Summary (1): Challenges for LE Nuclear Theory
Our field
• Establish the FRIB Theory Center. Theory centers were crucial for RHIC and Jlab communities
• Support TALENT educational initiative
Nuclear Theory in general
• Enhanced support for nuclear theory to realize the full scientific promise enabled by experimental investments
• Computational initiative: new investments in people, advanced software, and complementary capacity computing directed toward nuclear theory
• Continuation of Topical Collaborations: a very effective way to target specific science questions
• Adequate support for INT: a resource belonging to the entire nuclear theory community
Summary (2): The LRP 2014 Request
• The nuclear many-body problem is very complex, computationally difficult, and interdisciplinary.
• With a fundamental picture of nuclei based on the correct
microphysics, we can remove the empiricism inherent today, thereby giving us greater confidence in the science we deliver and predictions we make
• For reliable model-based extrapolations, we need to improve predictive capability by developing methods to quantify
uncertainties
• We need a paradigm shift to optimize a theory-experiment loop
• New-generation computers will continue to provide unprecedented opportunities for nuclear theory
• New theory initiatives for the LRP 2014
Summary (3, final)
BACKUP
dim ens ion of th e pr oble m
How to explain the nuclear landscape from the bottom up? Theory roadmap
• A first rate theory predicts
• A second rate theory forbids
• A third rate theory explains after the facts
Alexander I. Kitaigorodskii
FRIB TC
SAB
FRIB TC
SAB
INT
JINPA/ORNL JINA
NSCL/MSU
NUCLEI
TALENT
CUSTIPEN FUSTIPEN ICNT
NPAC/LANL ACFI
CEEM MWT/ANL
TORUS NuN
LVOC/LLNL
university national lab
