Anthropic Principle
h9p://en.wikipedia.org/wiki/Anthropic_principle The anthropic principle (from Greek anthropos, meaning "human") is the philosophical considera+on that observa+ons of the physical Universe must be compa+ble with the conscious life that observes it. Some proponents of the anthropic principle reason that it explains why the universe has the age and the fundamental physical constants necessary to accommodate conscious life. Anthropic considera+ons in nuclear physics: U. Meissner. h9p://arxiv.org/abs/1409.2959 The nucleosynthesis of carbon-­‐12 and Hoyle state Non-­‐anthropic scenario Anthropic scenario (fine-­‐tuned Universe) Dean Lee •  "Viability of Carbon-­‐Based Life as a Func+on of the Light Quark Mass", Phys. Rev. Le9. 110 (2013) 112502 •  "Dependence of the triple-­‐alpha process on the fundamental constants of nature", Eur. Phys. J. A 49 (2013) 82 •  "Varying the light quark mass: impact on the nuclear force and Big Bang nucleosynthesis", Phys. Rev. D 87 (2013) 085018 Ab ini+o calcula+on of the neutron-­‐proton mass difference Science 347, 1452 (2015) “The result of the neutron-­‐proton mass splifng as a func+on of quark-­‐mass difference and electromagne+c coupling. In combina+on with astrophysical and cosmological arguments, this figure can be used to determine how different values of these parameters would change the content of the universe. This in turn provides an indica+on of the extent to which these constants of nature must be fine-­‐tuned to yield a universe that resembles ours.” Fusion of Light Nuclei
Computational nuclear physics enables us to
reach into regimes where experiments and
analytic theory are not possible, such as the
cores of fission reactors or hot and dense
evolving environments such as those found in
inertial confinement fusion environment.
NIF
Ab ini+o theory reduces uncertainty due §  The n-3H elastic cross section for 14 MeV neutrons,
to conflic+ng data important for NIF, was not known precisely enough. §  Delivered evaluated data with required 5%
uncertainty and successfully compared to
measurements using an Inertial Confinement Facility §  “First measurements of the differential cross sections for the
elastic n-2H and n-3H scattering at 14.1 MeV using an
Inertial Confinement Facility , by J.A. Frenje et al., Phys.
Rev. Lett. 107, 122502 (2011)
http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.122502
Configuration interaction techniques
•  light and heavy nuclei
•  detailed spectroscopy
•  quantum correlations (lab-system description)
Input: configura+on space + forces NN+NNN interac+ons Renormaliza+on Matrix elements fi9ed to experiment Method Diagonaliza+on Trunca+on+diagonaliza+on Monte Carlo Observables • Direct comparison with
experiment
• Pseudo-data to inform
reaction theory and DFT
Average one-body Hamiltonian
120Sn
Coulomb !
barrier!
Unbound!
states!
Discrete!
(bound)!
states!
0!
εF
εF
Surface!
region!
n
A
Flat !
bottom!
2
ˆ
H 0 = ∑ hi , hi = − 2M ∇ 2i + Vi
i=1
hiφ k (i) = ε k φ k (i)
p
Nuclear shell model
Hˆ =
∑t
i
i
+ 12 ∑ vij = ∑ (ti + Vi ) +
i,j
i≠j
i
One-body
Hamiltonian
$
'
&1 v − V )
∑
ij
i)
&2 ∑
i, j
i
% i≠ j
(
Residual
interactioni
• Construct basis states with good (Jz, Tz) or (J,T)
• Compute the Hamiltonian matrix
• Diagonalize Hamiltonian matrix for lowest eigenstates
• Number of states increases dramatically with particle number
Full fp shell for 60 Zn : ≈ 2 × 109 J z states
5,053,594
81,804, 784
J = 0,T = 0 states
J = 6,T = 1 states
• Can we get around this problem? Effective interactions in
truncated spaces (P-included, finite; Q-excluded, infinite)
• Residual interaction (G-matrix) depends on the configuration
space. Effective charges
• Breaks down around particle drip lines
P +Q=1
Microscopic valence-space Shell Model Hamiltonian
Coupled Cluster Effective Interaction
(valence cluster expansion)
8
3+
4+
7
4+
2+
4+
6
0+
3+
0+
4
3+
3+
3
4
7
2
+
2+
2+
2+
+
3
5
22
1
0
4
O
0+
US
D
EI
+
4
+
2
+
+
0+
3
+
+
0
(0+ )
3
+
3
+
2
+
3
2
+
2
1
0+
0+
CC
(4 )
+
(2 )
+
4
2
+
0
0
0
+
O
+
2
2
22
2
6
Energy (MeV)
5
+
8
+
2+
Exp
.
Energy (MeV)
In-medium SRG Effective Interaction
MBPT
+
0
+
+
0
IM-SRG
IM-SRG
NN+3N-ind NN+3N-full
0
Expt.
S.K. Bogner et al., Phys. Rev. Lett. 113, 142501 (2014)
G.R. Jansen et al., Phys. Rev. Lett. 113, 142502 (2014)
Diagonalization Shell Model
(medium-mass nuclei reached;dimensions 109!)
Honma, Otsuka et al., PRC69, 034335 (2004)
Martinez-Pinedo
ENAM’04
26
Nuclear Density Functional Theory and Extensions
Technology to calculate observables
Input NN+NNN interac+ons Global properties
Spectroscopy
Density Matrix Expansion Density dependent interac+ons DFT Solvers
Functional form
Functional optimization
Estimation of theoretical errors
Op+miza+on Fit-­‐observables • experiment • pseudo data Symmetry restora+on Mul+-­‐reference DFT (GCM) Time dependent DFT (TDHFB) •  two fermi liquids
•  self-bound
•  superfluid (ph and pp channels)
•  self-consistent mean-fields
•  broken-symmetry generalized product states
Energy Density Func+onal DFT varia+onal principle HF, HFB (self-­‐consistency) Symmetry breaking Observables • Direct comparison with experiment • Pseudo-­‐data for reac+ons and astrophysics Mean-Field Theory ⇒ Density Functional Theory
Degrees of freedom: nucleonic densities
Nuclear DFT
•  two fermi liquids
•  self-bound
•  superfluid
•  mean-field ⇒ one-body densities
•  zero-range ⇒ local densities
•  finite-range ⇒ gradient terms
•  particle-hole and pairing
channels
•  Has been extremely successful.
A broken-symmetry generalized
product state does surprisingly
good job for nuclei.
Nuclear Energy Density Functional
isoscalar (T=0) density
isovector (T=1) density
€
€
(ρ
(ρ
0
= ρn + ρ p )
1
= ρn − ρ p )
E=
+isoscalar and isovector densities:
spin, current, spin-current tensor,
kinetic, and kinetic-spin
+ pairing densities
3
H(r)d r
p-h density p-p density (pairing functional)
Expansion in densities
and their derivatives
•  Constrained by microscopic theory: ab-initio functionals provide quasi-data!
•  Not all terms are equally important. Usually ~12 terms considered
•  Some terms probe specific experimental data
•  Pairing functional poorly determined. Usually 1-2 terms active.
•  Becomes very simple in limiting cases (e.g., unitary limit)
•  Can be extended into multi-reference DFT (GCM) and projected DFT
Examples: Nuclear Density Functional Theory
Traditional (limited) functionals
provide quantitative description
BE differences
Mass table
δm=0.581 MeV
Goriely, Chamel, Pearson: HFB-17
Phys. Rev. Lett. 102, 152503 (2009)
Cwiok et al., Nature, 433, 705 (2005)
Description of observables and model-based extrapolation
Systematic errors (due to incorrect assumptions/poor modeling)
Statistical errors (optimization and numerical errors)
S2n (MeV)
24
N=76
8
4
4
0
58
16
62
proton number
FRDM
HFB-21
SLy4
UNEDF1
UNEDF0
SV-min
exp
12
8
4
0
66
Er
140
148
156
neutron number
164
Er
experiment
80
162
2
0
20
154
S2n (MeV)
S2p (MeV)
•
•
100
Erler et al., Nature 486, 509 (2012)
drip line
120
140
neutron number
160
Quantified Nuclear Landscape
stable nuclei
line
288
p
dri
known nuclei ~3,000
n
to
o
r
drip line
-p
o
w
t
S2n = 2 MeV Z=82
SV-min
80
tron
u
e
-n
two
110
Z=50
40
N=126
Z=28
N=82
Z=20
0
N=28
N=20
0
line
p
i
dr
N=258
Asymptotic freedom ?
N=184
N=50
40
proton number
proton number
120
100
Nuclear Landscape 2012
80
120
160
DFT FRIB 90 230
244
232
240
current 200
248
neutron number
240
256
280
from
B. Sherrill
neutron
number
How many protons and neutrons can be bound in a nucleus?
Erler et al. Nature 486, 509 (2012) Literature: 5,000-12,000
Skyrme-­‐DFT: 6,900±500syst From nuclei to neutron stars (a multiscale problem)
Gandolfi et al. PRC85, 032801 (2012)
J. Erler et al., PRC 87, 044320 (2013)
1.4
1
NN
+N
NN
0
9
10
11
12
1.1
1.0
0.9
CAB=0.82
0.8
NN
0.30 fm
0.15 fm
8
_
Rskin( Pb)/Rskin
1.97(4)
2
SV-min
208
M (Msolar)
1.2
R (km)
13
14
15
0.8
0.9
1.0
1.1
_
R(1.4 M . )/R
1.2
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.
Major uncertainty: density
dependence of the symmetry
energy. Depends on T=3/2
three-nucleon forces
ISNET: Enhancing the interac+on between nuclear experiment and theory through informa+on and sta+s+cs JPG Focus Issue: h9p://iopscience.iop.org/0954-­‐3899/page/ISNET Around 35 papers (including nuclear structure, reac+ons, nuclear astrophysics, medium energy physics, sta+s+cal methods… and fission…) “Remember that all models are wrong; the prac+cal ques+on is how wrong do they have to be to not be useful” (E.P. Box) Error es+mates of theore+cal models: a guide J. Phys. G 41 074001 (2014) Informa+on Content of New Measurements J. McDonnell et al. Phys. Rev. Le9. 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) Bivariate marginal estimates of the posterior distribution for the 12-­‐dimensional DFT UNEDF1 parameterization. We can quantify the statement:
“New data will provide stringent constraints on theory”