h9p://en.wikipedia.org/wiki/Anthropic_principle
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
“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.”
Science 347, 1452 (2015)
Ab ini+o calcula+on of the neutron-‐proton mass difference
Fusion of Light Nuclei
Ab ini+o theory reduces uncertainty due to conflic+ng data § The n-3H elastic cross section for 14 MeV neutrons,
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
NIF
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.
Configuration interaction techniques • light and heavy nuclei • detailed spectroscopy • quantum correlations (lab-system description)
NN+NNN interac+ons Renormaliza+on
Diagonaliza+on Trunca+on+diagonaliza+on
Monte Carlo
Observables
• Direct comparison with experiment
• Pseudo-data to inform reaction theory and DFT
Matrix elements fi9ed to experiment
Input: configura+on space + forces Method
n p
120Sn
εF εF
Coulomb !barrier!
Flat !bottom!
Surface!region!
0!
Unbound!states!
Discrete!(bound)!states!
Average one-body Hamiltonian
€
ˆ H 0 = hi, hi = − 2
2Mi=1
A
∑ ∇i2 +Vi
hiφk i( ) = ε kφk i( )
ˆ H = tii∑ + 1
2 viji , ji≠ j
∑ = ( ti +Vi)i∑ + 1
2 viji, ji≠ j
∑ − Vii∑
$
%
& &
'
(
) )
Nuclear shell model
Residual interactioni
One-body Hamiltonian
• 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
• 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
Full fp shell for 60Zn : ≈ 2 ×109 Jz states5,053,594 J = 0,T = 0 states81,804, 784 J = 6,T =1 states
P +Q = 1
Microscopic valence-space Shell Model Hamiltonian
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
En
erg
y (
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
CCEI Exp.
USD
012345678
Energy
(MeV
)
0+
2+
3+
0+
2+4+
3+
0+
2+
3+0+
0+
2+
3+
2+4+4+
22O
G.R. Jansen et al., Phys. Rev. Lett. 113, 142502 (2014)
S.K. Bogner et al., Phys. Rev. Lett. 113, 142501 (2014)
Diagonalization Shell Model (medium-mass nuclei reached;dimensions 109!)
Martinez-Pinedo ENAM’04
Honma, Otsuka et al., PRC69, 034335 (2004)
26
NN+NNN interac+ons
Density Matrix Expansion
Input
Energy Density Func+onal
Observables
• Direct comparison with experiment
• Pseudo-‐data for reac+ons and astrophysics
Density dependent interac+ons
Fit-‐observables • experiment • pseudo data
Op+miza+on
DFT varia+onal principle HF, HFB (self-‐consistency)
Symmetry breaking
Symmetry restora+on Mul+-‐reference DFT (GCM) Time dependent DFT (TDHFB)
Nuclear Density Functional Theory and Extensions
• two fermi liquids • self-bound • superfluid (ph and pp channels) • self-consistent mean-fields • broken-symmetry generalized product states
Technology to calculate observables Global properties
Spectroscopy DFT Solvers
Functional form Functional optimization
Estimation of theoretical errors
Mean-Field Theory ⇒ Density Functional Theory
• 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 DFT • two fermi liquids • self-bound • superfluid
Degrees of freedom: nucleonic densities
• 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
Nuclear Energy Density Functional
p-h density p-p density (pairing functional)
isoscalar (T=0) density
€
ρ0 = ρn + ρp( )
isovector (T=1) density
€
ρ1 = ρn − ρp( )
+isoscalar and isovector densities: spin, current, spin-current tensor, kinetic, and kinetic-spin
+ pairing densities
E =�H(r)d3r
Expansion in densities and their derivatives
Mass table
Goriely, Chamel, Pearson: HFB-17 Phys. Rev. Lett. 102, 152503 (2009)
δm=0.581 MeV
Cwiok et al., Nature, 433, 705 (2005)
BE differences
Examples: Nuclear Density Functional Theory
Traditional (limited) functionals provide quantitative description
0
4
8
12
16
20
24
S2
n (
Me
V)
Er
neutron number
80 100 120 140 160
experimentdrip line
0
2
4
140 148 156 164
neutron number
0
4
8
58 62 66
proton number
N=76 162 154
S2
n (
MeV
)
S2
p (
MeV
)
FRDM
HFB-21
SLy4
UNEDF1
UNEDF0
SV-min
exp
Er
Description of observables and model-based extrapolation • Systematic errors (due to incorrect assumptions/poor modeling) • Statistical errors (optimization and numerical errors)
Erler et al., Nature 486, 509 (2012)
0 40 80 120 160 200 240 280
neutron number
0
40
80
120
prot
on n
umbe
r two-proton drip line
two-neutron drip line
232 240 248 256neutron number
prot
on n
umbe
r
90
110
100
Z=50
Z=82
Z=20
N=50
N=82
N=126
N=20
N=184
drip line
SV-min
known nucleistable nuclei
N=28
Z=28
230 244
N=258
Nuclear Landscape 2012
S2n = 2 MeV
How many protons and neutrons can be bound in a nucleus?
Skyrme-‐DFT: 6,900±500syst Literature: 5,000-12,000
288 ~3,000
Erler et al. Nature 486, 509 (2012)
Asymptotic freedom ?
from B. Sherrill
DFT FRIB
current
Quantified Nuclear Landscape
8 9 10 11 12 13 14 15R (km)
0
1
2
M (M
sola
r)
�l �
�l �
1.4
1.97(4)
NN
�l �
�l�
0.30 fm
0.15 fm
l�
NN
+NNN
Gandolfi et al. PRC85, 032801 (2012)
SV-min
CAB=0.82
0.8 0.9 1.1 1.21.0R(1.4 M )/R.
_
R skin
(208 Pb
)/Rsk
in
_
0.8
0.9
1.1
1.2
1.0
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.
J. Erler et al., PRC 87, 044320 (2013)
From nuclei to neutron stars (a multiscale problem)
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”