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”