Nuclear Structure, Neutron Radii, Error Bars, and … Structure, Error Bars, and Correlations:...

Nuclear Structure, Neutron Radii,Error Bars, and Correlations

Calcium Radius EXperiment (CREX) Workshop

Organizing Committee

Chuck Horowitz (Indiana)

Kees de Jager (JLAB)

Jim Lattimer (Stony Brook)

Witold Nazarewicz (UTK, ORNL)

Jorge Piekarewicz (FSU

Sponsors: Jefferson Lab, JSA

PREX is a fascinating experiment that uses parity

violation to accurately determine the neutron

radius in 208Pb. This has broad applications to

astrophysics, nuclear structure, atomic parity non-

conservation and tests of the standard model. The

conference will begin with introductory lectures

and we encourage new comers to attend.

For more information contact [email protected]

Topics

Parity Violation

Theoretical descriptions of neutron-rich nuclei and

bulk matter

Laboratory measurements of neutron-rich nuclei

and bulk matter

Neutron-rich matter in Compact Stars / Astrophysics

Website: http://conferences.jlab.org/PREX

JLAB - March 17-19, 2013

J. Piekarewicz (FSU) Nuclear Structure, Neutron Radii, Error Bars, ... JLAB - March 17-19, 2013 1 / 15

My FSU Collaborators

Genaro Toledo-SanchezKarim HasnaouiBonnie Todd-RutelBrad FutchJutri TarunaFarrukh FattoyevWei-Chia Chen

My Outside Collaborators

B. Agrawal (Saha Inst.)M. Centelles (U. Barcelona)G. Colò (U. Milano)C.J. Horowitz (Indiana U.)W. Nazarewicz (U. Tennessee)N. Paar (U. Zagreb)M.A. Pérez-Garcia (U.Salamanca)P.G.- Reinhard (U.Erlangen-Nürnberg)X. Roca-Maza (U. Milano)D. Vretenar (U. Zagreb)


Density Functional Theory (W. Kohn: 1998 Chemistry Nobel Prize)

DFT enormously successful in chemistry/condensed-matter physicsHohenberg, Kohn, Sham, ...DFT shifts the emphasis from the wave function to the densityfrom the 3N-dimensional Ψ(r1, . . . , rN) to 3-dimensional ρ(r)

Ground-state properties uniquely determined by an electron densityElectron density obtained by minimizing a suitable energy functionalIn principle, DFT incorporates all many-body effects (Kohn Nobel lecture)


Nuclear Density Functional Theory

ab-initio calculations of heavy nuclei remain a daunting taskSearch for an energy functional valid through the entire nuclear chart:to compute ground-state properties, collective excitations, ...to compute neutron-star structure, dynamics, composition, ...Incorporate physical insights into the construction of the functionalEmpirical constants directly fitted to many-body observables... such as masses, charge radii, pseudo-data, ...Complicated many-body dynamics encoded in the empirical constantsEmpirical constants obtained from the optimization of a quality measure

Electric Magnetic

isoscalar isovector isoscalar isovector


Neutron Skins and Density Dependence of the Symmetry Energy

Neutron densities are as fundamental as proton (charge) densitiesYet, still elusive after more than 80 years of nuclear physics

Hinders our understanding of density dependence symmetry energyPenalty for breaking N =Z symmetry [B(Z ,N) = −aa(N−Z )2/A + . . .]

Neutron matter as a resonant Fermi Gas with large effective rangeUniversality of dilute Fermi gases with infinite scattering length

Neutron skin strongly correlated to the symmetry pressure L∝PPNMSlope (pressure) of pure neutron matter poorly constrained

Symmetry (or PNM) pressure pushes against surface tension⇒ n-skin

0.2 0.4 0.6 0.8 1.0 1.2kF (fm-1)

0

2

4

6

8

E/N

(MeV

)

Schwenk-PethickFriedman-PandharipandeHF-Vlow-k (S-P)Hebeler-SchwenkGandolfi et al.Gezerlis-CarlsonVidana et al.NL3FSUIU-FSU

Pure Neutron Matter

Ferm

i Gas


Neutron Stars and Density Dependence of the Symmetry Energy

Stellar radius strongly correlated to the symmetry pressure L∝PPNM

Symmetry (or PNM) pressure pushes against gravity⇒ NS radius

Symmetry (or PNM) pressure pushes against surface tension⇒ n-skin

L and rskin correlated to a myriad of NS observablesNS-radii, proton fraction, core-crust transition density, DUrca cooling, ...

PREX-II places a significant constraint on neutron-star radii!

40 50 60 70 80L (MeV)

12

12.5

13

13.5

14

14.5

R NS [

M/M

sun]

(km

) RNS[0.8]RNS[1.4]

CAB=0.988

FSUGold

CAB=0.946

0 0.2 0.4 0.6 0.8 1Correlation with skin of 208Pb

skin 132Sn

RNS[0.8]RNS[1.4]

skin 48Ca

lt

skin 208Pb

L

Ypt

MDUrca

Icrust[0.8]

Stru

ctur

ePa

sta

Cooling

Glitches


Heaven on Earth: Neutron Skins and Neutron StarsDemorest et al., Nature 467, 1081 (2010)

Same dynamical origin to neutron skin and NS radiusCorrelation among observables differing by 18 orders of magnitude!The larger the neutron skin, the larger the neutron-star radius ...Enormous uncertainty in the prediction of neutron-star radiiPREX-II places a significant constraint on neutron-star radii!r208skin = (0.207±0.037) fm; R0.8

NS =(13.509±1.060) km; R1.4NS =(12.655±0.470) km

0.16 0.20 0.24 0.28rskin[208Pb] (fm)

12

12.5

13

13.5

14

R[1.4

] (km

)

phase transition?

FSUGold

NL3


PREX: The Lead Radius EXperiment [PRL 108, 112502 (2012)]

Ran for 2 months on April-June 2010 Organizing Committee

Chuck Horowitz (Indiana)

Kees de Jager (JLAB)

Jim Lattimer (Stony Brook)

Witold Nazarewicz (UTK, ORNL)

Jorge Piekarewicz (FSU

Sponsors: Jefferson Lab, JSA

PREX is a fascinating experiment that uses parity

violation to accurately determine the neutron

radius in 208Pb. This has broad applications to

astrophysics, nuclear structure, atomic parity non-

conservation and tests of the standard model. The

conference will begin with introductory lectures

and we encourage new comers to attend.

For more information contact [email protected]

Topics

Parity Violation

Theoretical descriptions of neutron-rich nuclei and

bulk matter

Laboratory measurements of neutron-rich nuclei

and bulk matter

Neutron-rich matter in Compact Stars / Astrophysics

Website: http://conferences.jlab.org/PREX

First purely electroweak (clean!) measurement of Rn(208Pb)

Uses parity violation as Z0 couples preferentially to neutrons[Donnelly, Dubach, Sick, NPA 503, 589 (1989)]

up-quark down-quark proton neutronγ-coupling +2/3 −1/3 +1 0Z0-coupling ≈ +1/3 ≈ −2/3 ≈ 0 −1

gv =2tz − 4Q sin2 θW≈2tz−Q

A Physics case for PREX-II, CREX, and beyond!


The Electric Dipole Polarizability in 208PbRCNP: A. Tamii et al., PRL 107, 062502 (2011)

IVGDR: Coherent oscillations of protons against neutronsNuclear symmetry energy as the restoring forceRCNP: polarized proton inelastic scattering at very forward anglesCross sections at very small angles arise purely from CoulExHigh-resolution exp. in excellent agreement with photo-absorption dataAccurate measurement of E1 polarizability: αD =(20.1±0.6) fm3

E1 polarizability as a complement to R208skin

0.16 0.18 0.2 0.22 0.24 0.26rskin[208Pb] (fm)

18

19

20

21

22D[20

8 Pb] (

fm3 )

rskin /2

CAB=0.911

rminskin=0.015 fm

RCNP

FSUGold

0.12 0.16 0.2 0.24 0.28 0.32rskin[208Pb](fm)

18

19

20

21

22

23

24

25

26

_D[20

8 Pb](f

m3 )

PREX-IIS-PREX

NL3/FSUDD-MESkyrmeSkyrme (SV)

RCNP

CABmodels =0.769


Proton, Neutron, Charge, and Weak-Charge Densities

Charge densities known with exquisite accuracy (Hofstadter Nobel Prize 1961)R48

ch =3.4771(20)fm and R208ch =5.5012(13)fm

Neutron (Weak) densities are as fundamental as proton densities, yet ...R48

wk =3.68(3)fm and R208wk =5.75(6)fm

Charge and Weak-Charge Form Factors: [G p,nwk ≈−G n,p

ch ]

F (q)=GE (q2)FV (q) +

(GM(q2)−GE (q2)

1 + τ

)[τFV (q) +

q2M

FT (q)

]︸︷︷︸

spin-orbit contribution

0 2 4 6 8 10r (fm)

0.00

0.02

0.04

0.06

0.08

0.10

l(fm

-3)

ExperimentNL3 (5.740)FSU (5.676)IU-FSU (5.592)

208Pb

charge

neutron

0 2 4 6r (fm)

0.00

0.02

0.04

0.06

0.08

0.10

l(fm

-3)

NL3(3.583)FSU(3.559)IUFSU(3.542)

neutron

proton

48Ca

if7/2

B/A=8.667MeVSn=9.950MeVRp=3.362fm

Rn(fm)

0 2 4 6r (fm)

0.00

0.02

0.04

0.06

0.08

0.10

l(fm

-3)

NL3(0.275)FSU(0.247)IUFSU(0.222)

-weak-chargecharge

48Ca weak-skin(fm)


Nuclear Structure, Error Bars, and Correlations: StatisticalReinhard-Nazarewicz, PRC81 (2010) 051303(R) Fattoyev-Piekarewicz, PRC86 (2012) 015802; PRC84 (2011) 064302

Empirical constants determined from optimization of a quality measure

χ2(p) =N∑

n=1

(O(th)

n (p)−O(exp)n

∆On

)2

= χ2(p0) + xT Σ̂−1 x + . . .

Predictions accompanied by meaningful theoretical errorsCovariance analysis least biased approach to uncover correlations

Cov(A,B) = ∂i A Σ̂ij ∂j B ; Corr(A,B) =Cov(A,B)√Var(A)Var(B)

Isovector sector constrained mostly from “pseudo data”

0 0.2 0.4 0.6 0.8 1|correlation| with Fw(48Ca)

RMF-

FSU

(sim

ilar t

o SH

F SV

-min

)Rn(132Sn)Rn(208Pb)rskin(208Pb)rskin(48Ca)_D(208Pb)

Rw(48Ca)

LJ

Rn(48Ca)

PPNM

room

for i

mpr

ovem

ent

5.6 5.64 5.68 5.72 5.76Rn[208Pb] (fm)

3.52

3.54

3.56

3.58

3.6

R n[48

Ca] (

fm)

CREX

PREX-II ±0.06 fm

±0.0

3fmCAB=0.952

FSUGold


Nuclear Structure, Error Bars, and Correlations: SystematicJP et al., PRC85 (2012) 041302 Horowitz-Piekarewicz, PRC86 (2012) 045503

Assess systematic errors by comparing 48 accurately calibrated EDFsEach model incorporates its own prejudices and theoretical biases

Correlation between Rn[208Pb] and Rn[132Sn] remains very strongCorrelation between Rn[208Pb] and Rn[48Ca] weakens significantly48Ca is a smaller nucleus than 208Pb and thus strongly affected by surface/shell effects

Weak-skin of 48Ca strongly affected by spin-orbit correctionsProvides new insights into an unexplored “tensor” form factor

Together PREX-II and CREX provide powerful and stringent constraints!

0.12 0.16 0.20 0.24 0.28 0.32rskin[208Pb](fm)

0.16

0.2

0.24

0.28

0.32

0.36

r skin

[132 Sn

](fm

)


CABmodels=0.997

PREX

PREX-II

0.12 0.16 0.20 0.24 0.28 0.32rskin[208Pb](fm)

0.12

0.16

0.2

0.24

0.28

0.32r sk

in[48

Ca](

fm)

Neutron Skin

Weak Skin (sp

in orbit)

6rskinCa =0.14fm

6rskinPb =0.16fm

CABmodels=0.852

0.05

fm


0.12 0.16 0.20 0.24 0.28 0.32rskin[208Pb](fm)

0.12

0.16

0.2

0.24

0.28

0.32

r skin

[48Ca

](fm

)

PREX-II

CREX


CABmodels=0.852


A Last Word on Errors and CorrelationsP.-G. Reinhard et al., in preparation

Correlation between Rn and Fwk as a function of qOther than at the diffraction minima, correlation remains strong

A theorist dream: a second q pointNeed two q-points to resolve radius and diffuseness

Correlation between Rn and Fwk as a function of q sensitive to s-quarkSensitivity develops due to error in r2

s even though r2s '0

0 0.4 0.8 1.2 1.6q(fm-1)

0

0.2

0.4

0.6

0.8

1

F wk(q)

48Ca [0.207(6)]208Pb[0.223(6)]

FSUGold

6Fw×10

qPREX

qCREX

0.4 0.8 1.2 1.6q(fm-1)

0.6

0.7

0.8

0.9

1|Co

rrel(R

n,Fwk)| qPREX

qCREX

48Ca208Pb

FSUGold


PREX-II and CREX as Anchors for FRIB Physics“One of the main science drivers of FRIB is the study of nuclei with neutron skins 3-4 times thicker than is currently possible.FRIB will provide rare isotopes to explore the properties of halos and skins. JLab uses parity violation to measure the neutronradius of stable lead and calcium nuclei. Studies of neutron skins at JLab and FRIB will help pin down the behavior of nuclearmatter at densities below twice typical nuclear density” 2013 Subcommittee Report to NSAC

The Traditional Approach: Proton-Nucleus ScatteringFRIB will scatter protons from radioactive nuclei in inverse kinematicsLarge and uncontrolled uncertainties in the reaction mechanismEnormous ambiguities yield an energy dependent neutron skinFRIB must use PREX-II and CREX as calibrating anchors!


Conclusions and OutlookStatistical/systematic analyses validate “CREX after PREX”Covariance analysis uncover correlations among observables anddictate the required accuracy of laboratory experimentsSystematics suggest a “mild” correlation between R48

n and R208n

suggesting they provide complementary informationElectroweak measurements of neutron skins should serve asanchors for future hadronic experiments at FRIB-type facilitiesA three-legged “isovector” stool: Rn[48Ca],Rn[208Pb], αD[208Pb]

The combination of precise data on dipole polarizability andneutron skins will provide stringent constraints on nuclearstructure models (from W. Nazarewicz talk)Accurate measurements of neutron radii will continue to playa fundamental role in elucidating the fascinating physics ofneutron-rich systems in both heaven and earth!


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