Why CREX After PREX?

Witold Nazarewicz (UTK/ORNL)

Calcium Radius Experiment (CREX) Workshop at Jefferson Lab, Mar. 17-19, 2013

Main contributors:

Jochen Erler

Chuck Horowitz

Jorge Piekarewicz

Paul-Gerhard Reinhard

+ Milano, Zagreb, Kolkata groups

+UNEDF/NUCLEI

OUTLINE

• General principles

o Theoretical strategies

• Ab initio theory and 3N forces

o T=1/2 and T=3/2 channels

• Leptodermous expansion

o Is 48Ca as good “piece of nuclear matter” as 208Pb?

• Density Functional Theory expectations

• Neutron star relevance

o Yes, there is some, but…

• Systematic trends

o … and uncertainties

• Bottom line: why CREX

48Ca

208Pb

n

Physics of nuclei is demanding

Input

Forces, operators

• rooted in QCD

• insights from Density Functional Theory

• many-body interactions

• in-medium renormalization

• low-energy coupling constants optimized to data

• crucial insights from exotic nuclei

Many-body

dynamics

• many-body techniques

o direct ab-initio schemes

o symmetry-based truncations

o symmetry breaking and restoration

• high-performance computing

Open

channels

nuclear structure impacted by couplings to

reaction and decay channels

Interfaces provide

crucial clues

dimension of the problem

H.-W. Hammer, A. Nogga, A. Schwenk

Three-body forces: From cold atoms to nuclei, Rev. Mod. Phys. 85, 197 (2013)

A.T. Gallant et al.,

Phys. Rev. Lett. 109, 032506 (2012)

Three-body forces and shell structure in calcium isotopes

J.D. Holt et al.,

J.Phys.G 39, 085111 (2012)

Ab-initio description of Calcium isotopes

G. Hagen et al., Phys. Rev. Lett. 109, 032502 (2012)

RIKEN

500 MeV N3LO NN potential combined with N2LO 3NF

Neutron matter based on SRG-evolved chiral three-nucleon

interactions

K. Hebeler and R. J. Furnstahl

Phys. Rev. C 87, 031302(R) (2013)

Neutron matter EOS including NN, 3N and 4N cEFT forces at

N3LO

I. Tews et al.

Phys. Rev. Lett. 110, 032504 (2013)

The counting of triples seems to work only in very light nuclei…Local density estimates based on

infinite matter suggest a ratio of three-body to two-body scaling proportional to the first power of

the density.

From Finite Nuclei to the Nuclear Liquid Drop

Leptodermous Expansion Based on the Self-consistent Theory

P.G. Reinhard et al., Phys. Rev. C 73, 014309 (2006)

The limitations of applying the leptodermous expansion for finite nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very

precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.

We expand the smooth energy in terms of 1/R and I2…

Liquid-Drop Expansion

O(0) O(1) O(2)

asurf

300 12510008000

Conclusion: Properties of 48Ca are dramatically affected by surface effects

Quantities of interest…

bulk equilibrium

symmetry energy

symmetry energy

at surface density

slope of binding energy

of neutron matter

dipole polarizability

neutron skin

Information content of a new observable

P.G. Reinhard and WN, Phys. Rev. C 81, 051303 (R) (2010)

Good isovector

indicators

Poor isovector

indicators

more in talk by Jorge Piekarewicz

F.J.Fattoyev et al., Phys.Rev. C 86, 025804 (2012)

M. Kortelainen et al.,

Phys. Rev. C 82, 024313 (2010)

Phys.Rev. C 85, 024304 (2012)

Early attempts to employ statistical methods of linear-regression and error analysis have been revived recently and been applied to determine the correlations

between model parameters, parameter uncertainties, and the errors of calculated observables. This is essential for providing predictive capability and extrapolability,

and estimate the theoretical uncertainties.

M. Kortelainen et al., Phys. Rev. C 77, 064307 (2008)

J. Toivanen et al., Phys. Rev. C 78, 034306 (2008)

P. Klüpfel et al., Phys. Rev. C 79, 034310 (2009)

U. Lombardo, Prog.Theor.Phys.(Kyoto), Suppl. 196, 39 (2012)

Lots of action on a DFT front

Erler et al. Nature 486, 509 (2012)

• Surface (shell) effects very large in 48Ca

• Isovector properties not fully controlled

• Important insights from ab-initio theory

Gandolfi et al. PRC85, 032801 (2012)

Erler et al., arXiv:1211.6292 (2012)

PREX:

Tamii et al.:

Theory:

E1 polarizability provides excellent constaint

J. Piekarewicz et al., Phys. Rev. C 85, 041302(R) (2012)

J. Piekarewicz et al.,

Phys. Rev. C 85, 041302(R) (2012).

P.G. Reinhard et al.,

in preparation (2013)

P.G. Reinhard et al., in preparation (2013)

the large span of predictions for 48Ca

rskin

=(0.168 ± 0.022) fm in 208Pb

J. Piekarewicz et al.,

Phys. Rev. C 85, 041302(R) (2012)

rskin

=(0.168 ± 0.022) fm in 208Pb

rskin

=(0.176 ± 0.018) fm in 48Ca

Mammei (Sunday):

Drskin

= ± 0.06 fm in 208Pb

Drskin

= ± 0.03 fm in 48Ca

Projected uncertainties

2013

Summary: Why CREX after PREX?

• Precise PREX-II data needed to clarify the situation after PREX. (If the mean value of PREX for neutron skin is

correct, there is something basically wrong with our current models of nuclei).

• The isovector data for 48Ca offer stronger model dependence than the corresponding 208Pb data; hence,

they provide tighter constraints.

• 48Ca can be computed with ab-initio approaches and with DFT.

• 48Ca data can provide a test of 3N forces (T=3/2 and T=1/2), which are important for the neutron matter EOS;

hence, neutron star physics.

• The combination of precise data on dipole polarizability and neutron skin will provide stringent constraints on

nuclear structure models.

• 48Ca is affected by surface/shell effects more dramatically than 208Pb. Therefore, the main motivation is in nuclear structure.

Astrophysical motivation is secondary, mainly related to 3N forces and/or gradient terms.

• Lots of activities worldwide on optimization/quantification of nuclear models.