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Why CREX After PREX? Witold Nazarewicz (UTK/ORNL) Calcium Radius Experiment (CREX) Workshop at Jefferson Lab, Mar , 2013 Main contributors: Jochen Erler Chuck Horowitz Jorge Piekarewicz Paul-Gerhard Reinhard + Milano, Zagreb, Kolkata groups +UNEDF/NUCLEI

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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 48 Ca as good “piece of nuclear matter” as 208 Pb? Density Functional Theory expectations Neutron star relevance o Yes, there is some, but… Systematic trends o … and uncertainties Bottom line: why CREX

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48 Ca 208 Pb 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

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Interfaces provide crucial clues Interfaces provide crucial clues dimension of the problem

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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, (2012) Three-body forces and shell structure in calcium isotopes J.D. Holt et al., J.Phys.G 39, (2012)

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Ab-initio description of Calcium isotopes G. Hagen et al., Phys. Rev. Lett. 109, (2012) RIKEN

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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, (R) (2013) Neutron matter EOS including NN, 3N and 4N EFT forces at N3LO I. Tews et al. Phys. Rev. Lett. 110, (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.

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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, (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 I 2 … Liquid-Drop Expansion O(0)O(1) O(2)

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

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Quantities of interest… bulk equilibrium symmetry energy at surface density slope of binding energy of neutron matter dipole polarizability Information content of a new observable P.G. Reinhard and WN, Phys. Rev. C 81, (R) (2010)

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Good isovector indicators Good isovector indicators Poor isovector indicators Poor isovector indicators more in talk by Jorge Piekarewicz

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F.J.Fattoyev et al., Phys.Rev. C 86, (2012) M. Kortelainen et al., Phys. Rev. C 82, (2010) Phys.Rev. C 85, (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, (2008) J. Toivanen et al., Phys. Rev. C 78, (2008) P. Klüpfel et al., Phys. Rev. C 79, (2009) U. Lombardo, Prog.Theor.Phys.(Kyoto), Suppl. 196, 39 (2012) Lots of action on a DFT front

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Erler et al. Nature 486, 509 (2012) Surface (shell) effects very large in 48 Ca Isovector properties not fully controlled Important insights from ab-initio theory

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Gandolfi et al. PRC85, (2012)

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Erler et al., arXiv: (2012)

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PREX: Tamii et al.: Theory: E1 polarizability provides excellent constaint J. Piekarewicz et al., Phys. Rev. C 85, (R) (2012)

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J. Piekarewicz et al., Phys. Rev. C 85, (R) (2012). P.G. Reinhard et al., in preparation (2013)

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P.G. Reinhard et al., in preparation (2013) the large span of predictions for 48 Ca r skin =(0.168 ± 0.022) fm in 208 Pb

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J. Piekarewicz et al., Phys. Rev. C 85, (R) (2012) r skin =(0.168 ± 0.022) fm in 208 Pb r skin =(0.176 ± 0.018) fm in 48 Ca Mammei (Sunday): r skin = ± 0.06 fm in 208 Pb r skin = ± 0.03 fm in 48 Ca Projected uncertainties 2013

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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 48 Ca offer stronger model dependence than the corresponding 208 Pb data; hence, they provide tighter constraints. 48 Ca can be computed with ab-initio approaches and with DFT. 48 Ca 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. 48 Ca is affected by surface/shell effects more dramatically than 208 Pb. 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.

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