Nuclear charge and neutron radii and nuclear matter: correlation analysis

Transcription

1 Nuclear charge and neutron radii and nuclear matter: correlation analysis Witold Nazarewicz (FRIB/MSU) INT Program INT-16-2a: Bayesian Methods in Nuclear Physics June 13 - July 8, 2016 Perspective Correlation analysis and model mixing (intra- and inter-model correlations) Proton-, neutron radii, skins, and nuclear matter properties Conclusions

2 Classification of theories (according to Alexander I. Kitaigorodskii) A third rate theory explains after the event (postdictive, retrodictive) A second rate theory forbids A first rate theory predicts (predictive) UQ is crucial to make this assessment

3 How to explain the nuclear landscape from the bottom up? Theory roadmap The resolving power of a theoretical model should always be as low as reasonably possible for the question at hand

4 J. Phys. G 43, (2016) Theory Prediction Observation Experiment Today's posterior is tomorrow's prior

5 Consider a model described by coupling constants θ ={θ 1, θ 2 θ κ ). Any predicted expecta8on value of an observable Y i is a func8on of these parameters. Since the number of parameters is much smaller than the number of observables, there must exist correla8ons between computed quan88es. Moreover, since the model space has been op8mized to a limited set of observables, there may also exist correla8ons between model parameters. Objec8ve func8on Model predic8ons Expected uncertain8es fit- observables (may include pseudo- data)

6 How to quantify inter-model correlations? Low-resolution models High-resolution models Y G Y α Y Parameter estimation. The set of fit-observables

7 =y 1 Example of inter-model correlation analysis (1) J. Piekarewicz et al., Phys. Rev. C 85, (R) (2012) D [ 208 Pb] Model CAB model Slope Intercept Skyrme DD-ME NL3/FSU D [ 208 Pb] (fm 3 ) r skin [ 208 Pb] (fm) =y 2 Purpose: Determine the new global relation/law Determine unknown y 2 given measured y 1 Learn about constraints on models

8 Example of inter-model correlation analysis (2) G. Hagen et al., Nature Physics 12, 186 (2016) =y R p (fmd a b c R skin (fmd =y R n (fmd=y α D (fm n 3 D=y 4

9 θ 1 (SM) θ (SM) θ 3 (SM) please help! Talk by Bulaevskaya θ 2 (SM)

10 Beware of spurious correla8ons! hlp:// correla8ons C= C=0.9668

11 Naïve nuclear theorist s approach to a systematic (model) error estimate: Take a set of reasonable models M i Make a prediction E(y;M i ) Compute average and variation within this set Compute rms deviation from existing experimental data. If the number of fit-observables is large, statistical error is small and the error is predominantly systematic.

12 UNEDF2 functional Phys. Rev. C 89, (2014) 12 parameters Masses (sph) Radii OES FI spe Masses (def)

13 Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements, J. McDonnell et al., Phys. Rev. Lett. 114, (2015). Pilot Study Applied to UNEDF1 Massively Parallel Approach 130 data points (including deformed nuclei) Gaussian process response surface 200 Test Parameter Sets La8n hyper- rectangle UNEDF1 UNEDF1 CPT No improvement on model s predictibility except for postdictions on additional data

14 How to assess systematic trends? θ 1 (SM) θ (SM) θ 3 (SM) θ 2 (SM) Optimize model M. This provides E(y), var(y). Vary variable y in a reasonable range given by var(y). Refit θ for each value of y. Study E(y i y). Example: SV-bas, PRC (2009)

15 Radii in nuclear DFT S. Mizutori et al., Phys. Rev. C 61, (2000) neutron density (fm 3 ) Sn RHB/NL3 q F(q) N= 70 N=100 N= radius r (fm) momentum q (fm 1 ) first zero of F(q)

16 Neutron & proton density distribu8ons 0.10 Diffuseness Density (fm -3 ) (n) (p) 150 Sn Skin Radius (fm)

17 Finite size effects and leptodermous expansion Phys. Rev. C 73, (2006) residual shell effects Wigner-Seitz radius around 1fm

18 Neutron-skin uncertainties of Skyrme EDF M. Kortelainen et al., Phys. Rev. C 88, (2013) stat Δr skin (fm) r skin (fm) Ca SV-min UNEDF0 (a) (b) Zr Er Z= (c) (e) (g) (d) (f) (h) neutron number σ 2 (10-3 fm 2 ) rskin a sym L remaining C ρδρ 1 left bars: UNEDF0 right bars: SV-min A

19 Nuclear charge and neutron radii and nuclear matter: trend analysis in Skyrme-DFT approach P.-G. Reinhard and WN, PRC 93, (R) (2016) 14-parameter model, optimized to 2 different sets of fit-observables (Y=E, R) (Y=E) stiff stiff sloppy sloppy sloppy

20 Nuclear charge and neutron radii, and nuclear matter: intra-model trend analysis P.-G. Reinhard and WN, PRC (R) (2016) σ ch r ch r n r skin α D L J E GDR κ TRK E GQR m*/m E GMR K ρ 0 E/A E/A ρ 0 K E GMR m*/m SV-E E GQR κ TRK E GDR J L SV-min α D r ch σ ch r n r skin

21 (a) 3.54 (b) r ch (fm) ρ 0 κ TRK K J m*/m L SV-min SV-min 298 Fl r ch (fm) Ca r n (fm) r n (fm)

22 protons neutrons rrms rrms,0 (fm) (a) Fl (d) Pb (e) Ca (f) (b) 208 (c) ρ0 (fm ) 2000 Gaussian samples of L(θ) L (MeV) 15 20

23 (a) (d) Fl r skin (fm) (b) 208 Pb (e) 0.16 (c) (f) Ca J (MeV) L (MeV)

24 Δr skin (10-3 fm) Δr rms,n (10-3 fm) (c) (d) Δr rms,ch (10-3 fm) Fl 208 Pb 48 Ca (e) 0 SV-E fix L fix ρ 0 fix ρ 0 +L fix J fix ρ 0 +J 0 SV-E fix L fix ρ 0 fix ρ 0 +L fix J fix ρ 0 +J

25 We explored various trends of charge and neutron radii with nuclear matter properties. There exist, at least within the Skyrme-DFT theory, only two strong correlations: o one-to-one relation between charge radii in finite nuclei and ρ 0 : r p ρ 0 o one-to-one relation between neutron skins in finite nuclei and L: r skin L By including charge radii in a set of fit-observables, as done for the majority of realistic Skyrme EDFs, one practically fixes the saturation density. The relation r n ρ 0 is much weaker than that for r p, so by constraining the saturation density alone does not help significantly reducing the uncertainty on neutron (and mass) radii. However: r n =r p +r skin The r n r p relation is fairly complex: various trends are possible when moving along a trajectory in a parameter space.

26 N2LO sat describes low- energy NN and Nuclei A. Ekström et al. Phys. Rev. C 91, (R) (2015) Order- by- order op8miza8on Constrained by data on few- body systems and light nuclei Coupled Cluster informing DFT and DFT informing Coupled Cluster