EoS constraints from a model-independent approach Francesca - - PowerPoint PPT Presentation

Francesca Gulminelli, Debarati Chatterjee - LPC Caen Jerome Margueron – IPNL Adriana Raduta – IFIN

EoS constraints from a model-independent approach

EoS and empirical constraints

• E
• S c a n b e

c ha ra c te rize d b y e mpiric a l pa ra me te rs

/ e x:J,L

,…

• DF

T mo de ls c o rre spo nding to diffe re nt E

• S a re

c o mpa re d to e xp.da ta

• ∆ de te rmine d

fitting the mo de l to the da ta

• Co rre la tio ns a mo ng

a re typic a lly o b se rve d

M.Fortin et al, PRC 94,035804

Problems

• Nuc le i a re no t simply

dro ple ts o f nuc le a r ma tte r! E ne rg y func tio na ls c o nta in ma ny te rms

=> Unc e rta inty in g ra die nt c o upling s g e ts mixe d up with unc e rta inty in Pk

• Phe no func tio na ls

c o nta in spurio us c o rre la tio ns a mo ng e mp.pa ra me te rs

=> re sults a re mo de l de pe nde nt

C.Ducoin et al PRC 2011

Problems

• Nuc le i a re no t simply

dro ple ts o f nuc le a r ma tte r! E ne rg y func tio na ls c o nta in ma ny te rms

=> Unc e rta inty in g ra die nt c o upling s g e ts mixe d up with unc e rta inty in Xn

• Phe no func tio na ls

c o nta in spurio us c o rre la tio ns a mo ng e mp.pa ra me te rs

 re sults a re mo de l de pe nde nt

C.Ducoin et al PRC 2011

A model independent approach

• Nuc le i a re no t simply

dro ple ts o f nuc le a r ma tte r! E ne rg y func tio na ls c o nta in ma ny te rms

=> Unc e rta inty in g ra die nt c o upling s g e ts mixe d up with unc e rta inty in Pk

• Phe no func tio na ls

c o nta in spurio us c o rre la tio ns a mo ng e mp.pa ra me te rs

=> re sults a re mo de l de pe nde nt

A single effective isoscalar gradient term to be fitted on nuclear masses , Taylor expansion around n0 , 1 !

• 3
• /

Steiner, Lattimer, Brown ApJ722(2010)33

HNM: Quality of the Taylor expansion

Chiral EFT

I.Tews, T.Kruger,K.Hebeler,A.Schwenk PRL110(2013)032504

Sly5

E.Chabanat, P.Bonche, P.Hansel, J.Meyer, R.Schaeffer, NPA627(1997)710

Symmetry energy

Present uncertainty on Pk: prior distribution

HNM: Constraints from neutron star physics

• Ca usa lity: 0
• NS sta b ility: 0 fo r in -e q uilib rium
• Mma x>2Mo
• L

imit o n DURCA:

• No DURCA up to 2Mo – DURCA0
• DURCA o nly fo r M>1.8Mo – DURCA1
• DURCA o nly fo r M>1.6Mo – DURCA2

Results

Finite nuclei

• Nuc le i a re no t simply

dro ple ts o f nuc le a r ma tte r! E ne rg y func tio na ls c o nta in ma ny te rms

=> Unc e rta inty in g ra die nt c o upling s g e ts mixe d up with unc e rta inty in Pk

A single effective isoscalar gradient term to be fitted on nuclear masses , Observables from -ETF with parametrized density profiles

• 1
• Analytical integration of the

Fermi integrals

F.Aymard et al., J.Phys.G43,045105(2016)

Calibrating the gradient term

• ,

, N= Z ∆ C 20 Optimized C Sly4

• Residual deviations are

due to the semi- classical approximation

Semi-magic isotopic chains

(N-Z)/ A + Z= 2 0 Z= 2 8 Z= 5 0 Z= 8 2

Exploring the parameter space

Average binding-energy deviation Average binding-energy deviation

Results: radii

• Afte r filte r; c uto ff=0.2 Me V

Exp data

Results: n-skin

Results: correlations

∗

∆

∗

∆

∗

∆

Conclusions

• Co nstra ints o n E
• S e mpiric a l pa ra me te rs ne e d b o th NS

physic s a nd la b o ra to ry e xpe rime nts

• We pro po se a n e mpiric a l E
• S a vo iding spurio us

c o nstra ints fro m the e ne rg y de nsity func tio na l fo rm

• F

inite nuc le i o b se rva b le s fro m E T F with a sing le g ra die nt te rm fixe d fro m nuc le a r ma ss

• Ba ye sia n de te rmina tio n o f pa ra me te rs with fla t o r

g a ussia n prio r

• T

hird orde r de riva tive s still la rg e ly unc onstra ine d

• SKIN CORRE

L AT E D T O L

• AL

MOST NO CORRE L AT ION AMONG E MP.PARAME T E RS