EoS constraints from a model-independent approach Francesca Gulminelli, Debarati Chatterjee - LPC Caen Jerome Margueron – IPNL Adriana Raduta – IFIN
EoS and empirical constraints • E o 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 o 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 P k • 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 X n • 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 A single effective isoscalar ma tte r! E ne rg y gradient term func tio na ls c o nta in to be fitted on nuclear masses � �, � � � �� � � �� � 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 P k � � � � � � � /� • Phe no func tio na ls Taylor expansion around n 0 c o nta in spurio us � � �� �, � � � 1 � � � � �� � � � �� � � �! � � c o rre la tio ns a mo ng 3� � � e mp.pa ra me te rs Steiner, Lattimer, Brown ApJ722(2010)33 => re sults a re mo de l de pe nde nt
HNM: Quality of the Taylor expansion Sly5 E.Chabanat, P.Bonche, P.Hansel, J.Meyer, R.Schaeffer, NPA627(1997)710 Chiral EFT I.Tews, T.Kruger,K.Hebeler,A.Schwenk PRL110(2013)032504
Symmetry energy
Present uncertainty on P k : prior distribution
HNM: Constraints from neutron star physics Ca usa lity: 0 � � � � � • NS sta b ility: �� � 0 fo r � � � � in � -e q uilib rium • • � ��� � 0 • M ma x >2M o • L imit o n DURCA: No DURCA up to 2M o – DURCA0 o DURCA o nly fo r M>1.8M o – DURCA1 o DURCA o nly fo r M>1.6M o – DURCA2 o
Results
Finite nuclei • Nuc le i a re no t simply dro ple ts o f nuc le a r A single effective isoscalar ma tte r! E ne rg y gradient term to be fitted on nuclear masses func tio na ls c o nta in � �, � � � �� � � �� � ma ny te rms Observables from � � -ETF with => Unc e rta inty in g ra die nt parametrized density profiles c o upling s g e ts mixe d up with � �� unc e rta inty in P k � � � � ��� � � � 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 + Z= 2 0 Z= 2 8 Z= 5 0 Z= 8 2 (N-Z)/ A
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 o 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 o 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
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