Many-body theory of Nuclear Matterand the Hyperon matter puzzle
M. Baldo, INFN Catania
Many-body theory of Nuclear matter ( “old” stuff )
Can we reproduce all data extracted from phenomenology ?
OUTLOOK
The strangeness puzzle
Constraints on the “exotic” components
Ladder diagrams for the scattering G-matrix
Ge
QVVG
Two and three hole-line diagrams in terms of the Brueckner G-matrixs
The BBG expansion
The ladder series for the three-particlescattering matrix
A
Akkk kk
h
kkGkke
kkkXXTkkke
kkGkk
E
Te
QGXGT
212''1
3213321
2]'''[
121
3
33
3
||'''
1''''||''
1
''||2
1
321
F
F
kkkkk
kkkk
'','',','
,,
2121
321
Three hole-line contribution
Evidence of convergenceThe three hole-line contribution is small
in the continuous choice
Symmetric nuclear matter
Neutron matter
Using different prescription s for the auxiliary potential.
Neutron matter
Microscopic EOS of symmetric and neutron matterIntroducing three-body forces
EOS from BBG
EOS of Akmal & Pandharipande
M.B. & C. Maieron, PRC 77, 015801 (2008)
A. Gezerlis and J. Carlson, Pnys. Rev. C 77,032801 (2008)Quantum Monte Carlo calculation
Neutron matter at very low density
M.B. & C. Maieron, PRC 77, 015801 (2008)
QMC
Developing a density functionalfrom nuclear matter to finitenuclei following Khon-Sham
scheme.M.B., P.Schuck and X. Vinas,
PLB 663, 390 (2008)
arXiv:1210.1321
Average deviation for thetotal binding energy
d(E) = 1.58 MeV
Competitive with the bestdensity functional s
Up to saturation density
The parameters L and Ksym characterize the density dependence of the symmetry energy around the saturation point
1313
Around saturation point ρ0 for symmetric matter, the binding energy is usually expanded as
Saturation pointDensity = 0.17 +/- 0.03 fm-3 Energy/part = -16. +/- 1. MeV
Symmetry energy
Boundaries by P. Danielewicz 2012, from IAS analysis
213 230 +/- 30
31.9 30 +/- 35
-96.75 -200 --- 150
52.96 55 +/- 25
Theory Phen.
Nuclear matter physical parameters near saturation
FURTHER CONSTRAINTSAROUND SATURATION
M. Dutra et al. , PRC85, 035201 (2012)M.B. Tsang et al., PRC86, 015803 (2012)
Kortelainen et al., PRC 2010
Chen et al., PRC 2010 Piekarewicz et al.,
1201.3807 Trippa et al., PRC2008 Tsang et al., PRL2009
Steiner et al., ApJ2010
Lattimer & Lim, arXiv:1203.4286
Getting S and L
HIGHER DENSITYCONSTRAINTS FROM HEAVY ION REACTIONS
K+
Flow
K+ : Lynch et al. , Prog. Part. Nucl. Phys. 62, 427 (2009)
Flow : Danielewicz et al. , Science 298, 1592 (2002)
EOS
Andrew A. Steiner et al., ApJ 722, 33 (2010)
Inference from 6 NS data on X-ray bursts or transients
Boundaries to the eos from astrophysical observations
Together with heavy-ion contraints it is tested the symmetry energy at high density
DU process test
……………..
QPO
Cooling
Other EOS tests, T. Klahn et al., PRC, 035802 (2006)
Superluminal speed of sound
PSR J1614-2230
Maximum Mass constraint
If neutron stars are assumed to be composed only of neutrons, protons
and electrons/muons, there is at least one microscopic EOS that is compatible
with phenomenological constraints andit is able to produce a maximum
mass of about two solar masses.Remind that for a free neutron gas
the maximum mass is 0.7 solar mass !(Volkoff-Openheimer)
No “exotic” component is needed !BUT …….
Looking at the chemical potentials of neutrons , protons and hyperons
np
ep
n
pn
e
epn
2
Nijmegen soft core potentialfor hyperon-nucleon interaction
PRC 58, 3688 (1998)
PRC 61, 055801 (2000), M.B., G. Burgio and H. Schulze
Nijmegen potential for NY interaction, no YY interaction
Free hyperons
N-Y interactionincluded
Softening of the EOS
The N-Y interaction produces a slightly repulsive effect on the EOS
The huge softening is mainly due to the presence
of additonal degrees of freedom
Drastic decrease of the maximum mass if Hyperons interact according to standard
potential s tuned at saturation
Other 3BF and BHF variantsCompensation effects between stiffness
and Hyperon fraction
Including Quark matter
Since we have no theory which describes both confined and deconfined phases, one has to use two separate EOS for baryon and quark matter and look at the crossing in the P-chemical potential plane
Try Quark matter EOS. MIT bag model Nambu-Jona Lasinio Coloror dielectric model FCM model Dyson-Schwinger model
Summarizing the quark matter effect
The MIT bag model, CDM, NJL, FCM, DS models produce a maximum mass not
larger than 1.7 solar mass. They cannot be considered compatible with the
“observed” NS maximum mass. Even if we exlude strange matter .
WAY OUT ?1. Some additional repulsion is presentfor BOTH hyperons and quark matter
that prevents the appearence of “exotic” components in the core.
2. The EOS for hyperon and/or quark matter mimics the EOS of nucleonic
matter
From astrophysical observations we have learnedsome fundamental properties of high density EOS
HOWEVER ………
Aaaaah !
3030
2.7 !!!!