Transcript Diapositiva 1

Many-body theory of Nuclear Matter
and the Hyperon matter puzzle
M. Baldo, INFN Catania
OUTLOOK
Many-body theory of Nuclear matter ( “old” stuff )
Can we reproduce all data extracted from
phenomenology ?
The strangeness puzzle
Constraints on the “exotic” components
Ladder diagrams for the scattering G-matrix
Q
G  V V G
e
The BBG expansion
Two and three hole-line diagrams in terms
of the Brueckner G-matrixs
The ladder series for the three-particle
scattering matrix
Q3
T3  G  GX
T3
e
E3h 
1
 k1k 2 | G | k1 'k 2 '  A


2 k1k 2 k3 [ k 'k '']
1
1
 k1 ' k 2 ' k3 | XT3 X | k1 ' ' k 2 ' ' k3 
e
e'
 k1'' k 2 ' ' | G | k1k 2  A
k1, k2 , k3  kF
k1 ' , k2 ' , k1 ' ' , k2 ' '  kF
Three hole-line contribution
Symmetric nuclear matter
Evidence of convergence
The three hole-line contribution is small
in the continuous choice
Using different prescription s for the auxiliary potential.
Neutron matter
Neutron matter
Microscopic EOS of symmetric and neutron matter
Introducing three-body forces
EOS from BBG
EOS of Akmal & Pandharipande
Neutron matter at very low density
M.B. & C. Maieron, PRC 77, 015801 (2008)
A. Gezerlis and J. Carlson, Pnys. Rev. C 77,032801 (2008)
Quantum Monte Carlo calculation
QMC
M.B. & C. Maieron, PRC 77, 015801 (2008)
Up to saturation density
Developing a density functional
from nuclear matter to finite
nuclei following Khon-Sham
scheme.
M.B., P.Schuck and X. Vinas,
PLB 663, 390 (2008)
arXiv:1210.1321
Average deviation for the
total binding energy
d(E) = 1.58 MeV
Competitive with the best
density functional s
Saturation point
Density = 0.17 +/- 0.03 fm-3
Energy/part = -16. +/- 1. MeV
Around saturation point ρ0 for symmetric matter, the
binding energy is usually expanded as
The parameters L and Ksym characterize the density dependence
of the symmetry energy around the saturation point
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Symmetry energy
Boundaries by P. Danielewicz 2012, from IAS analysis
FURTHER CONSTRAINTS
AROUND SATURATION
Theory
213
Phen.
230 +/- 30
31.9
30 +/- 35
52.96
55 +/- 25
-96.75
-200 --- 150
Nuclear matter physical parameters near saturation
M. Dutra et al. , PRC85, 035201 (2012)
M.B. Tsang et al., PRC86, 015803 (2012)
Getting S and L
 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
HIGHER DENSITY
CONSTRAINTS FROM HEAVY ION REACTIONS
EOS
Flow
K+
K+ : Lynch et al. , Prog. Part. Nucl. Phys. 62, 427 (2009)
Flow : Danielewicz et al. , Science 298, 1592 (2002)
Boundaries to the eos from astrophysical observations
Andrew A. Steiner et al., ApJ 722, 33 (2010)
Inference from 6 NS data on X-ray bursts or transients
Together with heavy-ion contraints it is tested
the symmetry energy at high density
Other EOS tests, T. Klahn et al., PRC, 035802 (2006)
DU process test
Superluminal speed of sound
QPO
Cooling
……………..
Maximum Mass constraint
PSR J1614-2230
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 and
it 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
n   p  e
e  
2 n   p    
n  
 p  e    

   p  n    
Nijmegen soft core potential
for hyperon-nucleon interaction
PRC 58, 3688 (1998)
Free hyperons
N-Y interaction
included
PRC 61, 055801 (2000), M.B., G. Burgio and H. Schulze
Nijmegen potential for NY interaction, no YY interaction
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 variants
Compensation 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 present
for 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 learned
some fundamental properties of high density EOS
HOWEVER ………
Aaaaah ! 2.7 !!!!
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