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Nucleon PDF inside Compressed Nuclear Matter
Jacek Rozynek NCBJ Warsaw
‘‘Is it possible to maintain my volume constant when the pressure increases?”
- an nucleon when entering the compressed medium.
J. Phys. G: Nucl. Part. Phys. 42 (2015) 045109.
Nuclear Entalpies, 1311.3591; Pressure Corrections to the Equation of State in the Nuclear Mean Field, 1205.0431, Acta Phys. Pol. B Proc. Suppl. Vol. 5 No 2 (2012) 375
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Introduction• The aim is to check two approximations of
The nuclear Relativistic Mean Field Model
1. constant nucleon mass
2. no nucleon volumes i compressed NM
Possible applications in HI colisions and
inside neutron stars.
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Finite volume effect in compressed medium
Nucleon inside
saturated NM
Compressed inside
Neutron Star or in H I collision
Nucleon
Nucleon
pressure
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Two Scenariosfor NN repulsion with qq attraction
• Constant Volume= Constant Enthalpy
• Constant Mass= Increasing Enthalpy 1/R
Valparaiso QNP2015ΩA
ΩNΩN
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Two Scenariosaffecting nuclear compressibility KA
-1
• Constant Volume= Constant Enthalpy
• Constant Mass= Increasing Enthalpy 1/R
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Definitions
• Enthalpy is a measure of the total energy of a thermodynamic system. It includes the system's internal energy and thermodynamic potential (a state function), as well as its volume Ω and pressure pH (the energy required to "make room for it" by displacing its environment, which is an extensive quantity).
HA = EA + pH ΩA Nuclear Enthalpy (1)
HN = Mpr + pH ΩN Nucleon Enthalpy (2)
Specific Enthalpies
(3)hA(pH
hN() = HN/Mpr = 1+ pH/(cp Mpr
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Enthalpy vs Hugenholz - van Hove relation with chemical potential
(1a)
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Also valid for constant nucleon
volumes !!
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Nuclear convolution model
fN(y)
Light cone variables in
the rest frame
x=k+/pN+
y=pN+/PA
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RMF and Momentum Sum Rule
Frankfurt, Strikman Phys. Reports 160 (1988)
(4)
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(Jaffe)
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Finally with a good normalization of SN we have:
and Momentum Sum Rule
Flux Factor
Fermi Energy
Enthalpy/A
B-=B0 -B3
B-q=0
k k
No NN pairs
baryon current
P0A =EA =AA
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Bag Model in Compress Medium
pH=0
(7)
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Nucleon compressibilty
and two scenarios Constant Nucleon Mass
Constant Nuclear Radius
Semi-experimental Value
sum rules KN-1=>M Ex
2 <rN2 > (Morsch, Julich, PRL 1995)
From 7Gev/c (α,p) scattering in P11 region in SATURN
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K-1=235MeVfm-3
Nuclear compressibility for different constant nucleon radii in
compressed NM
Nucleon Mass for different nucleon radii in compressed NM
Our version of Hugenholz-Van Hove relation for finite nucleons in NM
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Nucleon radius in compressed NM
for a constant nucleon mass
Bag constant in function of nuclear
pressure
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RMF Equation of State for const Enthalpy scenario B
(8)
(9)
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Equation of state - different models
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Results
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SA
SB
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Two possible scenario of phase transitionA - constant nucleon radius, B - constant nucleon mass
Energy alignment
cr (cr) = cp M(cr)
R[fm]=0.8 -> 0.69
3rd International Conference on New Fronties in`Physics
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A model for parton distribution
σ =1/(2R) k+ = xp+
Kinematical conditions for Monte Carlo technique
Primodial quark transverse momentum distribution
Line cone variables in the nucleon rest frame
COMPRESSEDNuclear Case
p+rest= HN(R)
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Nuclear Models - equilibrium
JR G.Wilk PLB 473 (2000)
Only 1% of nuclear pions
Phys. Rev. C71 (2005)
Shifting pion mass
fN(y)
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Toy Model (Edin and Ingelman)
(Neglecting transverse quark momenta)
In our case dhmh => R*HN(R) is const.
But the x=k+/HN(R(ρ)) depends on nucleon density
where
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Finite Nucleon Volumes - Conclusions
A. Constant nucleon mass requires increasing enthalpy
STIFFER EOS
Shift in Bjorken X
B. Constant nucleon volume gives the constant enthalpy with decreasing nucleon
mass, lower compressibility
SOFTER EOS
A&B. In both cases the same width of parton distribution because R*HN(R) const.
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The toy model for phase transition
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PRC 74
our model
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