From Neutron Skins to Neutron
Stars to Nuclear Reactions with a
Self-Consistent and Microscopic
Approach
F. Sammarruca, University of Idaho
fsammarr@uidaho.edu
International Symposium on Nuclear Symmetry Energy
Smith College, June 17-20, 2011
Supported in part by the US Department of Energy.
Microscopic calculations of the equation of
state (EoS)
+
Empirical information from
EoS-sensitive systems/phenomena
=
Powerful combination to constrain the
in-medium behavior of the nuclear force
(Broad-scoped project)
2
Brief overview of our work
Nuclear matter predictions within the
Dirac-Brueckner-Hartree-Fock method
Applications to neutron skins, neutron stars
Exploring model dependence
Most recent/future work: applications to
nuclear reactions (with Larz White, UI)
3
Our present knowledge of the nuclear
force is the results of decades of struggle.
QCD and its symmetries led to the
development of chiral effective theories.
But, ChPT is unsuitable for applications in
dense matter. Relativistic meson-theory is
a better choice.
Our starting point : a realistic NN potential
developed within the framework of a
relativistic scattering equation (Bonn B).
Also, pv coupling for pseudoscalar mesons.
4
Ab initio:
realistic free-space NN forces,
potentially complemented by many-body
forces, are applied in the nuclear many-body
problem.
Most important aspect of the ab initio
approach:
No free parameters in the medium.
The isospin dependence of the nuclear force
Is constrained at the free-space level.
*
5
The many-body framework:
The Dirac-Brueckner-Hartree-Fock
(DBHF) approach to (symmetric and
asymmetric) nuclear matter.
DBHF allows for a better description of
nuclear matter saturation properties as
compared with conventional BHF.
An efficient alternative to BHF + TBF
models.
6
Z-diagram
(virtual nucleon-antinucleon
excitation)
7
The typical feature of the DBHF method:
Via dressed Dirac spinors, effectively takes into
account virtual excitations of pair terms
in the nucleon selfenergy. Z-diagram
u ( p,  ) 

 E   m
 p 
 2m

1/ 2






1




p

 
 E p   m 


Repulsive, density-dependent saturation effect
E / A  ( / 0 )(8/3)
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s.p. potentials (by-product of EoS calculation):
We obtain the single-particle potentials
self-consistently with the effective interaction.
For isospin-asymmetric matter:
U n   Gnp   Gnn
U p   Gpn   Gpp
*
kF  k F
n
9
p
…WHICH LEADS TO:
EoS for SNM and NM, an overview:
e(, )  e(,0)  esym ( )
2
esym  e(  ,1)  e(  ,0)
es  16.14MeV
3
s  0.185 fm
K  252MeV
 1
 0
esym (  0 )  33.7 MeV
L(  0 )  69.6 MeV
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The uncertainty in our knowledge
of the EoS is apparent through
the symmetry energy:
RED: DBHF predictions
Black: commonly used
parametrizations (consistent
with isospin diffusion data)

esym  C( / 0 )
  0.69  1.1
For more recent constraints, see
Tsang et al;
Trautmann, GSI.
11
To explore how different handlings of TBF
impact predictions of EoS-sensitive
“observables”, we have looked at several
microscopic “BHF + TBF” models from the
work of Li, Lombardo, Schulze, Zuo.
They are:
BOB=Bonn B + micro. TBF
N93=Nijmegen 93 + micro TBF
V18= Argonne V18 + micro TBF
UIX=Argonne V18 + phen. UIX
vs.
DBHF
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The density-dependence of the symmetry energy and
the neutron skin of 208-Pb.
Symmetry energy
as predicted by DBHF
and BHF+TBF
calculations.
BHF+TBF models from:
Li & Schulze, PRC78,028801 (2008)
13
L=symmetry pressure
Neutron skin (208-Pb)
vs. symmetry pressure with
various microscopic models.
Constraints on L:
L  88  25 MeV
(Chen, Ko, Li)
Most recently:
L  45  75MeV
(M. Warda et al., PRC80, 024316 (2009))
Even more recently (this workshop):
L = 60 MeV (20)
14
What we have learnt from this exercise:
Although microscopic models do not display
as much spreading as phenomenological ones,
there are large variations in the density
dependence of the symmetry energy (and
related observables.)
A measurement of the neutron skin of 208-Pb
with an accuracy of 0.05 fm (PREX??)
would definitely be able to discriminate
among EoS from microscopic models.
15
Collisions of neutron-rich nuclei are
useful to investigate, for instance,
distribution of nuclear matter in nuclei.
The reaction cross section is sensitive to both
the nuclear densities and the NN collisions.
We explored the sensitivity of the
A-A reaction cross section to medium
effects and isospin asymmetries .
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OPTICAL LIMIT (OLA) of GLAUBER MODEL:
NN x-sections
Nuclear densities
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n and p densities in 208-Pb
predicted through our EoS
Neutron excess
parameter
S=0.17 fm
Next, some sensitivity tests involving 208-Pb
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40-Ca + 208-Pb
Fermi momentum = 1.1 (1/fm)
Fermi momentum = 1.3 (1/fm)
1
free-space NN xsections
2
phenomen. formula by Xiangzhou et al.
3
Our microscopic in-medium NN xsections
4
“mass scaling” applied to free-space NN x-sections
19
40-Ca+208-Pb
E/A=100 MeV
Blue: our microscopic in-medium NN cross sections
Red: mass scaling applied to NN xsections in vacuum
Effects from n/p asymmetry are included in the NN
xsections.
20
Reaction cross section with neutron-rich isotopes:
Ca
Ar
Data by Licot et al.; E/A between 50 and 70 MeV.
Ca and Ar neutron-rich isotopes on a Silicon target.
21
IN SUMMARY:
We performed a sensitivity study of the reaction
cross section with a simple reaction model.
We observed considerable model dependence
of the reaction cross section with respect to medium effects
Better data precision required to resolve those differences
Important to be selective of an appropriate “laboratory”
to discern specific effects
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MAIN POINT OF THIS EXERCISE
Parameter-free continuous pipeline from:
Free-space NN interaction
Effective NN interaction
The EoS
Nuclear densities
In-medium NN xsections
Reaction x-section
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Main Conclusion
The microscopic approach is more fundamental:
Realistic NN interactions reproduce scattering
and bound state properties of the free 2N system.
In-medium correlations are built-in through
many-body techniques.
Isospin dependence is included naturally.
USING CONSISTENTLY MICROSCOPIC
INGREDIENTS IN THE MANY-BODY THEORY
(STRUCTURE AND REACTION)
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MAXIMIZES THE PREDICTIVE POWER