F. Sammarruca, University of Idaho

fsammarr@uidaho.edu

Supported in part by the US Department of Energy.

From Neutron Skins to Neutron Stars to Nuclear Reactions with a Self-Consistent and Microscopic

Approach

International Symposium on Nuclear Symmetry Energy Smith College, June 17-20, 2011

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 tonuclear reactions (with Larz White, UI)

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Our present knowledge of the nuclear force is the results of decades of struggle. QCD and its symmetries led to thedevelopment of chiral effective theories.But, ChPT is unsuitable for applications indense matter. Relativistic meson-theory isa 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.

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Ab initio: realistic free-space NN forces, potentially complemented by many-bodyforces, 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 forceIs 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.

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Z-diagram

(virtual nucleon-antinucleonexcitation)

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The typical feature of the DBHF method:

Via dressed Dirac spinors, effectively takes into account virtual excitations of pair terms in the nucleon selfenergy.

Repulsive, density-dependent saturation effect

( , )u p λ∗ =1/ 2

2pE m

m

∗ ∗

∗

⎛ ⎞+⎜ ⎟⎜ ⎟⎝ ⎠

p

p

E mλσ χ

∗ ∗

⎛ ⎞⎜ ⎟•⎜ ⎟⎜ ⎟+⎝ ⎠

1

(8/3)0/ ( / )E A ρ ρΔ ∝

Z-diagram

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We obtain the single-particle potentials self-consistently with the effective interaction.

For isospin-asymmetric matter:

n np nn

p pn pp

U G G

U G G

= +

= +

∫ ∫∫ ∫

s.p. potentials (by-product of EoS calculation):

n pF Fk k≠

9*

EoS for SNM and NM, an overview:

16.14se MeV=−30.185s fmρ −=

…WHICH LEADS TO:

2( , ) ( ,0) ( )syme e eρ α ρ ρ α≈ +

( ,1) ( ,0)syme e eρ ρ= −

1α =

0α =252K MeV=

0

0

( ) 33.7

( ) 69.6

syme MeV

L MeV

ρ

ρ

=

= 10

RED: DBHF predictions

Black: commonly usedparametrizations (consistentwith isospin diffusion data)

0( / )syme C γρ ρ=

The uncertainty in our knowledgeof the EoS is apparent throughthe symmetry energy:

0.69 1.1γ = −

For more recent constraints, seeTsang et al;Trautmann, GSI.

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To explore how different handlings of TBFimpact 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. UIXvs. DBHF

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The density-dependence of the symmetry energy andthe neutron skin of 208-Pb.

Symmetry energyas predicted by DBHFand BHF+TBF calculations.

13BHF+TBF models from:Li & Schulze, PRC78,028801 (2008)

Neutron skin (208-Pb) vs. symmetry pressure with various microscopic models.

L=symmetry pressure

Constraints on L:

Most recently:

45 75L MeV= −

MeV

(M. Warda et al., PRC80, 024316 (2009))

88 25L = ±(Chen, Ko, Li)

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Even more recently (this workshop):L = 60 MeV (20)

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-Pbwith an accuracy of 0.05 fm (PREX??) would definitely be able to discriminate among EoS from microscopic models.

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We explored the sensitivity of the A-A reaction cross section to medium effects and isospin asymmetries .

Collisions of neutron-rich nuclei are useful to investigate, for instance, distribution of nuclear matter in nuclei.

The reaction cross section is sensitive to boththe nuclear densities and the NN collisions.

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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-Pbpredicted through our EoS

Neutron excessparameter

S=0.17 fm

Next, some sensitivity tests involving 208-Pb 18

40-Ca + 208-Pb

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

Fermi momentum = 1.1 (1/fm) Fermi momentum = 1.3 (1/fm)

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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 NNxsections.

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Data by Licot et al.; E/A between 50 and 70 MeV.Ca and Ar neutron-rich isotopes on a Silicon target.

Ca Ar

Reaction cross section with neutron-rich isotopes:

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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:

Effective NN interaction

Nuclear densities

The EoS

In-medium NN xsections

Reaction x-section

Free-space NN interaction

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Main Conclusion

USING CONSISTENTLY MICROSCOPICINGREDIENTS IN THE MANY-BODY THEORY(STRUCTURE AND REACTION)MAXIMIZES THE PREDICTIVE POWER

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.

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