Part II: from Pygmy Resonances to Neutron Stars

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• Part II from Pygmy Resonances to Neutron
  Stars

symmetry energy (pressure) ? neutron skin ?
low-lying ("pygmy") strength
neutron star (crust)
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Calculations for 132Sn Pygmy at 8
12 MeV
132Sn
Pygmy Resonances Theoretical artifact or
Existing in Nuclei ? What is their true nature
? (skin vibration ?) What do we learn from it ?
N.Paar et al, Phys.Rev. C67(2003)34312
P.G.Reinhard, Nucl.Phys. A649(1999)305c
132Sn
Tsoneva, Lenske et al.
Sarchi,Bortignon,Colo
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Experiment - beam production and isotope
identification
Primary beam 108 238U ions / sec _at_ 550
MeV/u Secondary beam 10 ions / sec of 132Sn in
Cave B
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Experimental setup in Cave C at SIS/GSI
Neutron detector LAND
heavy fragment
neutrons
Dipole magnet Aladin
g-rays
20 m
Crystal Ball with target
sec. beam 500 AMeV
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Results for neutron-rich even Sn isotopes
Coulomb cross section
Photo-neutron cross section
stable (real photons)
radioactive (virtual photons)

• PDR
• located at 10 MeV
• exhausts a few TRK sum rule
• in agreement with theory
• GDR
• no deviation from systematics

P. Adrich et al., PRL 95 (2005) 132501
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Vretenar et al., Phys.Rev.C67, 34312 (2003)
Sarchi et al., Phys.Lett. B601,27 (2004)
Tsoneva et al., Phys.Lett. B586,213 (2004)
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Low-lying strength in 132Sn mass neighborhood
5 MeV lt E lt 9 MeV
observed in all isotopes difference between even
and odd isotopes due to neutron separation
threshold location and unpaired neutrons
Stable nuclei, Photoabsorption, from A.Zilges et
al., Phys.Lett. B 542,43 (2003) S.Volz et al.,
Nucl.Phys. A 779, 1 (2006) N. Ryezayeva et al.,
Phys.Rev.Lett. 89 (2002) K. Govaert et al., Phys.
Rev. C 57,2229 (1998)
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Symmetry energy in nuclear matter
Taylor expansion of the energy per particle in
nuclear matter
Isospin symmetric matter
Symmetry energy
a4 - symmetry energy per nucleon in pure neutron
matter p0 - slope parameter ('symmetry-energy
pressure') ?K0 - correction to incompressibility
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Symmetry energy S2(?) and neutron skin in 208Pb
R.J.Furnstahl NPA 706(2002)85-110

• strong linear correlation between neutron skin
  thickness and parameters a4, p0
• no distinct correlation with other quantities

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Claim (theory) Precise knowledge of skin
thickness would
constrain the density dependence of S(r)
Work Hypothesis Pygmy-Strength (since related
to skin) should do the same job, but,
experimentally, is accessed much easier !
Inspired by recent article of Piekarewicz (Phys.
Rev. C 73 , 044325 (2006))
Here Quantitative attempt by means of RHB
RQRPA, (density-dependent meson-exchange DD-ME
) Paar, Vretenar, Ring et al. (Phys. Rev. C67,
34312 (2003)) different sets of DD-ME
forces corresponding to varying sym.
energies, but all are 'good' forces, i.e. fit
standard set of exp.data (masses...)
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PDR strength versus a4, po
Result (averaged 130,132Sn) a4 32.0
1.8 MeV
po 2.3 0.8 MeV/fm3
RQRPA DD-ME N. Paar et al.
S(r) moderate stiffness (positive)
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Neutron skin thickness
Rn-Rp
Rn Rp 130Sn 0.23 0.04 fm 132Sn
0.24 0.04 fm
Notice The (experimentally very challenging)
parity-violating electron scattering experiment,
PREX at JLab, aims at an accuracy of
0.05 fm for neutron-matter radius (i.e. skin)
in 208Pb !
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208Pb analysis
?Bpdr(E1)1.98 e2 fm2 from N.Ryezayeva et al.,
PRL 89(2002)272501 ?Bgdr(E1)60.8 e2 fm2 from
A.Veyssiere et al.,NPA 159(1970)561
Rn Rp 0.18 0.035 fm
of course, there are open questions ?
joint effort theory / experiment but, in
principle, PDR strength carries
equivalent information than skin, .. and is
much easier to approach experimentally
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Neutron Skin and Neutron Star Radius
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C.J. Horowitz, J. Piekarewicz PRL 86(2001)5647
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Neutron skin in 208Pb vs neutron star
a4 31.4 0.8 MeV dr 0.17 0.02 fm
C.J. Horowitz, J. Piekarewicz PRL 86(2001)5647
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no direct URCA cooling ?
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Conclusion
Neutron Pygmy Resonance appear systematically
with increasing isospin and seem to go along
with neutron skins. Both carry information on
density dependence of the nuclear symmetry
energy,

an improved knowledge
of which will help in describing certain neutron
star properties. The upcoming new RIB
facilities do not only lead us towards more
extreme isospin, but provides us with new
experimental techniques and methods. Th
anks for your attention !