in-medium cluster binding energies and mott points in low density nuclear matter
DESCRIPTION
Clustering and Medium Effects in Low Density Nuclear Matter. In-Medium Cluster Binding Energies and Mott Points in Low Density Nuclear Matter. K. Hagel SSNHIC 2014 Trento , Italy 8-Apr-2014. Outline. Experimental Setup Clusterization and observables in low density nuclear matter. - PowerPoint PPT PresentationTRANSCRIPT
In-Medium Cluster Binding Energies and Mott Points in Low Density
Nuclear Matter
K. HagelSSNHIC 2014Trento, Italy8-Apr-2014
Clustering and Medium Effects in
Low Density Nuclear Matter
Outline
โข Experimental Setupโข Clusterization and observables in low
density nuclear matter.โข Clusterization of alpha conjugate
nucleiโข Summary
3
Cyclotron Institute, Texas A & M University
Beam Energy: 47 MeV/uReactions:40Ar + 112,124Sn
35 MeV/u40Ca + 181Ta, Ca, C
35 MeV/u28Si + 28Si
35 MeV/u40Ca + 181Ta, Ca, C
35 MeV/u28Si + 28Si
4
โข 14 Concentric Ringsโข 3.6-167 degreesโข Silicon Coverageโข Neutron Ball
S. Wuenschel et al., Nucl. Instrum. Methods. A604, 578โ583 (2009).
Beam Energy: 47 MeV/uReactions: 40Ar + 112,124SnNIMROD
beam
Low Density Nuclear Matterโข Systems studied
โ 47 MeV/u 40Ar + 112,124Snโ 35 MeV/u 40Ca + 181Ta (preliminary data)
โข Use NIMROD as a violence filterโ Take 30% most violent collisions
โข Use spectra from 40o ringโ Most of yield from intermediate velocity
sourceโข Coalescence analysis to extract
densities and temperaturesโ Equilibrium constantsโ Mott pointsโ Symmetry energy
Coalescence Parameters
๐ ๐๐ต (๐ ,๐ต ,๐ฌ๐จ )๐ ๐ฌ๐จ๐ ๐ด =๐น๐๐
๐ต ๐จโ๐
๐ต !๐ ! { ๐๐ ๐ ๐ท๐
๐
[๐๐๐ (๐ฌโ๐ฌ๐ ) ]๐/๐ }๐จโ๐
[ ๐ ๐๐ต (๐ ,๐ ,๐ฌ )๐ ๐ฌ๐ ๐ด ]
๐จ
๐ ๐๐ต (๐ ,๐ต )๐ ๐๐ =๐น๐๐
๐ต ๐จ๐ (๐ ๐+๐ )๐ (๐ฌ๐ /๐ป )
๐๐จ (๐๐
๐ฝ )๐จโ๐[ ๐ ๐๐ต (๐ ,๐)
๐ ๐๐ ]๐จ
๐=[( ๐ !๐ ! ๐ด32๐ด ) (2๐ +1 )๐ (๐ธ 0/๐ )]1
๐ดโ1 3h3
4๐ ๐03
๐ ๐๐ต (๐ ,๐ต )๐ ๐๐ โ๐น๐๐
๐ต ๐ (๐ท ๐)[ ๐ ๐๐ต (๐ ,๐)๐ ๐๐ ]
๐จ
PRC 72 (2005) 024603
vsurf, cm/ns
t avg,
fm/c
Temperatures and Densitiesโข Recall vsurf vs time calculationโข System starts hotโข As it cools, it expands
47 MeV/u 40Ar + 112Sn
Equilibrium constants from ฮฑ-particles model predictions
โข Many tests of EOS are done using mass fractions and various calculations include various different competing species.
โข If any relevant species are not included, mass fractions are not accurate.
โข Equilibrium constants should be independent of proton fraction and choice of competing species.
โข Models converge at lowest densities, but are significantly below data
โข Lattimer & Swesty with K=180, 220 show best agreement with data
โข QSM with p-dependent in-medium binding energy shifts PRL 108 (2012) 172701.
๐พ ๐ ( ๐ด ,๐ )= ๐(๐ด ,๐)๐๐๐ ๐๐
(๐ดโ๐ )
Density dependent binding energiesโข From Albergo, recall thatโข Invert to calculate binding energiesโข Entropy mixing term ๐๐ [๐พ ๐ /๐ถ (๐ )]=๐ต
๐ โ๐๐๐( ๐๐ด )โ๐๐๐ (๐๐ด )
๐ฒ ๐(๐จ ,๐ )=๐ (๐ )๐(๐ฉ(๐จ ,๐ )๐ป )
ฮ ๐น=๐ (๐๐๐( ๐๐ด )+๐๐๐(๐๐ด ))
PRL 108 (2012) 062702
Symmetry energy
โข Symmetry Free Energyโ T is changing as ฯ increasesโ Isotherms of QS calculation that includes in-medium modifications to cluster
binding energiesโข Entropy calculation (QS approach)โข Symmetry energy (Esym = Fsym + T Sโ sym)
โ quasiparticle mean-field approach (RMF without clusters) does not agree with the data
S. Typel et al., Phys. Rev. C 81, 015803 (2010).
PRC 85, 064618 (2012).
Alpha clustering in nucleiโข Ikeda diagram (K. Ikeda,
N. Takigawa, and H. Horiuchi, Prog. Theor. Phys. Suppl. Extra Number, 464, 1968.)
โข Clusterization of low density nuclear matter in collisions of alpha conjugate nuclei
โข Role of clusterization in dynamics and disassembly.
Estimated limit N = 10ฮฑ for self-conjugate nuclei(Yamada PRC 69, 024309)
40Ca + 40Ca
28Si + 40Ca
40Ca + 28Si 28Si + 28Si40Ca + 12C 28Si + 12C40Ca + 180Ta
28Si + 180Ta
Data Taken
10, 25, 35 MeV/u
Alpha-like multiplicities
โข Large number of events with significant alpha conjugate mass for all systems
Vparallel vs Amax
โข Observe mostly PLF near beam velocity for low E*โข More neck (4-7 cm/ns) emission of ฮฑ-like fragments with
increasing E*
๐ธโ=โ๐=1
๐
๐พ ๐๐ (๐ )+๐๐ โจ๐พ ๐โฉโ๐
โข Heavy partner is near beam velocity
โข alphas originate from neck emission
Origin of alpha conjugate clusters
Summaryโข Clusterization in low density nuclear matter
โ In medium effects important to describe dataโ Equilibrium constants
โข EOS Implicationsโ Density dependence of Mott pointsโ Symmetry Free energy -> Symmetry Energy
โข Clusterization of alpha conjugate nucleiโ Large production of ฮฑ-like nuclei
โข Ca + Caโข Ca + Taโข Ca + C
โ Neck emission of alphas important
Outlook and near futureโข Low density nuclear matter
โ We have a set of 35 MeV/u 40Ca+181Ta and 28Si+181Ta
โข Disassembly of alpha conjugate nucleiโ Analysis on presented systems
continuesโ Have Si + C, Si + Ta (almost calibrated)
and Ca + Si
Collaborators
J. B. Natowitz, K. Schmidt, K. Hagel, R. Wada, S. Wuenschel, E. J. Kim, M. Barbui, G. Giuliani, L. Qin, S. Shlomo, A. Bonasera, G. Rรถpke, S. Typel, Z. Chen, M. Huang, J. Wang, H. Zheng, S. Kowalski, M. R. D. Rodrigues, D. Fabris, M. Lunardon, S. Moretto, G. Nebbia, S. Pesente, V. Rizzi, G. Viesti, M. Cinausero, G. Prete, T. Keutgen, Y. El Masri, Z. Majka, and Y. G. Ma