in-medium cluster binding energies and mott points in low density nuclear matter k. hagel ssnhic...
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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
• Experimental Setup• Clusterization and observables in low
density nuclear matter.• Clusterization of alpha conjugate
nuclei• 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
• 14 Concentric Rings• 3.6-167 degrees• Silicon Coverage• Neutron Ball
S. Wuenschel et al., Nucl. Instrum. Methods. A604, 578–583 (2009).
Beam Energy: 47 MeV/uReactions: 40Ar + 112,124Sn
NIMROD
beam
Low Density Nuclear Matter• Systems studied
– 47 MeV/u 40Ar + 112,124Sn– 35 MeV/u 40Ca + 181Ta (preliminary
data)
• Use NIMROD as a violence filter– Take 30% most violent collisions
• Use spectra from 40o ring– Most of yield from intermediate
velocity source
• Coalescence analysis to extract densities and temperatures– Equilibrium constants– Mott points– Symmetry energy
Coalescence Parameters
𝒅𝟑𝑵 (𝒁 ,𝑵 ,𝑬𝑨 )𝒅 𝑬𝑨𝒅 𝜴
=𝑹𝒏𝒑𝑵 𝑨−𝟏
𝑵 !𝒁 ! { 𝟒𝝅𝟑
𝑷𝟎𝟑
[𝟐𝒎𝟑 (𝑬−𝑬𝒄 ) ]𝟏/𝟐 }𝑨−𝟏
[ 𝒅𝟑𝑵 (𝟏 ,𝟎 ,𝑬 )𝒅 𝑬𝒅𝜴 ]
𝑨
𝒅𝟑𝑵 (𝒁 ,𝑵 )𝒅𝒑𝟑 =𝑹𝒏𝒑
𝑵 𝑨𝟑 (𝟐 𝒔+𝟏 )𝒆 (𝑬𝟎 /𝑻 )
𝟐𝑨 (𝒉𝟑
𝑽 )𝑨−𝟏[ 𝒅𝟑𝑵 (𝟏 ,𝟎)
𝒅𝒑𝟑 ]𝑨
𝑉=[( 𝑍 !𝑁 ! 𝐴32𝐴 ) (2𝑠+1 )𝑒(𝐸 0/𝑇 )]1
𝐴−1 3h3
4𝜋 𝑃03
𝒅𝟑𝑵 (𝒁 ,𝑵 )𝒅𝒑𝟑 ∝𝑹𝒏𝒑
𝑵 𝒇 (𝑷𝟎)[ 𝒅𝟑𝑵 (𝟏 ,𝟎)𝒅𝒑𝟑 ]
𝑨
PRC 72 (2005) 024603
vsurf, cm/ns
t avg,
fm/c
Temperatures and Densities• Recall vsurf vs time calculation
• System starts hot• As it cools, it expands
47 MeV/u 40Ar + 112Sn
Equilibrium constants from α-particles model predictions
• Many tests of EOS are done using mass fractions and various calculations include various different competing species.
• If any relevant species are not included, mass fractions are not accurate.
• Equilibrium constants should be independent of proton fraction and choice of competing species.
• Models converge at lowest densities, but are significantly below data
• Lattimer & Swesty with K=180, 220 show best agreement with data
• QSM with p-dependent in-medium binding energy shifts
PRL 108 (2012) 172701.
𝐾 𝑐 ( 𝐴 ,𝑍 )= 𝜌(𝐴 ,𝑍)𝜌𝑝𝑍 𝜌𝑛
(𝐴−𝑍 )
Density dependent binding energies
• From Albergo, recall that• Invert to calculate binding energies• Entropy mixing term
𝑙𝑛 [𝐾 𝑐 /𝐶 (𝑇 )]=𝐵𝑇−𝑍𝑙𝑛( 𝑍𝐴 )−𝑁𝑙𝑛 (𝑁
𝐴)
𝑲 𝒄(𝑨 ,𝒁 )=𝐂 (𝐓 )𝒆( 𝑩(𝑨 ,𝒁 )
𝑻 )
Δ 𝐹=𝑇 (𝑍𝑙𝑛( 𝑍𝐴 )+𝑁𝑙𝑛(𝑁𝐴 ))
PRL 108 (2012) 062702
Symmetry energy
• Symmetry Free Energy– T is changing as ρ increases– Isotherms of QS calculation that includes in-medium modifications to
cluster binding energies• Entropy calculation (QS approach)• Symmetry energy (Esym = Fsym + T S∙ sym)
– 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 nuclei• Ikeda diagram (K. Ikeda,
N. Takigawa, and H. Horiuchi, Prog. Theor. Phys. Suppl. Extra Number, 464, 1968.)
• Clusterization of low density nuclear matter in collisions of alpha conjugate nuclei
• Role of clusterization in dynamics and disassembly.
Estimated limit N = 10α 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
• Large number of events with significant alpha conjugate mass for all systems
Vparallel vs Amax
• Observe mostly PLF near beam velocity for low E*• More neck (4-7 cm/ns) emission of α-like fragments with
increasing E*
𝐸∗=∑𝑖=1
𝑀
𝐾 𝑐𝑝 (𝑖 )+𝑀𝑛 ⟨𝐾 𝑛⟩−𝑄
• Heavy partner is near beam velocity
• alphas originate from neck emission
Origin of alpha conjugate clusters
Source Frame study of Origin of clusters
Origin of alpha conjugate clusters(continued)
Source Frame Origin of clusters(continued)
Summary
• Clusterization in low density nuclear matter– In medium effects important to describe data– Equilibrium constants
• EOS Implications
– Density dependence of Mott points– Symmetry Free energy -> Symmetry Energy
• Clusterization of alpha conjugate nuclei– Large production of α-like nuclei
• Ca + Ca• Ca + Ta• Ca + C
– Neck emission of alphas important
Outlook and near future
• Low density nuclear matter– We have a set of 35 MeV/u 40Ca+181Ta
and 28Si+181Ta
• Disassembly of alpha conjugate nuclei– Analysis on presented systems
continues– 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. Röpke, 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