Clustering and Medium Effects in Low Density Nuclear Matter
advertisement
In-Medium BindingEffects Energies ClusteringCluster and Medium inin Low Density and Mott Points Low Density Nuclear Nuclear MatterMatter K. Hagel SSNHIC 2014 Trento, Italy 8-Apr-2014 Outline • Experimental Setup • Clusterization and observables in low density nuclear matter. • Clusterization of alpha conjugate nuclei • Summary Beam Energy: 47 MeV/u Reactions:40Ar + 112,124Sn 35 MeV/u 35 MeV/u 40Ca + 181Ta, Ca, C 28Si + 28Si Cyclotron Institute, Texas A & M University 3 Beam Energy: 47 MeV/u Reactions: 40Ar + 112,124Sn 35 MeV/u 35 MeV/u 40Ca + 181Ta, Ca, C 28Si + 28Si NIMROD • • • • 14 Concentric Rings 3.6-167 degrees Silicon Coverage Neutron Ball beam S. Wuenschel et al., Nucl. Instrum. Methods. A604, 578–583 (2009). 4 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 π π π΅(π, π΅) π π π΅(π, π) π΅ ∝ πΉππ π(π·π ) π ππ π ππ π¨−π π/π π π π΅(π, π, π¬) π π¬π π΄ π¨ tavg, fm/c ππ π π· π π π΅(π, π΅, π¬π¨ ) π¨−π π π π΅ = πΉππ π π¬π¨ π π΄ π΅! π! πππ π¬ − π¬π π¨ vsurf, cm/ns PRC 72 (2005) 024603 π π π΅(π, π΅) π¨π ππ + π π π΅ = πΉ ππ π ππ ππ¨ π¬π /π» ππ π½ π¨−π π π π΅(π, π) π ππ 3 π= π! π! π΄ 2π΄ 2π + 1 π πΈ0 /π 1 π΄−1 π¨ 3β3 4ππ03 Temperatures and Densities • Recall vsurf vs time calculation • System starts hot • As it cools, it expands 47 MeV/u 40Ar + 112Sn Equilibrium constants from αparticles model predictions πΎπ π΄, π = • • • • • • π(π΄, π) π (π΄−π) ππ ππ 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. Density dependent binding energies • From Albergo, recall that π²π(π¨, π) = π π π • Invert to calculate binding energies π π • Entropy mixing term ΔπΉ = π πππ + πππ π©(π¨,π) π» π΅ π π ππ πΎπ /πΆ(π) = − πππ − πππ( ) π π΄ π΄ π΄ π΄ PRL 108 (2012) 062702 Symmetry energy S. Typel et al., Phys. Rev. C 81, 015803 (2010). • Symmetry Free Energy PRC 85, 064618 (2012). – 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 + TβSsym) – quasiparticle mean-field approach (RMF without clusters) does not agree with the data 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 selfconjugate nuclei(Yamada PRC 69, 024309) Data Taken 40Ca + 40Ca 28Si + 40Ca 40Ca + 28Si 28Si + 28Si 40Ca + 12C 28Si + 12C + 180Ta 28Si 40Ca + 180Ta 10, 25, 35 MeV/u Alpha-like multiplicities • Large number of events with significant alpha conjugate mass for all systems Vparallel vs Amax π πΈ∗ = πΎππ π + ππ πΎπ − π π=1 • Observe mostly PLF near beam velocity for low E* • More neck (4-7 cm/ns) emission of α-like fragments with increasing E* Origin of alpha conjugate clusters • Heavy partner is near beam velocity • alphas originate from neck emission 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 28Si+181Ta 40Ca+181Ta and • 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
