1. In-Medium Cluster Binding Energies and Mott Points in Low Density Nuclear Matter K. Hagel SSNHIC 2014 Trento, Italy 8-Apr-2014 Clustering and Medium Effects in Low Density Nuclear Matter

2. Outline Experimental Setup Clusterization and observables in low density nuclear matter. Clusterization of alpha conjugate nuclei Summary

3. 3 Cyclotron Institute, Texas A & M University Beam Energy: 47 MeV/u Reactions: 40 Ar + 112,124 Sn 35 MeV/u 40 Ca + 181 Ta, Ca, C 35 MeV/u 28 Si + 28 Si

4. 35 MeV/u 40 Ca + 181 Ta, Ca, C 35 MeV/u 28 Si + 28 Si 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/u Reactions: 40 Ar + 112,124 Sn NIMROD beam

5. Low Density Nuclear Matter Systems studied – 47 MeV/u 40 Ar + 112,124 Sn – 35 MeV/u 40 Ca + 181 Ta (preliminary data) Use NIMROD as a violence filter – Take 30% most violent collisions Use spectra from 40 o ring – Most of yield from intermediate velocity source Coalescence analysis to extract densities and temperatures – Equilibrium constants – Mott points – Symmetry energy

6. Coalescence Parameters PRC 72 (2005) 024603 v surf, cm/ns t avg, fm/c

7. Temperatures and Densities Recall v surf vs time calculation System starts hot As it cools, it expands 47 MeV/u 40 Ar + 112 Sn

8. 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.

9. Density dependent binding energies From Albergo, recall that Invert to calculate binding energies Entropy mixing term PRL 108 (2012) 062702

10. 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 (E sym = F sym + 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).

11. 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 = 10 α for self- conjugate nuclei( Yamada PRC 69, 024309) 40 Ca + 40 Ca 28 Si + 40 Ca 40 Ca + 28 Si 28 Si + 28 Si 40 Ca + 12 C 28 Si + 12 C 40 Ca + 180 Ta 28 Si + 180 Ta Data Taken 10, 25, 35 MeV/u

12. Alpha-like multiplicities Large number of events with significant alpha conjugate mass for all systems

13. V parallel vs A max Observe mostly PLF near beam velocity for low E* More neck (4-7 cm/ns) emission of α-like fragments with increasing E*

14. Heavy partner is near beam velocity alphas originate from neck emission Origin of alpha conjugate clusters

15. Source Frame study of Origin of clusters

16. Origin of alpha conjugate clusters (continued)

17. Source Frame Origin of clusters (continued)

18. 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

19. Outlook and near future Low density nuclear matter – We have a set of 35 MeV/u 40 Ca+ 181 Ta and 28 Si+ 181 Ta Disassembly of alpha conjugate nuclei – Analysis on presented systems continues – Have Si + C, Si + Ta (almost calibrated) and Ca + Si

20. 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