In-Medium Cluster Binding Energies and Mott Points in Low Density Nuclear Matter

1. In-Medium phenomena in Low Density Nuclear Matter In-Medium Cluster Binding Energies and Mott Points in Low Density Nuclear Matter K. Hagel 11th International Conference on Nucleus-Nucleus Collisions San Antonio, Texas, USA 28-May-2012

2. Outline • Motivation • Experimental Setup • Experimental Observables • Analysis • Low density nuclear equation of state • In medium cluster binding energies and Mott Densities • Low density symmetry energies • Summary

3. Motivation • Low density tests of nuclear equation of state • Treatment of correlations and clusterization in low density matter vital ingredient to astrophysical models. • Cluster yields of low density nuclear matter lead to direct test of different models. • Equilibrium constants should be independent of the choice of competing species assumed in a particular model. • In-medium cluster binding energies • Properties of species in equilibrium are the same as those of isolated species at low densities, but changes at higher densities where in-medium effects lead to dissolution of clusters and a transition to cluster free nuclear matter. • Quantum statistical approach that includes in-medium cluster correlations interpolates between exact low density limit and successful RMF approaches near saturation density. • Well defined clusters appear only for ρ < 1/10ρ0and maximum cluster density is reached around the Mott Density. • Low Density Symmetry energy • Symmetry energy of nuclear matter is fundamental ingredient to understand nuclear and astrophysical phenomena.

4. Beam Energy: 47 MeV/u Reactions:40Ar + 112,124Sn Cyclotron Institute, Texas A & M University

5. 14 Concentric Rings 3.6-167 degrees Silicon Coverage Neutron Ball Beam Energy: 47 MeV/u Reactions:p, 40Ar + 112,124Sn NIMROD beam S. Wuenschel et al., Nucl. Instrum. Methods. A604, 578–583 (2009).

6. Multiplicities

7. Energy Spectra

8. Invariant Velocity Plots Central Collisions Peripheral Collisions Central Collisions Peripheral Collisions

9. Tools used in the analysis = Neutron to proton ratio Usually t/3He ratio

10. Time dependence of particle average vsurf PRC 72 (2005) 024603

11. P0 extracted from 40Ar + 112Sn at 45o (~90o in center of mass) • P0 is a radius in momentum space • d, t and 3He are similar. • 4He is significantly larger over entire range of vsurf

12. Volume (Mekjian) Recall that therefore • t, 3He, 4He (A=3) are comparable • Deuteron V larger • Deuteron yield smaller • Easier to break up • Use A ≥ 3 to calculate densities

13. Temperatures and Densities • Recall vsurfvs time calculation • System starts hot • As it cools, it expands

14. Equilibrium constants • Many tests of EOS are done using mass fractions. • Various calculations include various different competing species. • In calculations, if any relevant species not included, mass fractions are not accurate. • Equilibrium constants should be independent of proton fraction and choice of competing species. Recall

15. α Equilibrium constant model predictions • 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.

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

17. Isoscaling parameters • T, ρ increase with vsurf • Decrease in α with vsurf • Fsym extracted for light particles (liquid)

18. Symmetry energy S. Typelet al., Phys. Rev. C 81, 015803 (2010). • 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∙Ssym)

19. Summary • Equilibrium constants • Constraints on model calculations • Models that treat in-medium effects fit the data better • Density dependence of Binding energies • Density dependence of Mott points • Good agreement with model which includes effective interaction to account for in-medium effects of clusters. • Astrophysical implications • Temperatures, densities of hot system • Symmetry Free energy -> Symmetry Energy • Calculations that account for in-medium effects

20. Collaborators L. Qin, K. Hagel, R. Wada, J. B. Natowitz, S. Shlomo, Bonasera, G. Röpke, S. Typel, Z. Chen, M. Huang, J. Wang, H. Zheng, S. Kowalski, M. Barbui, M. R. D. Rodrigues, K. Schmidt, 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,