1. The NSCL is funded in part by the National Science Foundation and Michigan State University. Determining the Impact Parameter and Cross-Section in Heavy Ion Collisions A. Ramos 1, R. Hodges 2, W. Lynch 2, M.B. Tsang 2, J. Winkelbauer 2 1 Physics Department, Florida International University, Miami, FL 33199 2 National Superconducting Cyclotron Laboratory, Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48223 Results Conclusion Motivation Experimental Setup Methodology Goal: to further restrict the value of the asymmetry energy constant, C 4, that will complete the nuclear Equation of State (EOS) for high and low density matter. Figure 1. A peripheral collision. The overlap region contains low density matter. The S800 mass spectrometer was used to look at the residues of the collision while the Large Area Silicon-Strip/CsI Detector Array (LASSA) and the Miniball (MB) and Miniwall (MW) array were used to detect charged particles in less optimum resolution. (Figure 2). In the full implementation, the MB consists of 188 separate detectors and MW consists of 256 (??) that wrap together around The violence of a collision can be identified by finding the impact parameters of the collisions using the following expressions: To normalize different reactions, a ratio between each impact parameter value and the highest value from the experiment is constructed. This ratio is called The lowest 20% of the cross-sections will be considered central collisions and the highest 20% peripheral collisions. N= particles/cm 2 in target I s = total scattered particles I in = total incoming particles N c = multiplicity Figure 2. Location of the Miniball and the S800 in the experimental setup. Figure 3. A schematic of a MB detector. The highest 20% reduced impact parameter values were considered peripheral collisions for this experiment. The lowest 20% reduced impact parameter values were considered central collisions. Based on Figure 9, it can be determined that those events with a Multiplicity of 7 and below are peripheral collisions and 21 or higher are central collisions. Figure 4. Cross-section vs. Multiplicity Figure 6. b-hat vs. Multiplicity Figure 5. Impact Parameter vs. Multiplicity Figure 4 shows the relationship of the charged particle multiplicity (N c ) and cross sections for each target-beam combination used in the experiment. The larger the multiplicity, the more violent the collisions and the smaller the cross section. The values for all beam-target combinations are close because the E/A was the same for all, 70MeV. Figure 6 shows the relationship between the reduced impact parameters, b-hat, and the charged particle multiplicity. Note that the three different curves in Figure 5, collapse into one curve. The larger the multiplicity, the smaller the reduced impact parameter, corresponding to more violent collisions. Figure 5 shows the relationship of the charged particle multiplicity (N c ) and the impact parameter determined from the cross-sections. The larger the multiplicity, the smaller the impact parameter. Further understanding of Neutron Star properties such as the mass and radius can be achieved if EOS is defined. In heavy ion collisions, low and high density nuclear matter can be formed. One focus of this experiment is on peripheral collisions and therefore the data corresponding to these must be identified. (see Figure 1) the target in a spherical shape. In this experiment, some MB/MW elements were removed to accommodate the LASSA array. Each detector is a 2 cm thick CsI (TI) crystal covered by a plastic scintillator foil 4 micrometers thick. (see Figure 3) Each CsI crystal is attached to a photo- multiplier tube (PMT) which converts incoming light into an electric signal through the photoelectric effect. References -Haensel, P.; Potekhin, A.Y.; Yakovlev, D.G. Neutron Stars: Equation of State and Structure. Astrophysics and Space Science Library. 2007 - Serway, R.; Moses, C.; Moyer, C. Modern Physics. 3rd edition. 2005. Thomson Brooks/Cole. -Tsang, M.B. Constraints the Symmetry Energy in the Nuclear Equation of State. Hira group http://groups.nscl.msu.edu/hira/highlightsscience.pdf -De Souza, R.T. The MSU Miniball 4pi Fragment Detection Arrray. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment Volume 295, Issues 1-2, 1 October 1990, Pages 109-122 -Green, Dan. The Physics of Particle Detectors. Cambridge University Press. 2000 Miniball S800

2. The NSCL is funded in part by the National Science Foundation and Michigan State University. Determining the Impact Parameter and Cross-Section in Heavy Ion Collisions A. Ramos 1, R. Hodges 2, W. Lynch 2, M.B. Tsang 2, J. Winkelbauer 2 1 Physics Department, Florida International University, Miami, FL 33199 2 National Superconducting Cyclotron Laboratory, Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48223 Results Conclusion Motives Experimental Setup Methodology -Goal: to further restrict the value of the asymmetry energy constant, C 4, that will complete the nuclear Equation of State (EOS) for high and low density matter. -Further understanding of Neutron Star properties such as the mass and radius can be achieved if EOS is defined. -In heavy ion collisions, low and high density nuclear matter can be formed. -One focus of this experiment is on peripheral collisions and therefore the data corresponding to these must be identified. (see Figure 1) Figure 1. Peripheral collisions. The overlap region contains low density matter. -The S800 mass spectrometer was used to look at the residues of the collision while the Large Area Silicon-Strip/CsI Detector Array (LASSA) and the Miniball (MB) and miniwall (MW) array were used to detect charged particles in less optimum resolution. (Figure 2). -In the full implementation, the MB consists of 188 separate detectors and MW consists of 256 (??) that wrap together around the target in a spherical shape. In this experiment, some MB/MW elements were removed to accommodate the LASSA array. -Each detector is a 2 cm thick CsI (TI) crystal covered by a plastic scintillator foil 4 micrometers thick. (see Figure 3) -Each CsI crystal is attached to a photo-multiplier tube (PMT) which converts incoming light into an electric signal through the photoelectric effect. -The violence of a collision can be identified by finding the impact parameters of the collisions using the following expressions: -To normalize different reactions, a ratio between each impact parameter value and the highest value obtained from the experiment is constructed. This ratio is called ?? -The highest 20% of the cross-sections will be considered central collisions and the lowest 20% peripheral collisions (see Figure 9). (?? Please use Rachel;s definition of b_hat.) N= particles/cm 2 in target I s = total scattered particles I in = total incoming particles N c = multiplicity Figure 2. Location of the Miniball (MB) and the S800 in the experimental setup. Figure 3. A side picture of one of the telescopes in the Miniball (MB). The MB is used to calculate the impact parameters. -Based on Figure 9, it can be determined that those events with a Multiplicity of 7 and below are peripheral collisions and 21 or higher are central collisions. Figure 4. Cross-section vs. Multiplicity Figure 6. b-hat vs. Multiplicity Figure 5. Impact Parameter vs. Multiplicity -Figure 4 shows the relationship of the charged particle multiplicity (Nc) and cross sections for the three target-beam combinations. -The larger the multiplicity, the more violent is the collisions and the smaller of the cross section. -Figure 5 shows the relationship of the charged particle multiplicity (Nc) and the impact parameter determined from the cross-sections. -The larger the multiplicity, the smaller the impact parameter. -Figure 6 shows the relationship between the reduced impact parameters, b-hat, and the charged particle multiplicity. Note that the three different curves in Figure 5 collapsed into one curve. -The larger the multiplicity, the smaller the b-hat corresponding to smaller impact parameter and more violent collisions. -?? Please use our standard definition from Rachel…The highest 20% values for b-hat were considered peripheral collisions for this experiment -T??he lowest 20% values for b-hat were considered head-on collisions.