Understanding the Isotopic Fragmentation of a Nuclear Collision Triesha Fagan Advisor: Dr. Sherry Yennello Cyclotron Institute REU 2009

Outline Liquid Drop Model- Binding Energy Formula Symmetry Energy Isoscaling Experimental Isoscaling Theoretical Isoscaling Observations Conclusions

Liquid Drop Model Binding Energy Equation Mp = mass of proton Mn = mass of neutron MA = mass of nucleus with the proton number ,Z , and the neutron number ,N . 1st term: Volume Energy 2nd term: Surface Energy 3rd term: Coulomb Energy 4th term: Asymmetry Energy 5th term: Pairing energy

Symmetry Energy Binding energy is greatest when N=Z Chart of the Nuclides Binding energy is greatest when N=Z If it wasn’t for Coulomb term, the most stable form of nuclei would be along the N=Z line

Symmetry Energy The Nuclear Equation of State is known for nuclei at normal: - Density, p/p0 = 1 - Temperature, T = 0 MeV of nuclear matter. Many Equation of States are used to define neutron stars, but understanding the behavior of Csym with respect to density will help verify which prediction is accurate. The coefficients of the binding energy formula hav been obtained from fitting them to known binding energies obtained from experimentally measuring nuclear masses in the ground state. The asymmetry term is not constant in the nuclear equation of state, it is a function of the temperature and density of nuclear material. The evolution of this term is of particular importance Symmetry energy as a function of energy: We know symmetry energy at ground state, but we want to look at it at densities and temperatures away from the ground state because that’s where its undefined. Plot shows all the different predictions. Predicts all the different trends of how the symmetry energy will change. Talk about Binding energy as a function of density, talk about how it varies as ou heat things up, and then the symmetry energy. The liquid drop model only works at ground state, then when you heat it up how do things change. Understanding what happens to the nuclear symmetry energy as density and tempearture changes, will help to describe the n / z ratio that neutron stars have at low densities and high temperatures. The nuclear euation of state d defined st other things , we just don’t know what it is. The euation of state is known at normal temperatures and desnitites and what we’re trying to do is figure out how it changes as we go to non normal densities and temperatures., and that will help us understand the structure of neutron stars and astrophysical things. All of the models that describe how they work have the equation of state in them. D.V. Shetty, S. J. Yennello, and G.A. Souliotis., Phy. Rev. C 76, 024606(2007)

Isoscaling Performed by comparing the isotopic yields of fragments from two different systems, which differ in their source N/Z. Y2(N,Z) and Y1 (N,Z) are the yields of a specific isotope for the neutron-rich source and the neutron-poor source, respectively. The isoscaling parameter , α, is associated with the symmetry energy coefficient by the formula:

Isoscaling Plot Z=6 Each point represents a R2,1(N,Z) as a function of the N of each isotope. Z=17 R2,1(N,Z): Ratio of the yields as a function of the N and Z of each isotope For Example N = 1, Z= 1 = Hydrogen N =2, Z = 1 = Deuterium N = 3, Z = 1 = Tritium Z=1 Z=13

Projectile Multifragmentation Quasi-projectile Projectile : 78,86Kr Interaction System Break-up Target : 58,64Ni Quasi-target

NIMROD-ISIS Experimental data1 for 86,78Kr projectiles on 64,58Ni targets at 35 MeV/u was taken on the NIMROD-ISiS array, a neutron and ion multi-detector , which contains telescopes with excellent isotopic resolution. To left: A photograph of the NIMROD-ISiS array housed inside the TAMU Neutron ball. Above: A schematic cross-section of the ring structure of the NIMROD-ISiS array. The detector is cylindrically symmetric about the x-axis. Once the heating method and reaction systems are chosen the detection system was chosen based on its ability to collect and retain exceptional isotopic data. NIMROD-ISIS *is a charged particle array Consists of telescopes with one or two Silicon energy loss detectors attached to Cesium Iodide stopping detectors. The Si detectors note the change in energy or delta E of the entry and exit energy of the particles. Only particles that are not greater than the threshhold energy for a Si detector are not acknowledged. If the particle is able to pass through the Si detector, the CsI detector notes the stopping energy of the particle. Since the Nimrod-isis is only able to detect charge particles, it was placed within the Neutron Ball, which detects a majority of the neutrons that pass through it. Neutron Ball provides neutron multiplicities for each event. Once the raw data signals are collected from Nimrod-Isis and the Neutron Ball and decoded into a usefule form??? Then the actual process of Isoscaling begins.s 1) S. Wuenschel, Thesis, Texas A&M University, 2009. 2) S. Wuenschel et al., Nucl. Instrum. Methods Phys. Res. A 604, 578 (2009).

Nimrod-ISIS and Neutron Ball Detector Reaction of 86,78Kr +64,58Ni Nimrod-ISIS and Neutron Ball Detector Neutron Ball Efficiency Correction Reconstructing Quasi-projectile

Reconstructing the Quasi-Projectile

Nimrod-ISIS and Neutron Ball Detector Reaction of 86,78Kr +64,58Ni Nimrod-ISIS and Neutron Ball Detector Neutron Ball Efficiency Correction Reconstructing Quasi-projectile Examine trends in isoscaling (Ex. α vs. N/Z bin width, α/Δ vs. E*/A, etc.) Isoscaling of Fragment Yields, α obtained #1 SumZ >= 30 Cut #2 Velocity Cut #3 SumZ = 30 – 34 #4 Quadropole Cut (N/Z)QP Source Selection, Δ calculated

Source Cuts Quasi-projectile Source Selection Reasoning #1 SumZ >= 30 Cut: Events had to consist of fragments that had a total combined charge (Z) greater than 30 in order to eliminate incomplete events and events from other sources. #2 Velocity Cut: Fragments within events that were moving much slower or much faster than the largest fragment were removed from accepted events. If a particle was too slow, it was assumed to be a part of the quasi-target, and if it was to fast, it was assumed to be from pre-equilibrium emission. #3 SumZ = 30-34 Cut: Applied to limit size effects in the observables by taking a narrow range for the quasi-projectile #4 Quadrupole Cut: Accept only spherically shaped events (in momentum space) while removing prolate and oblate shapes 5) Addition of Free Neutrons: Additional free neutrons were experimentally calculated back into the equation to account for the number of secondary neutrons that were generated by high energy neutrons that by-passed the detectors within the Neutron Ball. Assumptions about kinetic energy of free neutrons were made and free neutrons were added according to event-by-event neutron ball multiplicities in the events Prolate –to large of a diameter Oblate – diameter that is to short

Isoscaling Performed by comparing the isotopic yields of fragments from two different systems, which differ in their source N/Z. 86Kr 64Ni Z(protons) 36 28 N(neutrons) 50 Neutron –Rich System Read files to explain better For example we used 78Kr +58Ni and 84Kr+64Ni 1st equation: 1st equation : The yield ratios exhibit an exponential dependence on the neutron and proton number of the chosen fragments. 78Kr 58Ni Z(protons) 36 28 N(neutrons) 42 30 Neutron – Poor System

Isoscaling Performed by comparing the isotopic yields of fragments from two different systems, which differ in their source N/Z. Neutron –Rich System Neutron – Poor System Read files to explain better For example we used 78Kr +58Ni and 84Kr+64Ni 1st equation: 1st equation : The yield ratios exhibit an exponential dependence on the neutron and proton number of the chosen fragments.

Experimental Isoscaling System to System Isoscaling Neutron–Rich and Neutron–Poor Bins of the Reconstructed N/Z of the Quasi-projectile

Theoretical Simulation of Multifragmentation Deep Inelastic Transfer (DIT): Theoretical code to simulate nuclear collisions in which nucleons are exchanged between the projectile and target after interaction occurs. Statistical Multifragmentation Model (SMM): Attempts to describe the breakup pattern of any excited nuclei. As an excited nucleus expands, the density of the nuclear matter decreases, and a fragmentation process occurs. This is modeled in SMM by exploring all of the possible fragment distributions, or partitions. After SMM completes the primary and secondary decay, one is provided with a final fragment distribution in which each fragment is characterized by its charge, mass, energy and angle of emission. A) PRIMARY STAGE B) PARTITIONING STAGE The Deep Inelastic Transfer code was coupled to the Statistical Multifragmentation Model to simulate the collision of 78Kr + 58Ni and 86Kr + 64Ni at 35 MeV/u. -Deep Inelastic Transfer (DIT): Theoretical code to simulate nuclear collisions in which nucleons are exchanged between the projectile and target after interaction occurs. In peripheral collisions, quasi-projectile and quasi-target nuclei are formed in a highly excited state (E* between ~1-7 MeV/u). This excited quasi-projectile is then de-excited using the SMM code. -Attempts to describe the breakup pattern of any excited nuclei. As an excited nucleus expands, the density of the nuclear matter decreases, and a fragmentation process occurs. This is modeled in SMM by exploring all of the possible fragment distributions, or partitions. The simulation is carried out at a reduced density of ~1/6 ρ0, in order to account for the expansion of the nucleus. The first stage of the SMM model provides a primary fragment distribution. Some of these primary fragments still have some excitation energy and can undergo a secondary decay. After SMM completes the secondary decay, one is provided with a final fragment distribution in which each fragment is characterized by its chargea, mass, energy and angle of emission. C) BREAK-UP or EVAPORATION STAGE

Examine trends in isoscaling DIT/SMM Events Detector Filter Examine trends in isoscaling (Ex. α vs. N/Z bin width, α/Δ vs. E*/A, etc.) Isoscaling of Fragment Yields, α obtained #1 SumZ >= 30 Cut #2 Velocity Cut #3 SumZ = 30 – 34 #4 Quadropole Cut (N/Z)QP Source Selection, Δ calculated

Applying different Source Cuts Observations Changing N/Z Bin Width Applying different Source Cuts

N/Z Bin Widths Bin # Narrow (0.02) Standard (0.06) Wider (0.10) 0.92-0.94 0.90-0.96 0.88-0.98 0.85-1.01 2 1.02-1.04 1.00-1.06 0.98-1.08 0.95-1.11 3 1.12-1.14 1.10-1.16 1.08-1.18 1.05-1.21 4 1.22-1.24 1.20-1.26 1.18-1.28 1.15-1.31 5 1.32-1.34 1.30-1.36 1.28-1.38 1.25-1.41 Read files to explain better For example we used 78Kr +58Ni and 84Kr+64Ni 1st equation: 1st equation : The yield ratios exhibit an exponential dependence on the neutron and proton number of the chosen fragments.

Filtered with Varying Source Cuts w/ SumZ Minimum, and Velocity Cuts w/ All Cuts w/ SumZ Minimum Cuts w/ Detector Filter Cuts Unfiltered

Unfiltered with Changing N/Z Bin Widths Narrow Standard Wide Wider

c c c c c c c c c c c c Read files to explain better For example we used 78Kr +58Ni and 84Kr+64Ni 1st equation: 1st equation : The yield ratios exhibit an exponential dependence on the neutron and proton number of the chosen fragments.

Add SumN and SumZ graphs

Conclusions The theoretical simulation of quasi-projectile was comparable. The trends in the bin width are still being studied There was an improvement in the plotting of a/∆ as a function of E*. The similarity in the filter and unfiltered data show that there was no detector bias

Acknowledgements 1) Dr. Sherry Yennello 2) SJYGroup 3) Texas A & M University 4) TAMU Cyclotron Institute