SLB: 1 UC Davis 11 October 2002 DNP – East Lansing Composites in 2-8AGev Collisions in E895 Stephen Baumgart University of California, Davis for the E895 Collaboration N. Ajitanand (2), J. Alexander (2), M.G. Anderson (1), D. Best (4) *, F.P. Brady (1), T. Case (4), W. Caskey (1), D. Cebra (1), J.L. Chance (1), P. Chung (2), B. Cole (9), K. Crowe (4), A. Das (6), J.E. Draper (1), M.L. Gilkes (5), S. Gushue (8), M. Heffner (1), A.S. Hirsch (5), E.L. Hjort (5), L. Huo (10), M. Justice (3), M. Kaplan (7), D. Keane (3), J.C. Kintner (12), J.L. Klay (1), D. Krofcheck (11), R. Lacey (2), J. Lauret (2), M.A. Lisa (6), H. Liu (3), Y.M. Liu (10), R. McGrath (2), Z. Milosevich (7), G. Odyniec (4), D.L. Olson (4), S.Y. Panitkin (3), C. Pinkenburg (2), N.T. Porile (5), G. Rai (4), H.G. Ritter (4), J.L. Romero (1), R. Scharenberg (5), L. Schroeder (4), B. Srivastava (5), N. Stone (8), T.J.M. Symons (4), A.H. Tartir (1), R. Wells (6), J. Whitfield (7), T. Wienold (4), R. Witt (3), L. Wood (1), W.N. Zhang (10) (1) University of California, Davis, California (2) State University of New York, Stony Brook, New York (3) Kent State University, Kent, Ohio (4) Lawrence Berkeley National Laboratory, Berkeley, California (5) Purdue University, West Lafayette, Indiana (6) The Ohio State University, Columbus, Ohio (7) Carnegie Mellon University, Pittsburgh, Pennsylvania (8) Brookhaven National Laboratory, Upton, New York (9) Columbia University, New York, New York (10) Harbin Institute of Technology, Harbin , P.R. China (11) University of Auckland, New Zealand (12) St. Mary’s College, Moraga, California * Feoder Lynen Fellow of the Alexander v. Humboldt Foundation

SLB: 2 UC Davis 11 October 2002 DNP – East Lansing The TPC Detector The E895 experiment is a fixed target Au on Au experiment. Using the AGS at BNL, the experiment was run at the beam energies of 2,4,6, and 8 A Gev. After the ions collide the products move through the detector, ionizing the gas. Their curvature in the B-field gives their momentum. The amount of ionization gives the particle’s velocity from the Bethe-Bloch parameterization.

SLB: 3 UC Davis 11 October 2002 DNP – East Lansing Motivations The purpose of heavy ion experiments is to learn about hot, dense matter. Questions like “What are the properties of hot, dense matter?” and “Are there phase transitions at very high temperatures and densities?” can be answered. Using heavy ion accelerators, new regions of phase space can be probed. To learn about the nuclear equations of state, things like temperature, flow, the time evolution of the system, density, and other properties must be known. Because condensates like deuterons, and helions form only under certain conditions, by studying the condensates, the properties of the hot, dense matter of the fireball can be found.

SLB: 4 UC Davis 11 October 2002 DNP – East Lansing Fitting Spectra Particle yields are extracted from fitting spectra. The raw data from the detector is binned into a m t -m 0 vs. rapidity phase space. Then, the spectra are fitted by fixing the proton and pion yields based on temperature and dN/dy parameters from a previous analysis. (1/2  m t )(d 2 N/dydm t )

SLB: 5 UC Davis 11 October 2002 DNP – East Lansing Composites Coalescence occurs when two particles are close together in phase space and can combine to form a new particle. An example of this is when a proton and a neutron combine to form a deuteron. Tritons are created when a neutron combines with a deuteron. Helions are created when a proton combines with a deuteron. In this project the yields of composites were analyzed. Composites form in a process called “coalescence”. Once the spectra are found, one can draw inferences about hot, dense matter. The first thing done with the spectra was to fit them with Boltzmann curves for temperature and dN/dy parameters. The rapidity in the beam direction, y, is often correleated with a particle’s angle from beam direction. A phenomena that has an angular dependence will be noticed by finding dN/dy.

SLB: 6 UC Davis 11 October 2002 DNP – East Lansing Deuteron dN/dy Gaussian model for 4  yields: 2 AGeV 4 AGeV 6 AGeV 8 AGeV E beam E895 Deuterons Deuterons form from protons and neutrons. The process that occurs in a heavy ion collision is not so much different than what occurred in the hot, dense early universe.

SLB: 7 UC Davis 11 October 2002 DNP – East Lansing Triton dN/dy Gaussian model for 4  yields: 2 AGeV 4 AGeV 6 AGeV 8 AGeV E beam E895 Tritons ~8 Tritons must coalesce out of deuterons and neutrons. There are fewer deuterons than protons or neutrons so the triton yields are smaller.

SLB: 8 UC Davis 11 October 2002 DNP – East Lansing Helion dN/dY 2 AGeV 4 AGeV 6 AGeV 8 AGeV E beam E895 Helions Helions are rare compared to protons and deuterons in the E895 experiment but because they have twice the charge of other common particle species, they are easier to identify.

SLB: 9 UC Davis 11 October 2002 DNP – East Lansing dN/dy for Deuterons,Tritons, and Helions We can check to see if we have found all the protons in these events. The Total yield of protons will be the sum of the initial protons plus those neutrons converted into protons through the delta channel. The distribution is a Gaussian function with respect to rapidity. Integration will give the total number of protons. Once error propagation is done, the differences can be checked to make sure they are within errors.

SLB: 10 UC Davis 11 October 2002 DNP – East Lansing Calculating the Gaussian Radius of the Source Using the measured proton and deuteron spectra, one can calculate a coalescence radius for proton emission. A similar technique can be used to find a coalescence radius for protons and deuterons. Llope et. AL. Phys. Rev. C 52, 2004

SLB: 11 UC Davis 11 October 2002 DNP – East Lansing Coalescence Radii for Various Rapidities In order to compare different particles, all mt- m0s for coalescence radii assume proton mass.

SLB: 12 UC Davis 11 October 2002 DNP – East Lansing Coalescence Radii for Various Rapidities

SLB: 13 UC Davis 11 October 2002 DNP – East Lansing Radii from Helion Coalescence (y cm = 0)

SLB: 14 UC Davis 11 October 2002 DNP – East Lansing Interpretation of Gaussian Radii of Source The coalescence radii give the probability of particle emission by a Gaussian equation: Where A = constant R G = coalescence radius r = transverse distance As you can see from the graphs of coalescence radii for different rapidity, the radii vs. m t function changes as a function of y. Because y is correlated with the angle from the beam direction, this suggests that the source is not spherical. From the these graphs, one can see how coalescence radii show a transverse momentum dependence.

SLB: 15 UC Davis 11 October 2002 DNP – East Lansing Proton Phase Space Density Phase Space is defined as the density of particles per six dimensional momentum- coordinate space. Because the radii and the yields in momentum space are known, the phase space density can be calculated. This is a thermal system so the phase space density is expected to decrease exponentially with mt.

SLB: 16 UC Davis 11 October 2002 DNP – East Lansing Future Goals Do error propagation! Find source size as a function of rapidity. The temperature values from the spectra can be used to estimate the blast velocity of the fireball. Fits to determine chemical potential can be done. While fitting the spectra with Boltzmann curves, it became apparent that flow effects were occurring. This deserves further study.