My research this summer involved analyzing an experiment conducted a few years ago at the National Superconducting Cyclotron Laboratory at Michigan State University. In this experiment, a beam of projectile ⁸⁴Kr nuclei at 35 or 60 MeV per nucleon struck one of two targets: ¹⁹⁷Au and ²³²Th. The charged particles emitted as a result of these nuclear collisions were detected by the 4pi ball, an apparatus around six feet in diameter and containing hundreds of plastic scintillating detectors. The forward array, a group of 45 smaller detectors split into three rings, allows more precise detection of particle locations from 3 to 18 degrees relative to the beamline.

In our analysis this summer, we concentrated primarily on the most central collisions. A central collision is, as the name implies, one in which the target nucleus is struck by the projectile near its center. These head-on collisions leave an energetically excited, somewhat spherical composite system. A peripheral collision, by contrast, is a glancing blow by the projectile on the target, which leaves a much less energetic system. The difference in shape and slope of counts vs. energy spectra for these two types of collisions, especially at forward angles, calls for separate analyses of these two types of events. We are able to distinguish between central and peripheral events using "multiplicity". This is simply the number of light charged particles, specifically alpha particles, protons, and lithium nuclei, which are picked up by the 4pi ball from each event. Since central events are more violent, energetic collisions, the greater the multiplicity, the more central the collision.

It is possible to divide the emission of particles from nuclear collisions into two basic types. The more thoroughly understood of these is statistical emission. This process occurs after the target and projectile have fused into a single nuclear system. This system must get rid of excess thermal energy. It does so by emitting a variety of particles in more or less random directions. The probabilistic nature of this particle emission is why it is called statistical emission. Pre-equilibrium emission, on the other hand, occurs as a direct result of the nuclear collision itself. It is essentially composed of the bits of the two nuclei that fly off because of the violent impact of the projectile on the target. Because of the forward momentum carried by the projectile, pre-equilibrium emission is much more forward focused and can produce more energetic particles than statistical emission. The pre-equilibrium emission process has not been studied nearly as extensively as statistical emission. It is our goal in this project to better parameterize and gain a better understanding of this type of emission process.

Two computer models are assisting us in this task. Modgan predicts the statistical emission resulting from our collisions while BUU can be used to predict pre-equilibrium emission. By adding the results of the two models in counts per unit solid angle versus energy plots for proton data, we theoretically should do a reasonable job of reconstructing the data from the actual experiment. We have been able to do this quite well at angles subtended by the forward array. We have yet to complete our analysis at more backward angles, as we need to improve our energy calibrations for detectors outside of the forward array.

We are also examining the coalescence model as an additional guide. The coalescence model operates under the assumption that an alpha particle, composed of two protons and two neutrons, is basically just the sum of its parts. Any four nucleons moving with approximately identical momenta and physically near each other can thought of as collectively being approximately like an alpha particle. Thus, using a mathematical formula, we can coalesce protons into pseudo-alphas particles. This process should work better for particles resulting from pre-equilibrium emission than those from statistical, as the conditions of similar momenta and physical proximity are much more likely to be met for the forward-focused pre-equilibrium particles than the more random statistical process. In counts vs. energy plots for the region of 3 to 18 degrees, coalesced proton data does an excellent job of duplicating experimental alpha particle data at higher energies, where pre-equilibrium emission should be dominant. According to our predictions, the agreement should be less good at backward angles, but this analysis will also have to wait until we have finished our energy calibrations.

Click to see a slide show of Brennan Hughey's work.