Dana R. Burd's pictureDana R. Burd

Hope College

Dr. Mader

Supported by the NSF-REU

When a nuclear collision takes place the nuclei involved interact through individual nucleon-nucleon collisions and the strong nuclear force. In a heavy-ion collision a "hot" high- density, high-energy region is formed where the two nuclei contact each other. Within this region and throughout the collision, particles are being created, decaying, re-scattering off other particles, and being re-absorbed into the colder (low- energy) regions of the nuclei. Some of the particles move into excited states much like a nucleus itself would become excited into a different energy state.

Pions are created in these collisions through the excitation of a nucleon to a delta particle. The delta particle then decays into a pion and a nucleon. We can look at how the nucleons and pions interact with each other in nuclear collisions to gain a better understanding of how nuclei behave. We were interested in where the pions were created, where and with how much energy they were emitted from the collision zone, and their behavior during the reaction.

The Boltzmann-Uehling-Uhlenbeck Model (BUU) was used to simulate all collisions. BUU is a mathematical model that simulates heavy-ion collisions by basically solving Newton's Laws for particles moving in a nuclear and Coulomb field while experiencing two-particle collisions.

Particle Flow was used to look at the emission direction of a particular set of particles in the XZ-plane. A typical flow plot for would have on the vertical axis and Rapidity on the horizontal axis. Rapidity is just a measure of the Z-velocity. When two nuclei collide, nucleons (protons and neutrons) and other particles are emitted from the reaction. As the nuclei continue to pass through one another, the nucleons begin moving in a flow pattern which is characterized by negative rapidity values having positive , and positive rapidity values having negative .

The nucleons always produce these flow patterns in all energies we studied. Note that the nuclei do not reform after a central collision. The nuclei tend to blow apart because the collisions are head-on. This causes the nucleons to disperse out over space creating low density matter. In a peripheral (b=7) collision the nuclei only glance off each other producing a much less violent reaction with less flow, and leaving the nuclei much more intact than in a head-on collision.

We looked at pion flow patterns for: similarities to the nucleon flow, affects of charge interactions, and basically anything to help us better understand how the pions were behaving within the collision. We expected flow patterns for the negative pions at 400 MeV/A to be similar to nucleon flow because there would be an attractive Coulomb interaction between the positively charged protons and negatively charged pions causing them to be drug along with the nucleons when emitted. For both central and peripheral collisions we found this to be true. This argument would predict that repulsion between protons and positive pions would result in opposite flow or (antiflow) for both central and peripheral collisions at 400 MeV/A. This was not true for central collisions. This can be explained because the nuclear matter is dispersed out in space due to the violence of the collision, thus dispersing charge and reducing the Coulomb effect.

The high-energy collisions display primarily the same features for flow and antiflow. The peripheral collisions show more defined antiflow patterns for pi+ and pi- because the high- energy causes the nuclei to glance off each other and continue in their relative direction of motion too quickly for the Coulomb interaction effect to be large.

To better understand our flow results and the role of the Coulomb interaction we ran a version of BUU that turned off the effects of pion re-scattering and re-absorption so only the Coulomb interaction would effect the pions. The negative pions at both energies produced flow patterns and the positive pions produced antiflow patterns as we expected.

We also studied the actual emission angles by plotting pion counts as a function of the angles Theta and Phi, which cover all 4p-space. This allowed us to develop a three-dimensional view of where the pions were being emitted. A typical emission angle plot shows a two-dimensional view of pion counts indicated by color and Theta and Phi on the Y and X axes. These plots displayed an upside-down "V" shape which we came to understand as the characteristic for flow. Antiflow patterns displayed a right- side-up "V" shape. A three-dimensional picture of these plots would show planar disc where the pions were being emitted. All of our emission angle results supported our flow findings.

Many of our results were explained with the effects of the Coulomb interaction between the nucleons and pions. However, when we turned off re-scattering and re-absorption, we saw different results. This suggests that some other effects are taking place. To gain a more complete understanding of the pion behavior in heavy-ion collisions we are currently working on a set of time instance plots that will give us before and after pictures to trace the paths of the pions throughout the reaction. We will also look at collisions in which the Coulomb interaction is turned off in order to study the pion re-scattering and re- absorption effects more completely. Another future study may be looking at Energy as a function of time for various flow parameters.