#### Date of Award

2011

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Degree Program

Physics

#### University

Michigan State University

#### First Advisor

Bill Lynch, Pd.D.

#### Keywords

Nuclear reactions, transport theory, equation of state, symmetry energy, nucler astrophysics

#### Subject Categories

Nuclear | Physical Sciences and Mathematics | Physics

#### Abstract

In an experiment at NSCL, proton-proton (*p*-*p*) correlation functions were measured in ^{40}Ca+^{40}Ca and ^{48}Ca+^{48}Ca reactions, both at E/A = 80 MeV. The High Resolution Array (HiRA) detected light particles with excellent energy (**<**200 keV) and angular (**~**0.2^{o}) resolution. The MSU 4**pi **Array covered 77% of the total 4**pi **solid angle and was used to determine the impact parameter for collisions using transverse energy (E_{t}) as the relevant observable.

Two-particle correlation functions are employed in this work to measure the space-time extent of the source. A transport model previously predicted that the *p-**p* correlation functions would be sensitive to the density dependence of the symmetry energy, while other work had already shown the *p-**p* correlation functions to be sensitive to nucleon-nucleon (*NN*) in-medium cross sections.

More detailed calculations performed in this dissertation indicate that that sensitivity to the symmetry energy is subtle. Much less subtle is the dependence of the *p-**p* correlation functions on the laboratory angle of the total momentum vector of the two protons. At forward angles, where the correlation function is sensitive to the projectile spectator, the measured correlation functions appear consistent with sources that are very extended in space-time. The space-time extent of these sources exceed the predictions of BUU transport calculations, which are the main tool for probing the symmetry energy via correlation functions. At backward angles, where it is sensitive to the expanding participant source, the observed sources are more compact; there the trends can be reproduced by the BUU calculations.

At the most forward angles, we note that the qualitative trends of the correlation function with angle and energy run counter to the qualitative trends of smaller sources for particles with higher momentum typically reported by published work in this incident energy domain. While we observe this latter trend at backward angles, the momentum dependence in the source size observed at forward angles is comparatively weak and trends in the opposite direction, with the most energetic protons displaying the weakest correlation functions. These energetic protons are closer to the expected velocity for projectile spectator remnants, suggesting their origins in the decay of these remnants.

Further analysis of the correlation functions with gates on rapidity and transverse momentum allowed a clean exclusion of projectile decay. After excluding this kinematic domain, it was possible to obtain data that can be compared to a BUU transport model. This model, however, predicted a weak sensitivity to the density dependence of the symmetry energy that is too small to be experimentally probed. Consistent with prior work, we find a strong sensitivity to the *NN* in-medium cross section reduction as well as a strong previously unobserved sensitivity to the production of light clusters. Comparisons between the BUU calculations establish the sensitivity of data to these transport quantities as well as the range of values for these transport quantities that may be consistent with the present measurements.

#### Recommended Citation

Kilburn, Micha A. '95, "Proton-Proton Correlation Functions as a Probe to Reaction" (2011). *Doctoral Dissertations*. 17.

https://digitalcommons.imsa.edu/alumni_dissertations/17