Impact Parameter-Gated Two-Proton Intensity Interferometry in Intermediate Energy Heavy Ion Collisions.

Impact parameter gated two-proton intensity interferometry is employed to probe the space-time structure of emitting sources created in intermediate energy heavy ion collisions. The Koonin-Pratt formalism relating the single -proton phase space population density to the two-proton correlation function is discussed. Schematic calculations illustrate the sensitivity of the correlation function to source size and lifetime. Single- and two-proton yields, used to construct the two-proton correlation function, were measured with a high-resolution 56-element hodoscope for the reaction ^{36}Ar + ^ {45}Sc at E/A = 80 MeV. Coincident measurement of charged particle yields in a 4pi detector array provided information about the impact parameter of the collision. For both central and peripheral events, proton correlations are larger (indicative of a smaller space-time extent for the source) for proton pairs with larger total momentum. For central events, the total momentum dependence is stronger than for peripheral events, indicating a distinct reaction evolution for events with different impact parameter. Methods for comparing impact parameter-gated data to theoretical predictions are discussed, and predictions of a model based upon the Boltzmann-Uehling-Uhlenbeck (BUU) equation are compared to experimental correlation functions. For central collisions, the total momentum dependence of the correlations is well reproduced. For peripheral collisions, this dependence is underpredicted, suggesting that the model may be deficient in its description of peripheral heavy ion collisions. Differences between longitudinal and transverse correlation functions allow independent extraction of source size and lifetime. Potential difficulties in the search for such differences are discussed. For intermediate energy protons emitted from central ^{36} Ar + ^{45}Sc collisions at E/A = 80 MeV, a source with a Gaussian radius and lifetime of about 4.5 +/- 1.0 fm and 30 +/- 10 fm/c is indicated. For the reverse kinematics reaction ^{129}Xe + ^{27}Al at E/A=31 MeV, we observe lifetimes of about 1700 fm/c and 1200 fm/c for proton pairs with total momentum P >= 480 MeV/c and P >= 580 MeV/c, respectively; this behaviour is consistent with emission from a cooling system.