Probing transport theories via two-proton source imaging

Abstract

Imaging technique is applied to two-proton correlation functions to extract quantitative information about the space-time properties of the emitting source and about the fraction of protons that can be attributed to fast emission mechanisms. These new analysis techniques resolve important ambiguities that bedeviled prior comparisons between measured correlation functions and those calculated by transport theory. Quantitative comparisons to transport theory are presented here. The results of the present analysis differ from those reported previously for the same reaction systems. The shape of the two-proton emitting sources are strongly sensitive to the details about the in-medium nucleon-nucleon cross sections and their density dependence.Typeset using REVT E X 1 INTRODUCTION Transport theories have been extensively used to describe the main features of heavy ion collisions at intermediate energies [1][2][3][4]. Successful microscopic models have been based on the Boltzmann-Uehling-Uhlenbeck (BUU) equation, which describes the temporal evolution of the one-body phase-space density under the influence of the nuclear mean field and individual nucleon-nucleon collisions [1]. The importance of such models stems from the connections they provide between observables measured in nucleus-nucleus collisions and microscopic quantities like the nuclear mean fields and the in-medium cross section. Recently, this connection has been exploited to place constraints on the equation of state (EOS) of nuclear matter at densities of 2ρ 0 ≤ ρ ≤ 4ρ 0 , where ρ 0 is the nuclear saturation density [5]. Comparable constraints on the EOS at lower densities require a more detailed understanding of transport phenomena at intermediate energies where the delicate interplay of competing sources of pressure, such as collisions via the residual interaction, govern the collision dynamics [6].Two-proton correlation functions can provide an important test of transport theory [7][8][9], through their sensitivity to the space-time properties of nuclear reactions [10,9,12]. Initial applications of BUU transport theory to two-proton correlation functions at incident energies of E/A<100 MeV were successful and indicated a significant sensitivity of the calculated correlation functions to the in-medium cross section [7][8][9]. The application of such techniques to higher incident energies, however, revealed that there were significant problems in reconciling the stronger calculated correlation functions to the weaker measured ones [9]. These problems, discussed below, led to criticisms that BUU transport theory might be an inadequate theoretical tool for such studies, either due to the neglect of the many body correlations in the BUU approach [8] or due to the neglect of the long lived decays of unstable fragments emitted during a collision [9].In this paper, we largely resolve this issue by showing how more quantitative experimental analyses of two-proton correlations can provide information that can be quantitatively compared to BUU transport...

Angular dependence in proton-proton correlation functions in central40Ca + 40Ca and48Ca + Henzl1, Kilburn2, Chajęcki3 et al. 2012Phys. Rev. CSelf Cite11040View full textAdd to dashboardCite

“…[18,26,31] to extract the source distribution or its size. Results are presented in Table I for both reaction systems, both pair momentum ranges in the laboratory frame, and all three angular selections.…”

“…[18,[23][24][25][26], and describe the source function S(r) by an expression involving three positive definite spline functions, which decreases monotonically with radius. We take the half-width half-maximum of the extracted source profile, r 1/2 , as a measure of the spatial extent of the source.…”

Space-time characterization and collective motion at intermediate energies

“…This normalization factor was used to scale the BUU two-proton source functions to better compare to the imaged source profiles. A comparison between imaged sources (shaded area) and calculated sources (lines) using the BUU transport model [18] is shown. This comparison shows that source profiles obtained from imaging can be used to probe the nucleon-nucleon cross section.…”

“…In an attempt to constrain BUU transport model predictions, two-proton correlation functions measured in central Ar+Ac at E/A=80, 120 and 160 MeV have been imaged [17,18]. The main difficulty in performing this kind of analysis stems from the fact that BUU does not contain any fragment formation mechanisms.…”

“…Based on such considerations, the imaging analyses of the experimental data in Ref. [18] was performed to extract both the profile of the dynamical source and also a normalization constant that can be identified with the λ parameter in Fig. 5.…”