In this thesis, our focus is on studying particle correlations in heavy-ion collisions to gaininsights into nuclear systems in the final state reaction. Understanding these correlations is crucial for accessing the geometry, phase-space features, and time development of the collision’s final stages. We present two approaches to extract the relative distribution of particles at the last moment of the collision: the Gaussian parametrization source (GPS) and the deblurring method. In the GPS approach, we assume a Gaussian form source to approximate two-particle correlation functions using the Koonin-Pratt (KP) convolutional formula. This formula convolves the relative emission source with the squared two-particle relative wave function. We apply the approach to study the correlations of low-velocity alphas. We start by constructing the scattering wave function for the alpha-alpha pair by solving the Schrödinger equation, incorporating a potential tailored to match the measured phase shifts of the system. With this wave function, we interpret available data on alpha-alpha correlations in terms of emitting sources. In the deblurring approach, we propose using the Richardson-Lucy (RL) optical deblur- ring algorithm to deduce a source from the correlation function. The RL algorithm, derived from probabilistic Bayesian considerations, requires the optical object, image distributions, and convolution kernel to be positive definite. Fortunately, these conditions are satisfied by the corresponding quantities of interest within the KP formula. We demonstrate the success of the RL algorithm in restoring emitting sources from measured d–? correlations. Furthermore, we extend the deblurring approach to another field of nuclear physics by utilizing the RL algorithm on experimental nuclear physics data, leveraging only the observed energy spectrum and the detector’s response matrix (also known as the transfer matrix). This technique provides access to information regarding the shell structure of particle-unbound systems through the measured decay energy spectrum, which is not readily attainable through traditional approaches like chi-square fitting. In pursuit of the same objective, we develop a machine learning model that employs a deep neural network (DNN) classifier to identify resonance states from the measured decay energy spectrum. We evaluate the performance of both methods using simulated data and experimental measurements. Subsequently, we apply both algorithms to analyze the decay energy spectrum of 26O, as measured via invariant mass spectroscopy. Both the deblurring and DNN approaches indicate the presence of three peaks in the raw decay energy spectrum of 26O. Finally, we employ the transport model in this thesis to analyze two-proton (p-p) correlations in heavy-ion collisions at low incident energies per nucleon (E/A). Specifically, we utilize the Boltzmann-Uehling-Uhlenbeck (BUU) transport model to simulate the p–p source. Subsequently, we employ the source and the p-p kernel within the KP formula to calculate the correlations. Through a comparison between the correlations obtained from the BUU simulation and the RL algorithm, we gain a better understanding of the influence of fast and slow emissions on the measured correlations. We compute the angle-averaged and quadrupole components of the p-p source for the Ar + Sc and Xe + Au reactions at ?/? =80 MeV. These sources are computed considering both momentum-independent and momentum-dependent nuclear equation of states (EOS), enabling us to observe the effect of the momentum-dependent EOS on the quadrupole component source.
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