# Density and Temperature in Quantum Nuclear Systems

## Abstract

One of the goals of nuclear physics is to study the Equation of State (EOS) of nuclear matter. In order to create the nuclear matter at different densities, we collide different nuclei and detect the fragments after the collisions with different beam energies in the laboratory. Then we extract information about finite nuclei by analyzing the collected data with different assumptions.

As we know, quantum effects play an important role in many systems: the Cosmic Microwave Background (CMB) radiation, the specific heat of different metals, the suppression of density uctuations in a trapped Fermi gas, the enhancement of density fluctuations in a trapped Bose gas, the observation of Fermi pressure in trapped mixed Fermi and Bose gases, etc. The nucleus is a quantum many body system made of strongly interacting fermions, protons and neutrons (nucleons). Therefore, we are dealing with fermions and bosons in the nucleus-nucleus collisions. It is clear that we need to take into account the genuine quantum nature of particles when we extract the physical quantities for the EOS. In the past, some methods have employed the classical limit of low density and high temperature, e.g. double ratio thermometer, while other methods (e.g. two particle correlation) implement some quantum effects but they are only able to calculate one physical quantity, i.e. density p or temperature T.

We would like to develop a method which takes into account the quantum nature of particles to extract the temperature and density of nuclear matter created in heavy-ion collisions. In this dissertation, we propose a new thermometer which includes quantum effects as manifested in quadrupole momentum fluctuations and multiplicity fluctuations of the detected particles. In the same framework, we are able to calculate the density of the studied particles. To test our method, we use the Constrained Molecular Dynamics (CoMD) model, which incorporates the Pauli principle, and we simulate the 40Ca + 40Ca collisions at different beam energies at impact parameter b = 1 fm up to 1000 fm/c. Later, we apply our method to do data analysis and extract the temperatures and densities for fermions and bosons respectively. The Fermi quenching for fermions is found in the simulation data. It has been confirmed in different experimental data. We also studied the possible Bose-Einstein condensate (BEC) for bosons in the same framework with CoMD and CoMD? which includes the boson correlations. Comparing the results with neutron case, we can see that the Coulomb effects play a role in the data analysis. To explore our method even further, we introduce the Coulomb correction for charged particles (both fermions and bosons). A method borrowed from electron scattering was adopted and applied to classical as well as quantum systems. In the model calculations, it was observed that when taking into account those effects, the T of p and n (as well as composite fermions in the classical case) are very similar, while the densities are not affected by the corrections. But for bosons, the temperatures and densities are very similar to the neutron case.