Density and temperature in heavy-ion collisions: A test of classical and quantum approaches

Different methods to extract the temperature and density in heavy-ion collisions (HIC) are compared using a statistical model tailored to reproduce many experimental features at low excitation energy. The model assumes a sequential decay of an excited nucleus and a Fermi-gas entropy. We first generate statistical events as a function of excitation energy but stopping the decay chain at the first step. In such a condition the "exact" model temperature is determined from the Fermi-gas relation to the excitation energy. From these events, using quantum fluctuation (QF) and classical fluctuation (CF) methods for protons and neutrons, we derive temperature and density (quantum case only) of the system under consideration. Additionally, the same quantities are also extracted using the double ratio (DR) method for different particle combinations. A very good agreement between the "exact" model temperatures and quantum fluctuation temperatures is obtained. The role of the density is discussed. Classical methods give a reasonable estimate of the temperature when the density is very low, as expected. The effects of secondary decays of the excited fragments are discussed as well.