Coulomb corrections to experimental temperatures and densities in Fermi-energy heavy-ion collisions

The quantum-fluctuation method using Coulomb corrections is explored to extract temperatures and densities of hot nuclear systems produced in Fermi-energy heavy-ion collisions. The role of the neutron-proton asymmetry of the system was investigated. Temperature values were observed to not depend on the system neutron-proton asymmetry while a clear dependence is seen for density values. Coulomb corrections have been shown to lower temperature values by almost 2 MeV. On the other hand, density results exhibit a small variation.

Figure 1

(a) Temperature and (b) density values as a function of the $m_s$ bin width for an excitation energy of 5.5 MeV for the QP. All $m_s$ bins are centered around 0.14. Protons are used as the probe particle. The solid line is a linear fit to the data. Error bars represent statistical errors and are not shown when smaller than the symbols.

Figure 2

Temperatures of the gas phase for QPs that differ in neutron-proton asymmetry ($m_s$) as a function of the excitation energy per nucleon. Protons are used as the probe particle. Panels (a) and (b) correspond respectively to results without Coulomb and with Coulomb correction. Symbols correspond to data with $m_s$ bin width of 0.05 while the dashed line represents the extrapolation of data to zero-$m_s$ bin width (as seen in Fig. 1 for $\langle E^{*}/A\rangle =5.5$ MeV). Statistical errors are indicated by the bars and are not shown when smaller than the symbols.

Figure 3

Density as a function of the QP excitation energy per nucleon for different asymmetries $m_s$, as probed by protons in the quantum momentum quadrupole fluctuation method. Panels (a) and (b) correspond respectively to results without Coulomb and with Coulomb correction. Symbols correspond to data with $m_s$ bin width of 0.05 while the dashed line represents the extrapolation of data to zero-$m_s$ bin width (as seen in Fig. 1 for $\langle E^{*}/A\rangle =5.5$ MeV). Error bars corresponding to statistical errors are smaller than the points.

Figure 4

(a) Correlation between the density and the temperature of the system as probed by protons. (b) Energy density versus temperature. All quantities are corrected for Coulomb.