Effect of in-medium nucleon-nucleon cross section on proton-proton momentum correlation in intermediate-energy heavy-ion collisions

The proton-proton momentum correlation function from different rapidity regions is systematically investigated for the Au + Au collisions at different impact parameters and different energies from $400A$ MeV to $1500A$ MeV in the framework of the isospin-dependent quantum molecular dynamics model complemented by the Lednický-Lyuboshitz analytical method. In particular, the in-medium nucleon-nucleon cross-section dependence of the correlation function is brought into focus, while the impact parameter and energy dependence of the momentum correlation function are also explored. The sizes of the emission source are extracted by fitting the momentum correlation functions using the Gaussian source method. We find that the in-medium nucleon-nucleon cross section obviously influences the proton-proton momentum correlation function, which is from the whole-rapidity or projectile or target rapidity region at smaller impact parameters, but there is no effect on the mid-rapidity proton-proton momentum correlation function, which indicates that the emission mechanism differs between projectile or target rapidity and mid-rapidity protons.

Figure 1

Production of interacting particles 1 and 2 [42].

Figure 2

Momentum correlation function of proton pairs for Au + Au collisions at $1A$ GeV with different in-medium reduction factors. From top to bottom, each panel corresponds to impact parameters, namely, $b=3$, 6, 9 and 12 fm, respectively. From left to right, each panel represents the correlation function constructed for the proton pairs within whole rapidity, mid-rapidity and projectile or target rapidities, respectively.

Figure 3

(a) $C_{pp}$ strength at 20 MeV/$c$ as a function of the incident energy, which is calculated at an impact parameter of $b=3$ fm and in-medium reduction factor of $\eta =0.2$; (b) $C_{pp}$ strength at 20 MeV/$c$ as a function of the impact parameter, which is calculated at $1A$ GeV and the in-medium reduction factor $\eta =0.2$; (c) $C_{pp}$ strength at 20 MeV/$c$ as a function of the in-medium reduction factor, which is calculated at $b=3$ fm and $1A$ GeV. Note that the red circles correspond to the mid-rapidity cut and the blue squares to the whole-rapidity cut.

Figure 4

Gaussian source radius as a function of the incident energy for different $\eta$ factors at fixed impact parameter $b=3$ fm (left column), as a function of impact parameter with different $\eta$ factors (middle column), and as a function of in-medium nucleon-nucleon cross-section reduction factor at different impact parameter (right column). From top to bottom are the Gaussian radius of free protons emitted from the whole-rapidity window, the mid-rapidity window, and the target or projectile rapidity window, respectively.

Figure 5

The $\chi$-square obtained from the fits of the proton-proton momentum correlation function by the Lednický et al. analytical formalism calculation as a function of the radius of the Gaussian source. (a)–(d) Each panel represents different fixed impact parameters with different $\eta$ factor; (e)–(h) each panel represents different fixed $\eta$ factors at different impact parameters.

Figure 6

(a)–(c) Blast-wave fitting to $p_T$ spectra of protons in the mid-rapidity region: (a) incident energy dependence for $b=3$ fm and $\eta =0.2$, (b) impact parameter dependence at $E=1A$ GeV and $\eta =0.2$, and (c) in-medium cross-section dependence at $b=3$ fm and $1A$ GeV. (d)–(f) The fitted radial flow parameter ($\beta$) as a function of (d) beam energy, (e) impact parameter at $1A$ GeV and $\eta =0.2$, and (f) in-medium cross-section reduction factor at $1A$ GeV and $b=3$ fm.

Figure 7

Correlation strength at $q=20$ MeV/$c$ as a function of the radial flow parameter ($\beta$) in different conditions. (a) Beam energy is a variable as shown in figure, at fixed $b=3$ fm and $\eta =0.2$; (b) impact parameter is a variable as shown in figure, at fixed $E=1A$ GeV and $\eta =0.2$; and (c) the in-medium nucleon-nucleon cross-section reduction factor is a variable as shown in figure, at fixed $E=1A$ GeV and $b=3$ fm.