Effects of $P_{\mathrm{tot}}$ gates and velocity gates on light-particle momentum correlation in intermediate-energy heavy-ion collisions

Momentum correlation functions at small relative momenta are calculated for light particles ($n,p,d,t$) emitted from ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at different impact parameters and beam energies within the framework of the isospin-dependent quantum molecular dynamics model complemented by the analytical method of Lednický and Lyuboshitz. We first make sure our model is able to reproduce the FOPI detector data of proton-proton momentum correlation in a wide energy range from $0.4A$ to $1.5A$ GeV. Then we explore more physics insights through the emission times and momentum correlations among different light particles. The specific emphasis is on the effects of total pair momentum among different light particles, impact parameters, and in-medium nucleon-nucleon cross sections. Both two-deuteron and two-triton correlation functions are anticorrelated due to the final state interaction, and they are affected by the in-medium nucleon-nucleon cross section for higher total momentum of the particle pairs, but not for lower momentum. In addition, impact parameter and in-medium nucleon-nucleon cross section dependences of the emission source radii are extracted by fitting the momentum correlation functions. The results indicate that momentum correlation function gating with total pair momentum is stronger for smaller in-medium nucleon-nucleon cross section factor ($\eta$) or impact parameter ($b$). Nonidentical particle correlations ($np, pd, pt$, and $dt$) are also investigated by velocity-gated correlation functions, which can give information on the particles' emission sequence, and the result indicates that heavier ones (deuteron and triton) are, on average, emitted earlier than protons, in the small relative momentum region.

Figure 1

Two-dimensional distribution of yields of proton in the $P_t^0-y^0$ plane for central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reactions. Target and projectile rapidities are given by $y^0=-1$ and $+1$, respectively. The polar angle limits at 8.5 and 26.5 degrees.

Figure 2

Proton-proton correlation functions for the central Au + Au collisions at beam energies from $0.4A$ to $1.5A$ GeV. Experimental data (symbols) are compared to our predictions by the IQMD + FSI model calculation (lines).

Figure 3

Emission time distributions for neutrons (a), protons (b), deuterons (c), and tritons (d) for Au + Au collisions at $0.4A$ GeV with different in-medium nucleon-nucleon cross section factors $\left(\eta =0.2,0.5\right)$ and impact parameters $\left(b=0.0,6.0\text{fm}\right)$.

Figure 4

Average emission times of neutrons (a), protons (b), deuterons (c), and tritons (d) as a function of their c.m. kinetic energy for Au + Au collisions at $0.4A$ GeV.

Figure 5

Momentum correlation functions of particle pairs for Au + Au central collisions at $0.4A$ GeV with different cuts of total particle pair momentum. Open and filled circles correspond to high $P_{\mathrm{tot}}$ and low $P_{\mathrm{tot}}$ cuts, respectively. (a) Neutron pairs gated on $P_{\mathrm{tot}}$: low, 0–0.4 $\mathrm{GeV}/c$; high, 0.8–1.2 $\mathrm{GeV}/c$. (b) Proton pairs gated on $P_{\mathrm{tot}}$: low, 0–0.4 $\mathrm{GeV}/c$; high, 0.8-1.2 $\mathrm{GeV}/c$. (c) Deuteron pairs gated on $P_{\mathrm{tot}}$: low, 0–0.8 $\mathrm{GeV}/c$; high, 1.6–2.4 $\mathrm{GeV}/c$. (d) Triton pairs gated on $P_{\mathrm{tot}}$: low, 0–1 $\mathrm{GeV}/c$; high, 2–3 $\mathrm{GeV}/c$.

Figure 6

Momentum correlation functions of particle-pairs as a function of different $\eta$ factors in central collisions at incident energy $E=0.4A$ GeV. Panels from top to bottom correspond to the correlation functions of neutron-neutron, proton-proton, deuteron-deuteron, and triton-triton pairs gated on low $P_{\mathrm{tot}}$ (left panels) and high $P_{\mathrm{tot}}$ (right panels), respectively.

Figure 7

Gaussian source radius as a function of impact parameter at different $\eta$ factors at fixed incident energy $0.4A$ GeV. Panels (a) to (d) correspond to the Gaussian radius of neutron, proton, deuteron, and triton pairs, respectively.

Figure 8

Momentum correlation functions of nonidentical particle pairs for central Au + Au collisions at $0.4A$ GeV. The upper panel corresponds to proton-deuteron pairs, proton-triton pairs, deuteron-triton pairs, and neutron-proton pairs. The neutron-proton correlation function is scaled down 10 times. The bottom panel shows the ratio of both functions grouped into two velocity bins ($v+$ and $v-$), where $v+$ indicates that the first particle in a pair is faster than the second, and $v-$ is the reverse situation. See texts for details.