Impact parameter smearing effects on isospin sensitive observables in heavy ion collisions

The validity of impact parameter estimation from the multiplicity of charged particles at low-intermediate energies is checked within the framework of the improved quantum molecular dynamics model. The simulations show that the multiplicity of charged particles cannot estimate the impact parameter of heavy ion collisions very well, especially for central collisions at the beam energies lower than $\sim 70$ MeV/u due to the large fluctuations of the multiplicity of charged particles. The simulation results for the central collisions defined by the charged particle multiplicity are compared to those by using impact parameter $b=2$ fm and it shows that the charge distribution for ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ at the beam energy of 50 MeV/u is different evidently for two cases; and the chosen isospin sensitive observable, the coalescence invariant single neutron to proton yield ratio, reduces less than 15% for neutron-rich systems ${}^{124,132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at $E_{\mathrm{beam}}=50$ MeV/u, while the coalescence invariant double neutron to proton yield ratio does not have obvious difference. The sensitivity of the chosen isospin sensitive observables to effective mass splitting is studied for central collisions defined by the multiplicity of charged particles. Our results show that the sensitivity is enhanced for ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ relative to that for ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$, and this reaction system should be measured in future experiments to study the effective mass splitting by heavy ion collisions.

Figure 1

Upper panels show the integrated multiplicity distribution (black solid circle), as well as the multiplicity distribution for each impact parameter (colored lines). Bottom panels show the ${\overline{b}}_{\mathrm{real}}$ (red solid square) and ${\overline{b}}_{\mathrm{est}}$ (black solid circle) as a function of $M$ in ImQMD model, the contour plots are for event number at given $b$ and $M$. (a) and (d) are for Cascade mode, (b) and (e) are for Vlasov mode, (c) and (f) are for Full mode. All the results are obtained with SkM* for ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ at $E_{\mathrm{beam}}=50$ MeV/u.

Figure 2

Symbols are for ${\overline{b}}_{\mathrm{real}}$ (red solid square) and ${\overline{b}}_{\mathrm{est}}$ (black solid circle) as a function of $M$, the contour plots are for $N(b,M)$. Panels (a)–(d) are for the beam energy of 35, 50, 70, and 120 MeV/u.

Figure 3

The charge distributions obtained with $b=2$ fm (open circle) and ${\overline{b}}_{\mathrm{est}}$ (solid circle), blue curves with symbols represent the results of $E_{\mathrm{beam}}=50$ MeV/u and the red curves with symbols represent the results of $E_{\mathrm{beam}}=120$ MeV/u.

Figure 4

The CI-R($n/p$) ratios as a function of kinetic energy per nucleon, for ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ (left), ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ (middle), and ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ (right) obtained with SkM* (blue curve with circles) and SLy4 (red curve with diamonds). Open symbols are results obtained with $b=2$ fm, and solid symbols are for ${\overline{b}}_{\mathrm{est}}<0.2b_{\max }$. Upper panels are the results for $E_{\mathrm{beam}}=50$ MeV/u and bottom panels are for $E_{\mathrm{beam}}=120$ MeV/u.

Figure 5

CI-DR($n/p$) as a function of kinetic energy per nucleon. Left panels are the results for $a={}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and right panels are for $a={}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$, upper panels are for 50 MeV/u and bottom panels are for 120 MeV/u. The legend of curves is similar to Fig. 4.