Isobaric yield ratio difference between the $140A$ MeV ${}^{58}\mathrm{Ni}\mathrm{+}{}^9\mathrm{Be}$ and ${}^{64}\mathrm{Ni}+{}^9\mathrm{Be}$ reactions studied by the antisymmetric molecular dynamics model

Background: The isobaric yield ratio difference (IBD) method is found to be sensitive to the density difference of neutron-rich nucleus induced reaction around the Fermi energy.

Purpose: An investigation is performed to study the IBD results in the transport model.

Methods: The antisymmetric molecular dynamics (AMD) model plus the sequential decay model gemini are adopted to simulate the $140A$ MeV ${}^{58,64}\mathrm{Ni}+{}^9\mathrm{Be}$ reactions. A relative small coalescence radius $R_c=$ 2.5 fm is used for the phase space at $t=$ 500 fm/c to form the hot fragment. Two limitations on the impact parameter ($b1=0–2$ fm and $b2=0–9$ fm) are used to study the effect of central collisions in IBD.

Results: The isobaric yield ratios (IYRs) for the large-$A$ fragments are found to be suppressed in the symmetric reaction. The IBD results for fragments with neutron excess $I=$ 0 and 1 are obtained. A small difference is found in the IBDs with the $b1$ and $b2$ limitations in the AMD simulated reactions. The IBD with $b1$ and $b2$ are quite similar in the AMD + GEMINI simulated reactions.

Conclusions: The IBDs for the $I=0$ and 1 chains are mainly determined by the central collisions, which reflects the nuclear density in the core region of the reaction system. The increasing part of the IBD distribution is found due to the difference between the densities in the peripheral collisions of the reactions. The sequential decay process influences the IBD results. The AMD + GEMINI simulation can better reproduce the experimental IBDs than the AMD simulation.

Figure 1

The cross-sectional distributions of fragments with $I$ from 0 to 3, which are produced in the $140A$ MeV ${}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reactions. The triangles and circles denote the calculated cross sections with parameter ranges $b1$ ($b$ = 0–2 fm) and $b2$ ($b$ = 0–9 fm), respectively. The open and full symbols denote the results for the AMD and AMD + GEMINI calculations. The measured cross sections of fragments [18] are plotted as squares.

Figure 2

The cross-sectional distributions of fragments from $I=$ 0 to 3, which are produced in the $140A$ MeV ${}^{64}\mathrm{Ni}+{}^9\mathrm{Be}$ reactions. The triangles and circles denote the calculated cross sections with impact parameter ranges $b1$ ($b=$ 0–2 fm) and $b2$ ($b=$ 0–9 fm), respectively. The open and full symbols denote the results for the AMD and AMD + gemini calculations. The measured results by Mocko et al. [18] are plotted as squares.

Figure 3

The isobaric yield ratio for the $I=$ 0 and 1 chains in the $140A$ MeV ${}^{58,64}\mathrm{Ni}+{}^9\mathrm{Be}$ reactions. The measured results are plotted as squares. The triangles and circles denote the calculated results by AMD with the impact parameter limitations $b1$ (0–2 fm) and $b2$ (0–9 fm), respectively. The open and full symbols denote the results for the ${}^{58}\mathrm{Ni}$ and ${}^{64}\mathrm{Ni}$ reactions, respectively.

Figure 4

The isobaric yield ratio for the $I=$ 0 and 1 chains in the $140A$ MeV ${}^{58,64}\mathrm{Ni}+{}^9\mathrm{Be}$ reactions. The isobaric yield ratio for the measured results are plotted as squares. The triangles and circles denote the AMD + gemini simulated results with impact parameter ranges $b1$ (0–2 fm) and $b2$ (0–9 fm), respectively. The open and full symbols denote the results for the ${}^{58}\mathrm{Ni}$ and ${}^{64}\mathrm{Ni}$ reactions, respectively.

Figure 5

The isobaric yield ratio difference (IBD) for the $I=$ 0 [in panel (a)] and $I=$ 1 [in panel (b)] chains between the $140A$ MeV ${}^{58,64}\mathrm{Ni}$ + ${}^9\mathrm{Be}$ reactions. The IBDs for the measured results are plotted as squares. The triangles and circles denote the calculated results with impact parameter ranges $b1$ (0–2 fm) and $b2$ (0–9 fm), respectively. The open and full symbols denote the results for the AMD and AMD + gemini simulations, respectively.