## Isobaric Yield Ratio Difference in Heavy-ion Collisions, and Comparison to Isoscaling    [PDF]

Chun-Wang Ma, Shan-Shan Wang. Yan-Li Zhang, Hui-Ling Wei
An isobaric yield ratio difference (IBD) method is proposed to study the ratio of the difference between the chemical potential of neutron and proton to temperature ($\Delta\mu/T$) in heavy-ion collisions. The $\Delta\mu/T$ determined by the IBD method (IB-$\Delta\mu/T$) is compared to the results of the isoscaling method (IS-$\Delta\mu/T$), which uses the isotopic or the isotonic yield ratios. Similar distributions of the IB- and IS-$\Delta\mu/T$ are found in the measured 140$A$ MeV $^{40,48}$Ca + $^{9}$Be, and the $^{58,64}$Ni + $^{9}$Be reactions. The IB- and IS-$\Delta\mu/T$ both have a distribution of a plateaus in the small mass fragments plus an increasing part in the fragment of relative lager mass. The IB- and IS-$\Delta\mu/T$ plateaus show dependence on the $n/p$ ratio of the projectile. It is suggested that the height of the plateau is decided by the difference between the neutron density ($\rho_n$) and the proton density ($\rho_p$) distributions of the projectiles, and the width shows the overlapping volume of the projectiles in which $\rho_n$ and $\rho_p$ change very small. The difference between the IB- and IS-$\Delta\mu/T$ is explained as that the isoscaling parameters are constrained by the many isotopes and isotones, while the IBD method only uses the yields of two isobars. It is suggested that the IB-$\Delta\mu/T$ is more reasonable than the IS-$\Delta\mu/T$, especially when the isotopic or isotonic ratio disobey the isoscaling. As to the question whether the $\Delta\mu/T$ depends on the density or the temperature, the density dependence is preferred since the low density can result in low temperature in the peripheral reactions.
View original: http://arxiv.org/abs/1303.2924