Isobaric Yield Ratio Difference in Heavy-ion Collisions, and Comparison to Isoscaling

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 ratio. 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 with a plateau in the small mass fragments plus an increasing part in the fragments of relatively larger 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 little. The difference between the IB- and IS-$\Delta\mu/T$ is explained by the isoscaling parameters being 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 disobeys 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.Comment: 6 pages, 6 figures, mistake of reference correcte

Amplification effects in optomechanics via weak measurement

We revisit the scheme of single-photon weak-coupling optomechanics using post-selection, proposed by Pepper, Ghobadi, Jeffrey, Simon and Bouwmeester [Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the dynamical evolution. Positive and negative amplification effects of the displacement of the mirror's position can be generated when the Kerr phase is considered. This effect occurs when the post-selected state of the photon is orthogonal to the initial state, which can not be explained by the usual weak measurement results. The amplification effect can be further modulated by a phase shifter, and the maximal displacement state can appear within a short evolution time