Optimal collision-energy range for realizing macroscopic high-baryon-density matter

We investigate the volume and lifetime of the high baryon-density matter created in heavy-ion collisions and estimate the optimal collision-energy range to realize the high baryon-density region over a large spacetime volume. We simulate central collisions of gold ions for the center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=2.4-19.6\mathrm{G}\mathrm{e}\mathrm{V}$ with a microscopic transport model JAM. We discover that the optimal range is around $\sqrt{s_{NN}}=3-5\mathrm{G}\mathrm{e}\mathrm{V}$, where a baryon density exceeding three times the normal nuclear density is realized with a substantially large spacetime volume. Higher and lower energies are disfavored due to short lifetime and low density, respectively. We also point out that event-by-event fluctuations of the spacetime density profile are large, indicating the importance of the event selection in the experimental analysis.