Rapidity dependency of (Anti)-deuteron Coalescence in Au-Au collisions

The coalescence of protons and neutrons into deuterons is sensitive to the space-time extent of the baryon freeze-out region. The coalescence parameter and the phase space density recast the information contained in the proton and deuteron spectra into ``chemical" and ``dynamic" terms. The phase space density is sensitive to the chemical potential and the temperature of the system. The coalescence parameter $B_2$ can be interpreted in terms of a ``volume of homogeniety" which depends upon the temperature of the system and the radial flow. The large rapidity and $p_T$ coverage with good particle identification of the BRAHMS spectrometers allow us to measure the rapidity dependence of the volume, which is proportional to $1/B_2$, and the phase space density of the (anti)-proton source for central Au+Au collisions. We find that $B_2(p_T)$ is almost independent of rapidity and beam energy. Interpreting $1/B_2$ as a volume gives numbers that are very close to HBT data and a size which steadily drops with $p_T$. We find that $B_2(p_T)$ is the same for protons and antiprotons. The phase space density has a weak rapidity dependence but varies rapidily with energy. These results in conjunction with other forward rapidity data start to give us a picture of the longitudinal evolution of the source at RHIC energies. Supported by NSF CAREER award 0449913