F. Lamarche

Evaluation of the volume of intersection of a sphere with a cylinder by elliptic integrals

We have developed an analytic expression for the volume of intersection of any cylinder with any sphere in the usual three-dimensional space. To our knowledge, it is the first time that an exact expression, valid in all cases, is presented for this volume. Here we derive this expression, show how it can be implemented numerically, and give examples of its usefulness for physics, as for example the fast evaluation of the number of participants in relativistic collisions of nuclei.

STUDY OF HIGH ENERGY DENSITIES OVER EXTENDED NUCLEAR VOLUMES VIA NUCLEUS–NUCLEUS COLLISIONS AT THE CERN SPS

Nucleus–nucleus collisions at very high energy are believed to create the conditions for the existence of a new state of matter, the so-called quark–gluon plasma. This possibility depends on the magnitude of the energy density really achieved during the collisions. Estimates of the energy density are model dependent and have been attempted according to various approaches: fire-ball model and Bjorken model. The understanding of the transverse energy flow measurements and of the stopping power helps to define a proper way to estimate the energy density beyond naive approaches. A space- and time-averaged energy density is shown to be a more reliable probe for the QGP search than is a naive estimate of the maximum energy density. The computation is performed within the framework of hydrodynamics. The data considered in this paper were obtained by experiments performed to study nucleus–nucleus collisions at the CERN Super Proton Synchrotron (CERN-SPS). The incident nuclei were accelerated at energies of 60 and 200 GeV/nucleon.