Source Shape Determination with Directional Correlation Functions

From the recent results of the 4 INDRA campaign at GSI, it has been found that central collisions of heavy symmetric systems lead to the formation of a heavy, hot and expanding composite nucleus, which exhibits pronounced anisotropies in the fragment yields and kinetic energies, as it has been observed in the Au+Au and Xe+Sn systems studied in the energy range of 40 to 150 A.MeV [1]. Both break-up properties and anisotropies have been successfully reproduced [2] within the extension of the standard version of the Berlin statistical multifragmentation model (MMMC, ref. [3]) to non-spherical sources (D-MMMC, ref. [4]), assuming in all cases a prolate source in the coordinate space, elongated along the beam axis. In order to obtain additional evidence for the geometrical properties of the composite system, directional correlation functions in fragment relative velocity have been used, in comparison with models. Here, the correlations functions are generated for the longitudinal and the transversal projections – as regard to the beam axis – of the reduced velocity vred = vrel/ √ Z1 + Z2, where vrel, Z1 and Z2 are the relative velocity and the charges of the two fragments, respectively. In Fig. 1, D-MMMC predictions with three different source elongations are presented: prolate, oblate – i.e. elongated/compressed along the beam with axis ratios 1:0.70 and 1:1.67 – and spherical, with a size Z=79, 6 A.MeV excitation energy and 2.3 A.MeV collective flow. We observe that these functions exhibit a strong sensitivity to the deformation in the magnitude of their depletion at small vred. The correlations between the two biggest fragments of each event that are presented here give the strongest sensitivity within this model. The comparison to the experimental data of Xe+Sn central collisions at 50 A.MeV measured at GSI shows, in both longitudinal and transversal projections, a good agreement with the prolate deformation which had been derived from the study of the fragment anisotropies in yields and kinetic energies [2].