Constrained caloric curves and phase transition for hot nuclei

14 pages, 5 figures, accepted in Physics Letters BSimulations based on experimental data obtained from multifragmenting quasi-fused nuclei produced in central $^{129}$Xe + $^{nat}$Sn collisions have been used to deduce event by event freeze-out properties in the thermal excitation energy range 4-12 AMeV [Nucl. Phys. A809 (2008) 111]. From these properties and the temperatures deduced from proton transverse momentum fluctuations, constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonic behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a first order phase transition for hot nuclei