Tracing the evolution of temperature in near Fermi energy heavy ion collisions

The kinetic-energy variation of emitted light clusters has been employed as a clock to explore the time evolution of the temperature for thermalizing composite systems produced in the reactions of 26A, 35A, and 47A MeV ${}^{64}\mathrm{Zn}$ with ${}^{58}\mathrm{Ni}$, ${}^{92}\mathrm{Mo}$, and ${}^{197}\mathrm{Au}$. For each system investigated, the double-isotope ratio temperature curve exhibits a high maximum apparent temperature, in the range of 10–25 MeV, at high ejectile velocity. These maximum values increase with increasing projectile energy and decrease with increasing target mass. The time at which the maximum in the temperature curve is reached ranges from 80 to 130 fm/c after contact. For each different target, the subsequent cooling curves for all three projectile energies are quite similar. Temperatures comparable with those of limiting temperature systematics are reached 30 to 40 fm/c after the times corresponding to the maxima, at a time when antisymmetrized molecular dynamics transport model calculations predict entry into the final evaporative or fragmentation stage of deexcitation of the hot composite systems. Evidence for the establishment of thermal and chemical equilibrium is discussed.

Figure 1

Slope temperatures from three source fits to the experimental spectra. Open circles represent apparent temperatures for the emission from the IV source. Filled circles represent apparent temperatures for the emission from the TLF source.

Figure 2

Correlation of average emission time with surface velocity for early emitted nucleons as calculated by the AMD-V code. Solid symbols depict the results for the nine different reactions as labeled. Dashed lines indicate the linear fits assumed for time calibrations.

Figure 3

$T_{\mathrm{HHe}}$ vs surface velocity. See text. Vertical bars are at 3.25 cm/ns, taken to be limit for time derivations. Solid lines indicate fits to data.

Figure 4

$T_{\mathrm{HHe}}$ vs time. See text. Times terminate at points corresponding to surface velocities of 3–3.5 cm/ns.

Figure 5

Relationship between $T_{\mathrm{HHe}}$ peak values and $T_{\mathrm{slope}}$ of the IV source. The dotted line represents the locus of equality of the two temperatures. The solid squares show results for the reactions with Au targets. The solid circles show results for the reactions with Mo targets. The open circles show results for reactions with Ni targets.

Figure 6

Calculated values for the correlation of $A_{\mathrm{part}}/A_{\mathrm{proj}}$ and $\rho /{\rho }_0$ consistent with measured peak temperatures.