Double isotope-ratio thermometers: The influence of emission time scales

Isotope ratios are examined for several inclusive studies of light-ion and ${}^{14}\mathrm{N}$-induced reactions that involve significantly different reaction dynamics and bombarding energies. For adjacent isotope pairs that have one nuclide with $N<Z$, the ratios show a strong dependence on emission angle. Pairs with only $N>~Z$ isotopes depend weakly on $N/Z$ of the colliding system, but are otherwise not sensitive to angle of observation or beam energy. The double isotope-ratio method of Albergo has been used to determine apparent nuclear temperatures from these data. When empirically corrected for secondary decay effects, values in the range $T_{\mathrm{iso}}\approx 4.0\pm 0.4$ MeV are found for forward-angle measurements and $T_{\mathrm{iso}}\approx 2.4\pm 0.4$ MeV for backward angles. The double isotope-ratio temperatures are found to be systematically lower than temperatures derived from spectral shape analyses and Fermi gas estimates. This difference suggests the importance of time evolution in the application of temperature gauges. Relative emission-time differences between neutron-deficient and heavier isotopes arise from both nonequilibrium emission processes and cooling of the system during statistical decay. The importance of secondary feeding is also pointed out. These effects are illustrated by expanding, emitting source calculations.