Nuclear temperature and its dependence on the source neutron-proton asymmetry deduced using the Albergo thermometer

Albergo thermometers with double isotope, isotone, and isobar yield ratio pairs with one proton and/or neutron difference are investigated. Without any extra sequential decay correction, a real temperature value of $4.9\pm 0.5$ MeV is deduced from the yields of the experimentally reconstructed primary hot intermediate mass fragments (IMFs) from ${}^{64}\mathrm{Zn}+{}^{112}\mathrm{Sn}$ collisions at 40 MeV/nucleon using the Albergo thermometer for the first time. An experimental sequential decay correction from the apparent temperatures to the real ones for 12 other reaction systems with different neutron-proton ($N/Z$) asymmetries in the same experiment, ${}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Ni}$ on ${}^{112,124}\mathrm{Sn}$, ${}^{58,64}\mathrm{Ni}$, ${}^{197}\mathrm{Au}$, and ${}^{232}\mathrm{Th}$ at 40 MeV/nucleon, is performed using an empirical correction factor approach of Tsang et al. [Phys. Rev. Lett. 78, 3836 (1997)] with the deduced 4.9-MeV temperature value. The dependence of nuclear temperature on the source $N/Z$ asymmetry is further investigated using these deduced real source temperature values from the present 13 systems. It is found that the deduced real source temperatures at the present source $N/Z$ range show a rather weak dependence on the source $N/Z$ asymmetry. By comparison between our previous results and those from other independent experiments, a consistent description for the $N/Z$ asymmetry dependence of nuclear temperature is addressed.

Figure 1

Yield distributions of the experimentally measured secondary cold fragments (dots) and the reconstructed primary hot IMFs (squares) determined from the collisions of ${}^{64}\mathrm{Zn}+{}^{112}\mathrm{Sn}$ at 40 MeV/nucleon. The AMD results are plotted by circles for comparison. The figure is taken from Ref. [43] with permission.

Figure 2

$T\text{−}{T}_{\mathrm{app}}$ correlation determined from both primary hot and secondary cold fragment yields from the ${}^{64}\mathrm{Zn}+{}^{112}\mathrm{Sn}$ system using different Albergo thermometers. (a) The results are deduced from the thermometers constructed using all available pairs of double isotope, isotone, and isobar yield ratios with one proton and/or neutron difference within the present fragment determination region (see Fig. 1) and with a selection of the relative errors of $T$ and $T_{\mathrm{app}}$ both smaller than 20%. (b) Same as panel (a), but with a limitation of $B>10$ MeV to the thermometers. (c) Same as panel (a), but with both limitations of $B>10$ MeV and involved nuclei with the measured maximum excitation levels greater than 1 MeV/nucleon to the thermometers. For comparison, the real temperature values deduced in our two previous works [21, 48] are also plotted by shaded areas (see the text).

Figure 3

Average temperature $\langle T\rangle$ as a function of source $N/Z$ asymmetry ${\delta }_{IV}$. Solid line is the linear fit of the data points.