Testing the constant-temperature approach for the nuclear level density

Abstract

The nuclear temperature is calculated from the derivative of the logarithm of the level densities in $^{\text{60-62}}\mathrm{Ni}$ and $^{\text{170-172}}\mathrm{Yb}$. The latter are obtained within a method, which includes exact pairing for the levels around the Fermi surface in combination with the independent particle model for the rest of the single-particle spectrum. It is found that the increase in this temperature is relatively slow up to the excitation energy ${E}^{*}={E}_{f}^{*}$ so that, at 0 $<{E}^{*}\ensuremath{\le}{E}_{f}^{*}$, the level density can be described well by the constant-temperature model. The values of ${E}_{f}^{*}$ are found to be 10 MeV for $^{\text{170-172}}\mathrm{Yb}$ and 20 MeV for $^{\text{60-62}}\mathrm{Ni}$, that is much higher than the particle separation threshold. Within this energy interval, the constant temperature is found to be around 0.5 MeV for $^{\text{170-172}}\mathrm{Yb}$, whereas for $^{\text{60-62}}\mathrm{Ni}$ it can be any value between 1.3 and 1.5 MeV, in excellent agreement with the recent experimental finding. It is also shown that pairing plays an important role in maintaining this constant temperature at low excitation energy.