J.P. Lestone

The nuclear level density plays a central role in our theoretical modeling of the particle emission from, and fissioning of, hot compound nuclei. The density of nuclear levels as a function of thermal excitation energy (U) is often estimated assuming a weakly interacting Fermi-gas, and written as . Recent theoretical predictions of a temperature dependence of the Fermi gas level density parameter have been obtained numerically using the Thomas-Fermi (TF) approximation.¹ This work included a spatial and temperature dependence of the effective nucleon mass. We have considered these complexities associated with the effective mass of nucleons in atomic nuclei and have used the local density approximation (LDA)² to obtain the following expression for the temperature dependence of the inverse level density parameter (K=A/a)

(1)

The dashed lines in Fig. 3-5.1 show K(T) determined using Eq. (1) for systems with mass numbers 60 and 210. These results cannot be compared directly with the TF results shown in Fig. 1 of Ref. 1, since Shlomo and Natowitz adopted the definition a_eff(T)= A/K_eff(T) = U/T². The reflection a ~ U / T² is, however, only valid if da/dU=0 (see Ref. 2) and thus aa_eff. From Eq. (1) one can show that

(2)

Fig. 3.5-1 shows numerical TF calculations of K_eff(T) from Ref. 1 (solid lines) and K_eff(T) obtained using equations (1) and (2) (dashed-dotted lines). The excellent agreement between these two sets of calculations leads us to conclude that the LDA adequately describes the temperature dependence of the TF calculations of the nuclear level density parameter.

Fig. 3.5-1. K(T) determined using Eq. (1) (dashed lines); TF calculations of K_eff(T) from Ref. 1 (solid lines) and K_eff(T) obtained using equations (1) and (2) (dashed-dotted lines).