Temperature Dependence of the Nuclear Energy in Relativistic Mean-Field Theory

Abstract

Self-consistent relativistic mean-field (RMF) calculations with the NL3 parameter set were performed for 171 spherical even-even nuclei with 16 ≤ A ≤ 224 at temperatures in the range 0 ≤ T ≤ 4 MeV. For this sample of nuclei single-particle level densities are determined by analyzing the data obtained for various temperatures. A new shell-correction method is used to evaluate shell effects at all temperatures. The single-particle level density is expressed as function of mass number A and relative isospin I and compared with previous estimates.In fission dynamics and the decay of compound nuclei 1 as well as in all kinds of transport theories, the proper knowledge of the nuclear single-particle level density is needed. The aim of the present paper is to determine this quantity using the RMF theory 2 with the NL3 3 set of parameters and a revised version of the Strutinsky shell correction method.4 The smooth part of nuclear energy is evaluated in our approach by an averaging in particle-number space while in the traditional Strutinsky method 5 the smoothing is performed in single-particle energy space. The advantage of the new approach consists in that the particle number is exactly conserved which was only the case on the average in the old Strutinsky method.Mass-number and isospin dependence of the single-particle level density obtained in the RMF approach with the NL3 parameters 3 were already discussed in Ref.6 . Using the Strutinsky shell-correction method 5 we had "removed" shell effects from the selfconsistent RMF energies in a similar way as done in Refs. 7,8,9 for the Gogny hamiltonian 10 and the RMF-NL3 model. 3 Estimates of the macroscopic binding energies (i.e. free of shell and pairing effects) obtained in such a way at zero temperature were used as a reference to calculate the change of the total energies with temperature. To simplify the calculations, the temperature dependence of the shell-correction energy was approximated in 6 by an analytical function 11 instead of explicitly evaluating the Strutinsky shell correction at finite temperatures.

Constraints on the time scale of nuclear breakup from thermal hard-photon emission

“…9. The temperature increases smoothly with the excitation energy, the (ǫ ⋆ ,T) pairs obtained are below the expected Fermi fluid curves (T = √ Kǫ ⋆ (MeV) with K = 8/A -13/A MeV covering the known range of average nuclear level density parameters [40]). Peripheral reactions (classes A and B) lead to excitation energies ǫ ⋆ ≈ 3A MeV, near those identified as the onset of the leveling region of the caloric curve for nuclear systems of size A= 180-241 [4].…”

Nuclear Level Density at Finite Temperatures

“…14 , the variation of the macroscopic binding energies with temperature was approximated in Ref. 15,16,17 for RMFT NL3 model by a liquid-drop type expression, which leads to a simple form for the single-particle level-density parameter.…”

“…Average a values as function of A obtained with SkM* as compared to the RMFT NL316 and TF 23 results for β stable nuclei. The N dependence for Sn isotopes is also shown.…”