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Particle number projected energies at finite temperature

Jiawei Chen, Yu Qiang, Junchen Pei

Abstract

In this work, the particle number projection at finite temperature is incorporated into self-consistent Skyrme density functional calculations. In particular, the energies of compound nuclei as a function of deformations are calculated rigorously based on projected densities. Results show that the even-odd staggering effect in partition function gradually diminishes as the system approaches the critical temperature. The obtained fission barriers are similar to that without projection at finite temperature, although projected energies are different. The nuclear level density at the ground state and the barrier are also studied using the projection method and the discrete Gaussian method.

Particle number projected energies at finite temperature

Abstract

In this work, the particle number projection at finite temperature is incorporated into self-consistent Skyrme density functional calculations. In particular, the energies of compound nuclei as a function of deformations are calculated rigorously based on projected densities. Results show that the even-odd staggering effect in partition function gradually diminishes as the system approaches the critical temperature. The obtained fission barriers are similar to that without projection at finite temperature, although projected energies are different. The nuclear level density at the ground state and the barrier are also studied using the projection method and the discrete Gaussian method.
Paper Structure (6 sections, 23 equations, 4 figures)

This paper contains 6 sections, 23 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Results
  4. Summary
  5. Calculations of $\rho, \kappa, \lambda$
  6. Derivation of Discrete Gaussian Approximation

Figures (4)

  • Figure 1: The ratio of PNP partition function $Z_{\text{p}}/\Xi$ for $\ce{^{292}Fl}$ at various temperatures. The ratio actually denotes the component proportion with specific particle number in the compound nucleus. (a, b, c) the ratios are shown for $T=0.1,0.3$ and $0.5\,\text{MeV}$, where the three-dimensional coordinates correspond to proton number, neutron number, and the ratio, respectively. (d) the ratios are shown in terms of different neutron numbers at various temperatures. All temperatures are given in MeV units.
  • Figure 2: (a) At temperature $T=1.0\,\text{MeV}$, the exact PNP energies, and energies without PNP, and the energies based on approximate canonical energies of $\ce{^{292}Fl}$ as a function of quardpole deformation $\beta_2$. (b) the fission barriers by PNP energies and FT-BCS calculations at $T=1.0\,\text{MeV}$. (c) the fission barriers by PNP energies and Skyrme HF-BCS calculations at zero temperature.
  • Figure 3: Calculated level density of $\ce{^{238}U}$ with PNP partition function and the DG method. Note that the collective enhancement factors are included to compare with experimental dataguttormsenConstanttemperatureLevelDensities2013.
  • Figure 4: The extracted level density parameters for $\ce{^{238}U}$ and $\ce{^{292}Fl}$ based on the level densities from PNP partition function and the DG method. The level densities at the ground state deformation and the barrier are given as $a_{\text{0}}(E)$ and $a_{\text{f}}(E-V_\text{b})$, respectively. $a_{\text{f}}(E)$ are also shown to compare with $a_{\text{0}}(E)$.