From first to second minimum: Parity-dependent level densities in $^{240,242}$Pu

TL;DR

Problem: parity dependence of nuclear level densities in actinides affects reaction cross sections and prompt fission probabilities. Approach: parity-projected level densities for $^{240}$Pu and $^{242}$Pu are computed across deformations using a superfluid, finite-temperature framework with Nilsson single-particle energies and a smooth pairing prescription, yielding $R(U)$ and $E_{eq}$ defined by $R(U)=0.98$. Findings: $E_{eq}$ decreases at the second minimum due to combined deformation and negative shell corrections $E_{sh}$, amplifying opposite-parity mixing; $R(U)$ tends toward unity with increasing excitation energy, with occasional overshoots near shell gaps. Significance: the results refine statistical models of fission dynamics and isomer-population probabilities by incorporating parity asymmetry as a deformation- and shell-dependent effect.

Abstract

We calculate the parity-dependent level density ratios for $^{240,242}$Pu across a broad range of quadrupole deformations, from the spherical configuration up to the superdeformed region, explicitly including both the ground-state minimum and the second minimum (fission isomer). The parity-equilibration energy, defined as the excitation energy at which positive- and negative-parity level densities approach equilibrium, is compared between configurations. A significant reduction is observed near the second minimum, indicating a faster equilibration process in this region.

Figures (3)

• Figure 1: Ratios of negative- to positive-parity level densities as a function of excitation energy for $^{240}$Pu at various quadrupole deformations, as indicated in the legend.
• Figure 2: The ratio of negative- to positive-parity level densities $R=\rho^{-}/\rho^{+}$ as a function of excitation energy for $^{240}$Pu at quadrupole deformation $\beta_2=0.95$ (blue line with circles). The analytical expression of Eq. \ref{['Eqend']} is shown for comparison (red solid line). The horizontal dotted line marks $R=0.98$, and the vertical dashed line indicates the corresponding excitation energy, defined as the equilibration energy $E_{eq}$.
• Figure 3: Parity equilibration energy $E_{eq}$ (left vertical axis, blue solid line with circles) and shell correction energy $E_{sh}$ (right vertical axis, red dashed line with squares) as functions of quadrupole deformation $\beta_{2}$. The upper panel corresponds to $^{240}$Pu and the lower panel to $^{242}$Pu.