Isotope-Resolved Ba and Xe Yields in Actinide Fission and Correlated Heavy--Light Fragment Systematics

Abstract

Isotope-resolved post-neutron fission yields in the Ba and Xe chains are calculated and benchmarked against evaluated reference data, with emphasis on element-resolved isotopic chains $Y(N_f)$ at fixed fragment charge $Z$ and on the consistency of heavy--light fragment correlations. Calculations are performed within a four-dimensional (4D) Langevin framework employing Fourier-over-Spheroid shape parametrization. The benchmark covers spontaneous fission of selected Cm and Cf isotopes (including $^{244,246}$Cm and $^{250}$Cf) as well as neutron-induced fission at thermal and 14-MeV energies for representative actinides in the Th--Pu region (including $^{229}$Th, $^{235}$U, $^{239}$Pu, and $^{249}$Cf). The dominant neutron-number maxima are reproduced for a large fraction of the isotopic chains considered, indicating that the mean charge partition and the average neutron content of the main fission channels are described consistently. A systematic residual discrepancy is observed in the isotopic widths: the calculated yields often fall off too rapidly on the distribution tails, producing distributions that are narrower than the evaluated data, most notably for heavy-fragment chains.

Figures (8)

• Figure 1: Schematic representation of the Fourier-over-Spheroid (FoS) shape parametrization employed in the 4D Langevin description. The nuclear surface (solid black line) is modulated from a reference spheroid (green dashed line). The elongation is controlled by the dimensionless parameter $c$, defining the half-length $z_0 = cR_0$. Non-axiality is introduced via the elliptical cross-section with semi-axes $a$ and $b$, where the surface position is described by cylindrical coordinates $(\rho, \phi, z)$. The axial landmarks $z_l$ and $z_r$ denote the geometric centers of the left and right nascent fragments, respectively, with their relative separation given by $R_{12} = z_r - z_l$. The parameter $z_{\rm neck}$ indicates the location of the minimum neck radius, while $z_{\rm sh}$ represents the axial shift required to maintain the center of mass at the origin. The physical axial boundaries of the shape are defined by $-z_0 + z_{\rm sh}$ and $z_0 + z_{\rm sh}$.
• Figure 2: Free-energy landscape of $^{246}$Cm in the $(c, a_4)$ plane at $T = 1.4$ MeV, obtained by minimization with respect to $a_3$ and $\eta$. The "g.s." label indicates the ground-state basin. Red points A and B denote the first and second saddle points, respectively. The asymmetric and symmetric descent valleys are separated by a ridge that determines the final mass partition. The dashed "scission line" marks the boundary of fragment separation. Green icons at the top symbolize the nuclear shape evolution toward scission.
• Figure 3: Element-resolved post-neutron isotopic yields $Y(N_f)$ for $^{245}{\rm Cm}(n_{\rm th},f)$. Black symbols and curves represent the model calculations, while red symbols denote the evaluated reference data from ENDF/B-VIII.0 NNDC.
• Figure 4: Centroid positions of post-neutron isotopic chains as a function of fragment charge for the $^{245}{\rm Cm}(n_{\rm th},f)$ reaction. Black line show the calculated centroids $\bar{N}_f$ with gray bands representing $3\sigma$ uncertainty ranges. Red symbols denote the centroids of evaluated reference data with their corresponding $3\sigma$ ranges. All 36 element-resolved chains from Fig. \ref{['fig:cm246_overview']} are included.
• Figure 5: Element-resolved post-neutron isotopic yields $Y(N_f)$ for the heavier fission fragment with charge $Z=56$ (Ba). Black symbols and curves represent the model calculations, while red symbols denote the evaluated reference data from ENDF/B-VIII.0 NNDC.