Sensitivity of Isotopic Fission Yields in Actinides to the Macroscopic Liquid-Drop Model: LSD vs ISOLDA

Abstract

The impact of the macroscopic liquid-drop prescription on isotope-resolved fission-fragment yields in the actinide region is assessed by comparing two alternative parameterizations: the Lublin--Strasbourg Drop (LSD) model and the ISOscalar Liquid Drop Approximation (ISOLDA). The two prescriptions differ primarily in the treatment of isospin dependence in the volume and surface terms; in ISOLDA, an explicit dependence on the isospin square $T(T+1)$, where $T=|N-Z|/2$, is introduced in both coefficients. Using an identical set of fragment-yield observables and the same experimental reference (fission of $^{250}$Cf$^*$ at low and high energies), the propagation of the macroscopic-energy choice into the predicted yields is quantified in terms of (i) the location of the most probable post-neutron isotopes along elemental chains, (ii) the widths and asymmetries of the isotopic distributions, and (iii) the population of neighboring nuclides on the distribution tails. A comparable description of the gross properties of the isotopic yield pattern is obtained with both prescriptions, particularly for light and intermediate fragments, where peak positions and near-maximum curvatures are reproduced similarly. The most discriminating differences are found for heavy-fragment chains, for which the ridge location and isotopic centroids are rendered more sensitive to macroscopic isospin terms. Overall, a closer average agreement with the evaluated data is obtained with LSD, while the LSD--ISOLDA spread is shown to provide a practical estimate of the macroscopic-model uncertainty in isotope-resolved yields.

Figures (3)

• Figure 1: Potential energy map of $^{250}$Cf in the $(c,a_4)$ plane, obtained by minimization over $a_3$ (mass asymmetry) and $\eta$ (nonaxiality). The label "g.s." marks the first minimum; points $A$ and $B$ indicate reference configurations along a low-energy path; the dashed line denotes the approximate scission boundary. A separating ridge defines competing symmetric and asymmetric descent valleys.
• Figure 2: Isotopic fission-fragment yields for $^{249}$Cf$(n_{\rm th},f)$ calculated within the 4D Langevin framework using the LSD (points) and ISOLDA (squares) macroscopic prescriptions compared with evaluated experimental reference data (crosses) from NNDC. Each panel corresponds to a single elemental chain; the horizontal axis shows the post-neutron fragment neutron number $N_f$.
• Figure 3: Isotopic fission-fragment yields for $^{250}$Cf$^{*}$ ($L = 20\hbar$, $E^{*} = 46$ MeV) calculated within the 4D Langevin-plus-Master-Equation framework using the LSD (points) and ISOLDA (squares) macroscopic prescriptions compared with experimental data (crosses) from PhysRevC.99.024615. Each panel corresponds to a single elemental chain; the horizontal axis shows the post-neutron fragment neutron number $N_f$.