Fission-fragment charge yields: Variation of odd-even staggering with element number, energy, and charge asymmetry

Background: Fission-fragment charge-yield distributions exhibit a pronounced odd-even staggering. For actinide nuclei the staggering decreases with increasing proton number and with increasing excitation energy. In our calculations of fission yields [Phys. Rev. Lett. 106, 132503 (2011)] we obtained charge-yield distributions for a number of actinide nuclides by means of random walks on tabulated five-dimensional potential-energy surfaces. However, because the potential-energy model treats the system as a single, compound system during all stages of the fission process, in which individual fragment properties do not appear, no odd-even staggering appeared in the calculated yield curves. Purpose: We have recently become aware that in the experimental data displayed in Fig. 1 in the above paper, there is a remarkable similarity in the odd-even staggering in fission of Pu-240 at thermal neutron energy and fission of U-234 in photon-induced fission at around 11 MeV. We discuss how this similarity and how the variation in the magnitude of the odd-even staggering for three Th isotopes with charge asymmetry and isotope can be qualitatively understood based on strongly damped shape evolution on our calculated five-dimensional potential-energy surfaces. Methods: We conduct random walks on our tabulated five-dimensional potential-energy surfaces and study the difference between the total compound-nucleus energy and the potential energy for the different systems from saddle to scission. Under the strong-damping assumption this difference is the internal excitation energy. We also determine this quantity for different charge splits, symmetric and asymmetric. Results: We find that the magnitude of the odd-even staggering in the charge distribution in the several cases studied here correlates well, inversely, with the excitation energy above the potential-energy surface in the postsaddle region. Conclusions: Because the observed magnitude of the odd-even staggering correlates well with excitation energy over the region where the individual character of the fission fragments emerges, the Brownian shape-motion method can be expected to reproduce this feature, provided a potential-energy model is developed that accounts for how the nascent fragment properties are expressed in the calculated potential-energy surfaces.