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DOE OSTI2026

Structural Aspects of Neutron Survival Probabilities

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

r-Process Radioisotopes from Near-Earth Supernovae and Kilonovae

The astrophysical sites where r-process elements are synthesized remain mysterious: it is clear that neutron star mergers (kilonovae (KNe)) contribute, and some classes of core-collapse supernovae (SNe) are also possible sources of at least the lighter r-process species. The discovery of 60Fe on the Earth and Moon implies that one or more astrophysical explosions have occurred near the Earth within the last few million years, probably SNe. Intriguingly, 244 Pu has now been detected, mostly overlapping with 60 Fe pulses. However, the 244 Pu flux may extend to before 12 Myr ago, pointing to a different origin. Here, motivated by these observations and difficulties for r-process nucleosynthesis in SN models, we propose that ejecta from a KN enriched the giant molecular cloud that gave rise to the Local Bubble, where the Sun resides. Accelerator mass spectrometry (AMS) measurements of 244 Pu and searches for other live isotopes could probe the origins of the r-process and the history of the solar neighborhood, including triggers for mass extinctions, e.g., that at the end of the Devonian epoch, motivating the calculations of the abundances of live r-process radioisotopes produced in SNe and KNe that we present here. Given the presence of 244 Pu, other r-process species such as 93 Zr, 107 Pd, 129 I, 135 Cs, 182 Hf, 236 U, 237 Np, and 247 Cm should be present. Their abundances and well-resolved time histories could distinguish between the SN and KN scenarios, and we discuss prospects for their detection in deep-ocean deposits and the lunar regolith. We show that AMS 129 I measurements in Fe–Mn crusts already constrain a possible nearby KN scenario.

79 ASTRONOMY AND ASTROPHYSICS↗