Neal J. Snyderman

Electron radiative self-energy of highly stripped heavy atoms

Abstract A new algorithm is presented for the evaluation of the electron radiative self-energy in heavy atoms, for which Zα is not a perturbative expansion parameter. The algorithm for hydrogenic ions is presented in detail. The terms to be evaluated numerically are finite, free of spurious gauge dependent parts, and are not in the form of a subtraction. The extension to many electron ions is also discussed.

Statistical Theory of Fission Chains and Generalized Poisson Neutron Counting Distributions

Abstract The neutron counting probability distribution for a multiplying medium was shown by Hage and Cifarelli to be a generalized Poisson distribution that depends on the fission chain number distribution. An analytic formula is obtained for this number distribution, the probability to produce a number of neutrons in a fission chain. The formula depends on the probability that a fission spectrum neutron induces a subsequent fission and depends on the probability distribution for a specific number of neutrons to be produced in an individual induced fission. The formula is an exact solution to a functional equation due to Böhnel for the probability generating function. The Böhnel equation is derived as the t →∞ limit of a rate equation for a neutron population generating function, related to a rate equation studied by Feynman. The Böhnel equation is also shown to be a fixed point of an iteration problem, related to one studied by Hawkins and Ulam, where the iteration generates the chain a generation at a time. The discrete iteration problem is shown to be connected to the continuous time evolution of the chain. An explicit solution for the time evolution of the chain is given in the simplified approximation where at most two neutrons are created by an induced fission. The t →∞ limit of this equation gives a simple analytic expression for the solution to the Böhnel equation in this approximation. A generalized Poisson counting distribution constructed from the theoretical fission chain probability number distribution is compared to experimental data for a multiplying Pu sample.

Time Interval Distributions and the Rossi Correlation Function

Abstract For material spontaneously generating fission chains, the arrival times of neutron and gamma-ray counts create a clustering pattern distinctly different from a random source. A theory for the time interval distribution between counts is given. As well as the distribution of nearest-neighbor counts, we give the general distributions for all n’th-neighbor intervals. The sum of these distributions gives the Rossi correlation function. This theory supplies the direct link between the experimentally measured quantities and the theory of the Rossi correlation function.

Active Detection of Shielded SNM With 60-keV Neutrons

Fissile materials, e.g., 235U and 239Pu, can be detected non-invasively by active neutron interrogation. A unique characteristic of fissile material exposed to neutrons is the prompt emission of high-energy (E > 1 MeV) fission neutrons. One promising mode of operation subjects the object to a beam of low-energy (E < 1 MeV) neutrons, generated by a proton beam impinging on a Li target. The emergence of high-energy secondary neutrons then clearly indicates the presence of fissile material. Our interrogation system comprises a low-dose 60-keV neutron generator (5 times 106/s ), and a 1 m2 array of scintillators for high-energy neutron detection. Preliminary experimental results demonstrate the detectability of small quantities (376 g) of 235U shielded by steel (200 g/cm2) or plywood (30 g/cm2), with a typical measurement time of 1 min.

Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions

Abstract We solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutrons in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. Explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.

Neutron Time Interval Distributions with Background Neutrons

Abstract A single cosmic ray air shower event can produce multiple neutrons. The arrival times of neutron counts from such an event creates a clustering pattern distinctly different from random sources. A theory for the time interval distribution between neutron counts from both a correlated source and cosmic ray air showers is given and a method is developed to compute the probability distributions for a cosmic ray air shower to create detected neutrons.

Fission Chain Restart Theory

Abstract Fast nanosecond timescale neutron and gamma-ray counting can be performed with a (liquid) scintillator array. Fission chains in metal evolve over a timescale of tens of nanoseconds. If the metal is surrounded by moderator, neutrons leaking from the metal can thermalize and diffuse in the moderator. With finite probability, the diffusing neutrons can return to the metal and restart the fast fission chain. The timescale for this restart process is microseconds. A theory describing time evolving fission chains for metal surrounded by moderator, including this restart process, is presented. This theory is sufficiently simple for it to be implemented for real-time analysis.

Time-Correlated Particles Produced by Cosmic Rays

This report describes the NA-22 supported cosmic ray experimental and analysis activities carried out at LLNL since the last report, dated October 1, 2013. In particular we report on an analysis of the origin of the plastic scintillator signals resembling the signals produced by minimum ionizing particles (MIPs). Our most notable result is that when measured in coincidence with a liquid scintillator neutron signal the MIP-like signals in the plastic scintillators are mainly due to high energy tertiary neutrons.

beta. -Decay in the Skyrme-Witten representation of QCD

The renormalized coupling strength of the β‐decay axial vector current is related to π± p cross sections through the Adler‐Weisberger sum rule, that follows from chiral symmetry. We attempt to understand the Adler‐Weisberger sum rule in the 1/Nc expansion in QCD, and in Skyrme‐Witten model that realizes the 1/Nc expansion in the low energy limit, using it to explicitly calculate both gA and the π± p cross sections.