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Concept# Elastic scattering

Summary

Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified (by interaction with other particles and/or potentials) meaning the two particles in the collision do not lose energy. Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not. Generally, elastic scattering describes a process in which the total kinetic energy of the system is conserved. During elastic scattering of high-energy subatomic particles, linear energy transfer (LET) takes place until the incident particle's energy and speed has been reduced to the same as its surroundings, at which point the particle is "stopped".
Rutherford scattering
When the incident particle, such as an alpha particle or electron, is diffracted in the Coulomb potential of atoms and

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PHYS-443: Physics of nuclear reactors

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We derive the leading spin-dependent gravitational tail memory, which appears at the second post-Minkowskian order and behaves as u(-2) for large retarded time u. This result follows from the classical soft graviton theorem at order omega In omega as a low-frequency expansion of the gravitational waveform with frequency omega. First, we conjecture the gravitational waveform from the classical limit of the quantum soft graviton theorem up to sub-subleading order in a soft expansion, and then we derive it for a classical scattering process without any reference to the soft graviton theorem. We show that the final result of the gravitational waveform in the direct derivation completely agrees with the conjectured waveform.

Sodium-cooled fast reactor (SFR) technologies have the potential to guarantee energy supply and to reduce the burden of nuclear waste for future generations. For an adequate simulation of these reactor systems, well-established tools that have so far been applied mainly to light water reactor (LWR) concepts need to be validated and enhanced.
For licensing purposes, there is an increasing interest in replacing conservative calculations by best-estimate calculations supplemented by uncertainty analyses. Nuclear data are a major source of uncertainties in reactor physics calculations. The propagation of nuclear data uncertainties to important system responses is important for determining appropriate safety margins in safety analyses.
A systematic approach for quantifying nuclear data--induced uncertainties for all stages of modeling is needed to assess the performance of traditional methods for uncertainty and sensitivity analysis and to unveil the major drivers of observed uncertainties in SFRs. This thesis presents a basis for such a systematic approach through the use of sub-exercises that address different levels of modeling as addition to the OECD/NEA Benchmark for Uncertainty Analysis in Modelling of SFRs.
The major analysis method applied within this thesis was the random sampling--based XSUSA method in which nuclear data is varied based on the corresponding covariance data. As a basis for analyses using several multigroup neutron transport codes from the SCALE code system, new multigroup cross section and covariance libraries were developed and optimized for the analysis of SFR systems. In order to use the time-efficient XSUSA method in combination with the SCALE 6.2 release, SCALE's random sampling sequence Sampler was extended to allow the perturbation of cross sections after the self-shielding calculation, including an optional approximation for consideration of implicit effects.
XSUSA allowed for the determination of one correlation-based sensitivity index to identify the main contributors to observed uncertainties. This sensitivity analysis was extended by a second correlation-based sensitivity index, as well as variance-based Sobol' sensitivity indices. Furthermore, corresponding indices that use sensitivity coefficients from perturbation theory were developed to allow for comparisons between the various approaches.
Finally, systematic uncertainty and sensitivity analyses with respect to nuclear data were performed based on the developed specifications and the described developments. It was found that the analysis of simple models is sufficient for initial assessments of the impact of nuclear data uncertainties on larger scale models as well as the corresponding identification of the uncertainties' major drivers. In general, significantly larger uncertainties for eigenvalues and reactivity coefficients were observed than in corresponding LWR calculations. The main contributor to the uncertainty for most output quantities was identified as inelastic scattering of U-238. Other relevant contributors are the scattering reactions of the coolant and the structural material.
By comparing results based on various methods and models, the studies presented in this thesis contribute to the development and assessment of calculation methods and models for uncertainty analysis accompanying best-estimate reactor simulations of SFR.

This thesis presents a quantum-state-resolved molecular beam study of the non-reactive scattering of methane (CH4) from a Ni(111) surface. It is one of the first experimental investigations in which the internal quantum state distribution of a polyatomic molecule is measured after surface scattering.
The quantum state populations of scattered CH4 were probed by selective rovibrational excitation using a high-power continuous-wave (cw) infrared (IR) laser in combination with a cryogenic bolometer. This technique is introduced as Bolometric detection with Infrared Laser Tagging (BILT) and its experimental realization is described in detail. Example data illustrates the capabilities and the performance of the method.
Scattering experiments were conducted in a near-specular geometry at grazing incidence 65°) and exit angles (70°). The surface temperature was in all cases 673 K. Two aspects of the scattering dynamics of CH4 at Ni(111) were investigated.
First, the fate of initial vibrational energy in the gas-surface encounter between CH4 and Ni(111) was studied in a state-to-state scattering experiment. Here, incident CH4 was prepared with one quantum of the anti-symmetric C-H stretch vibration (v3) and in rotational state J=1 by coherent IR pumping. The results include the first observation of vibrational energy redistribution in the direct scattering of a molecule from a surface. Specifically, a portion of the CH4 molecules, which were initially in the v3 state, were detected in the symmetric C-H stretch state (v1) after scattering. The probability for this vibrationally inelastic process is about 40% compared to the vibrationally elastic process in which CH4 remains in the initially prepared v3 state. This branching ratio is insensitive to changes in incidence kinetic energy in the range 100-370 meV. Rotational excitation is in all cases significant, where molecules that underwent v3-to-v1 conversion carry away an increased amount of rotational energy. The results are discussed in the context of previously observed mode-specific reactivity in this gas-surface system.
Second, the rotational excitation of scattered CH4 in its vibrational ground state was investigated. The scattering is likewise direct and the final rotational state distributions are non-Boltzmann, revealing a propensity for scattering into low-J states. Extended analysis of the rotational-state-resolved angular distributions and the Doppler-broadened absorption profiles suggest that, at low incidence kinetic energies, rotational excitation is dominated by energy transfer from the surface, i.e. phonon annihilation. This conclusion is supported by classical scattering simulations, which recover the rotational excitation at low incidence kinetic energies. However, they strongly overestimate the efficiency of translational-to-rotational energy transfer.
The highly detailed scattering data obtained in this work can serve as stringent test of multi-dimensional dynamical models of this prototypical gas-surface reaction, thereby paving the way toward a predictive understanding of heterogeneous catalysis. This work also proves that BILT detection using state-of-the-art IR light sources is sufficiently sensitive to enable state-to-state surface scattering experiments on polyatomic molecules, opening the possibility to study their dynamics at surfaces with unprecedented detail.

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