Proton radiotherapy has recently become a popular form of cancer treatment. For maximum effectiveness, accurate models are needed to calculate proton angular scattering and energy loss. Scattering events are statistically independent and may be calculated from the effective number of events per reciprocal multiple scattering angle or energy loss. It is shown that multiple scattering distributions from Molière’s scattering law can be convolved by depth for accurate numerical calculation of angular distributions in several example materials. This obviates the need for correction factors to the analytic solution and its approximations. It is also shown that numerically solving Molière’s scattering law in terms of the complete (non-small angle) differential cross section and large angle approximations extends the validity of Molière theory to large angles. To calculate probability energy loss distributions, Landau-Vavilov theory is adapted to Fourier transforms and extended to very thick targets through convolution over the probability energy loss distributions in each depth interval. When the depth is expressed in terms of the continuous slowing down approximation (CSDA) the resulting probability energy loss distributions rely on the mean excitation energy as the sole material dependent parameter. Through numerical calculation of the CSDA over the desired energy loss, this allows the energy loss cross section to vary across the distribution and accurately accounts for broadening and skewness for thick targets in a compact manner. An analytic, Fourier transform solution to Vavilov’s integral is shown. A single scattering nuclear model that calculates large angle dose distributions that have a similar functional form to FLUKA (FLUktuierende KAskade) Monte Carlo, is also introduced. For incorporation into Monte Carlo or a treatment planning system, lookup tables of the number of scattering events or cross sections for different clinical energies may be used to determine angular or energy loss distributions.

I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral interaction up to next-to-next-to-leading-order and the Argonne $v_6'$ interaction. Compared with diffusion based quantum Monte Carlo methods such as Green's function Monte Carlo and auxiliary field diffusion Monte Carlo, path integral quantum Monte Carlo has the advantage that it can directly calculate the expectation value of operators without tradeoff, whether they commute with the Hamiltonian or not. For operators that commute with the Hamiltonian, e.g., the Hamiltonian itself, the path integral quantum Monte Carlo light-nuclei results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo results. For other operator expectations which are important to understand nuclear measurements but do not commute with the Hamiltonian and therefore cannot be accurately calculated by diffusion based quantum Monte Carlo methods without tradeoff, the path integral quantum Monte Carlo method gives reliable results. I show root-mean-square radii, one-particle number density distributions, and Euclidean response functions for single-nucleon couplings. I also systematically describe all the sampling algorithms used in this work, the strategies to make the computation efficient, the error estimations, and the details of the implementation of the code to perform calculations. This work can serve as a benchmark test for future calculations of larger nuclei or finite temperature nuclear matter using path integral quantum Monte Carlo.

Quantum Monte Carlo is one of the most accurate ab initio methods used to study nuclear physics. The accuracy and efficiency depend heavily on the trial wave function, especially in Auxiliary Field Diffusion Monte Carlo (AFDMC), where a simplified wave function is often used to allow calculations of larger systems. The simple wave functions used with AFDMC contain short range correlations that come from an expansion of the full correlations truncated to linear order. I have extended that expansion to quadratic order in the pair correlations. I have investigated this expansion by keeping the full set of quadratic correlations as well an expansion that keeps only independent pair quadratic correlations. To test these new wave functions I have calculated ground state energies of 4He, 16O, 40Ca and symmetric nuclear matter at saturation density ρ = 0.16 fm−3 with 28 particles in a periodic box. The ground state energies calculated with both wave functions decrease with respect to the simpler wave function with linear correlations only for all systems except 4He for both variational and AFDMC calculations. It was not expected that the ground state energy of 4He would decrease due to the simplicity of the alpha particle wave function. These correlations have also been applied to study alpha particle formation in neutron rich matter, with applications to neutron star crusts and neutron rich nuclei. I have been able to show that this method can be used to study small clusters as well as the effect of external nucleons on these clusters.

This work presents analysis and results for the NPDGamma experiment, measuring

the spin-correlated photon directional asymmetry in the $\vec{n}p\rightarrow

d\gamma$ radiative capture of polarized, cold neutrons on a parahydrogen

target. The parity-violating (PV) component of this asymmetry

$A_{\gamma,PV}$ is unambiguously related to the $\Delta I = 1$ component of

the hadronic weak interaction due to pion exchange. Measurements in the second

phase of NPDGamma were taken at the Oak Ridge National Laboratory (ORNL)

Spallation Neutron Source (SNS) from late 2012 to early 2014, and then again in

the first half of 2016 for an unprecedented level of statistics in order to

obtain a measurement that is precise with respect to theoretical predictions of

$A_{\gamma,PV}=O(10^{-8})$. Theoretical and experimental background,

description of the experimental apparatus, analysis methods, and results for

the high-statistics measurements are given.

The OLYMPUS experiment measured the two-photon exchange contribution to elastic electron-proton scattering, over a range of four-momentum transfer from \(0.6 < Q^2 < 2.2\) \((\mathrm{GeV/c})^2\). The motivation for the experiment stemmed from measurements of the electric-to-magnetic form factor ratio of the proton \(\mu G_E/G_M\) extracted from polarization observables in polarized electron-proton scattering. Polarized electron-proton scattering experiments have revealed a significant decrease in \(\mu G_E/G_M\) at large \(Q^2\), in contrast to previous measurements from unpolarized electron-proton scattering. The commonly accepted hypothesis is that the discrepancy in the form factor ratio is due to neglected higher-order terms in the elastic electron-proton scattering cross section, in particular the two-photon exchange amplitude.

The goal of OLYMPUS was to measure the two-photon exchange contribution by measuring the positron-proton to electron-proton elastic scattering cross section ratio, \(\sigma_{e^+p}/\sigma_{e^-p}\). The two-photon exchange contribution is correlated to the deviation of the cross section ratio from unity.

In 2012, the OLYMPUS experiment collected over 4 fb\(^{-1}\) of \(e^+p\) and \(e^-p\) scattering data using electron and positron beams incident on a hydrogen gas target. The scattered leptons and protons were measured exclusively with a large acceptance spectrometer. OLYMPUS observed a slight rise in \(\sigma_{e^+p}/\sigma_{e^-p}\) of at most 1-2\% over a \(Q^2\) range of \(0.6 < Q^2 < 2.2\) \((\mathrm{GeV/c})^2\). This work discusses the motivations, experiment, analysis method, and the preliminary results for the cross section ratio as measured by OLYMPUS.

A search for Klong to pi0 nu nubar was performed on the initial Physics data taken by the KOTO collaboration by the 30-GeV proton synchrotron at JPARC, located in Tokai, Japan. The detector used in the experiment is an upgraded version of the E391 detector, KOTO's predecessor experiment performed at KEK. The analysis was performed on 2.49 E+11 ± (0.91%)stat ± (2.50%)syst kaon decays. The analysis uses Klong to 3pi0, Klong to 2pi0, and Klong to 2 gamma; for normalization and Monte Carlo validation. Based on my independent analysis, the single event sensitivity was determined to be 1.31 E-8 ± (1.22%)stat ± (7.12%)syst, comparable with the E391 result. An upper limit of 5.12 E-8 was measured for the Klong to pi0 nu nubar branching ratio at a 90% confidence level.