<p> This dissertation describes a search for charged Higgs bosons decaying to a tau and a neutrino (<i>H</i>⁺ &rarr; &tau;⁺ &nu;_&tau;) or the charge-conjugate process) in association with a leptonically decaying top quark, using 36.1 fb^&ndash;1 of <i>pp</i> collision data collected with &#129;&radic;s = 13 TeV by the ATLAS detector. The theoretical motivation, including a review of the Standard Model, is given, along with a description of the ATLAS detector and particle reconstruction. A multi-variate analysis approach uses stochastic gradient boosted decision trees to improve the separation between <i> H</i>^&plusmn; signal and background. The semi-leptonic channel described in this thesis is used in combination with a fully hadronic channel to search for charged Higgs bosons in a mass range of 90 GeV &le; <i> m_H</i>&#129;&plusmn; 2000 GeV. Finding no significant excess, limits are set at the 95% confidence level on the charged Higgs production cross section times the branching fraction into &tau;&nu; ranging from 4.2 pb to 2.5 fb. These limits are interpreted in the hMSSM benchmark scenario as an exclusion at 95% confidence on tan &beta; as a function of <i> m_H</i>&plusmn;. In this scenario, for tan &beta; = 60, the <i> H</i>^&plusmn; mass range up to 1100 GeV is excluded, with all values of tan &beta; exclude for <i>m_H</i>&plusmn; &le;160 GeV</p><p>

The scattering of slow positrons by Helium atoms is of particular interest now that positron beam experiments are being performed. The purpose of this thesis is to carry out an examination of past theoretical investigations of the problem as well as to explore various approximation schemes for describing the problem within the framework of the close-coupling method, where the total wave function is expanded in terms of the eigenstates of the target Hamiltonian and of the positronium system. The numerical techniques associated with solving the ensuing coupled intego-differential equations are described in detail. A novel use of a graphical display device as an aid to debugging the computer code is illustrated. The theoretical approximations include (l) allowing for all partial waves (2) taking into account the 2P states of both Positronium and Helium (3) the addition of correlation terms (a means of allowing for short-range effects).

The decay schemes of three intermediate mass nuclei, ¹⁵²Gd, ¹⁵²Sm and ¹⁸²W were studied using a dual-parameter energy-time spectrometer employing Ge (Li) detectors for gamma-gamma coincidence measurements. The applicability of current nuclear models to the properties of these nuclei were investigated. In particular these nuclei were chosen to test the interacting boson model as they spanned the vibrational SU(5) limit (¹⁵²Gd), through the transitional SU(5) to SU(3) limit (¹⁵²Sm), to the rotational SU(3) limit (¹⁸²W). The half-lives of four nuclear states which lie in the nanosecond range were measured using the technique of delayed coincidence with plastic-Ge (Li) detectors. These values were used to calculate the absolute reduced transition probabilities for transitions depopulating these nuclear states. New energy levels have been suggested as a result of the observation of new transitions in singles spectra, and their existence confirmed from coincidence data. The energy level schemes were constructed; nuclear properties of the levels deduced and compared with model predictions.

A 40 cc Ge(Li) detector has been used to study the gamma rays emitted in the decay of Cobalt-60, Areenic-74 and Neodymium-147. A system for measuring directional correlations has been constructed with a fast-slow electronics arrangement utilising the Ge(Li) detector and a NaI(Tl) scintillation counter, and the directional correlations of gamma-gamma cascades in Germanium-74 and Promethium-147 have been studied.

The differences Δσ_L (Δσ_T) between proton-proton total cross sections for longitudinal (transverse) spin states parallel and antiparallel to the incident beam momentum have been measured at the TRIUMF laboratory from 200 to 520 MeV. A beamline was designed to produce a transverse or longitudinal polarization from the vertically polarized beam extracted from the cyclotron. The polarization of the beam was measured using a polarimeter which had been previously calibrated to +/-1.5%. The polarization of the dynamically polarized butanol target was monitored by an NMR system under microprocessor control. In addition, multiwire proportional chambers detected elastically scattered protons and enabled an independent value of the target polarization to be calculated. Careful attention was paid to the removal of systematic effects by talcing data with different combinations of beam and target polarizations. The beam transmitted through the target was detected by six closely spaced circular scintillation counters. The transmission ratios were corrected for Coulomb-Barrier and Coulomb-Nuclear interference effects before final total cross sections were evaluated. Values of Δσ_L (Δσ_T) were measured at six (seven) energies. At the two lowest energies (203 and 325 MeV), where inelasticity is zero or negligible, excellent agreement was obtained with phase shift predictions. The results were incorporated into a phase shift analysis.

Two large volume Ge(Li) detectors and a plastic scintillation counter incorporated in a dual-parameter energy-time spectrometer are used to measure gamma-gamma coincidences following the beta decay of ¹²⁴Sb and ¹⁵⁴Eu. Such an assembly of the detectors also allowed the lifetime of the first excited state of ¹⁵⁴Gd to be determined. A 12% efficient Ge(Li) detector, an intrinsic Ge detector and a Compton suppression system have been employed in the measurement of gamma-ray energies and relative intensities, allowing the log ft values, multipolarities, spins/ parities and transition probabilities to be deduced for the two medium mass isotopes ¹²⁴Te and ¹⁵⁴Gd. Consequently following the coincidence measurements, the energy level schemes for both nuclei are built up incorporating several new energy levels and transitions; evidence is also found regarding levels which had been tentatively reported earlier, and are now considered as confirmed from the coincidence data. The apparent vibrational shape of ¹²⁴Te and the deformation mode of ¹⁵⁴Gd are investigated in light of the experimental results concerning their positive parity states. Negative parity states are also considered in terms of Coriolis coupling acting between three octupole bands in the ¹⁵⁴Gd nucleus. The calculated electric dipole transition probabilities show good agreement with the experimental values. Comparisons are made with the predictions of current nuclear models. In particular the application of the group theoretical symmetries of the interacting boson approximation are discussed. The calculations are carried out using the program package PHINT for determining the energy levels, in conduction with FBEM for evaluating the transition rates. In case of ¹⁵⁴Gd the consequences of using the hybrid parameters, resulting from proton subshell closure at Z=64 are considered. Earlier nuclear models applied to both nuclei are discussed and compared with the present nuclear predictions.

This thesis describes both a theoretical study of low-energy electron scattering by positronium (Ps), below the n=2 threshold and the photo detachment of the positronium negative ion (Ps-.) E+/- + Ps(1s) &rarr; e+/- + Ps(1s) Ps- + hv &rarr; Ps(1s) + e- The importance of the photodetachment of Ps- was recognized by Mills (in 1981) since it can be used as a possible mechanism of producing a slow monoenergetic Ps beam. Accurate 1,3S and 1,3P phase shifts were evaluated by the Kohn and inverse Kohn variational methods in which very flexible trial functions were used. Higher order phase shifts were determined by the static exchange and adiabatic ex-change models in order to obtain the total elastic, momentum-transfer, ortho-para conversion and elastic differential cross sections for the scattering process. In the variational calculation, the lowest 1S, 1P and the two lowest 3P resonances, which lie just below the n=2 threshold were revealed. The scattering results for ea-Ps were compared with those for ea-H. Using a variational bound-state wave function, which contained 95 linear and 2 non-linear parameters, and a p-wave continuum function, which contained 220-linear and 3 non-linear parameters, the photo detachment cross section was calculated in both the length and velocity formulation. The agreement between the length and velocity forms was to better than 1.6% for lambda 27.5 x 10³A, and the sum-rule was satisfied to within 2%. By systematically improving both the bound-state and continuum wave functions separately, the reliability of the cross section was determined. A comparison of the photo detachment of Ps- was made with the corresponding atomic ion, H-.

Gamma-rays were detected in both singles and coincidence in order to establish the decay schemes of the nuclei 152Gd, 152Sm and 182W, which arise from the radioactive decay of 152Eu and 182Ta prepared from the (n,gamma) reaction on 151 Eu and 181Ta. Two high resolution Ge(Li) detectors and one intrinsic germanium detector were employed for the measurements of the 7-ray energies and relative intensities, allowing the logft values, multipolarities, spins/parities and transition probabilities to be deduced for the 152Gd, 152Sm and 182W. The fast-slow coincidence technique was used with two Ge(Li) detector and data recorded with a microcomputer for off-line analysis. Consequently, following these measurements, the level schemes of the above nuclei were built up incorporating several new energy levels and transitions. Comparisons are made with the predictions of current nuclear models. In particular, the application of the group theoretical symmetries of the Interacting Boson Model (IBM) are discussed. The calculations were carried out using the program package PHINT for determing the energy levels, in conjunction with FBEM for evaluating the transition rates. The nuclei investigated test the SU(5)&rarr; SU(3) transitional region in the case of 152Gd and 152Sm, and the SU(3) rotational limit for the 182W.

The properties of the low-lying energy states of ¹¹⁰Cd, ¹⁹²Pt, ¹⁹²Pt and ¹⁶⁶Er following the radioactive decays of 110mAg, 192Ir and ^166mHo were investigated. Two high resolution Ge(Li) detectors, one intrinsic germanium detector and a Compton suppression system were employed for the measurements of the gamma-ray energies and relative intensities, gamma-gamma coincidence measurements using a conventional fast-slow coincidence technique were performed by coupling the Ge(Li) detectors to a 4096X4096 Dual Parameter Data Collection System. The level schemes of the above nuclei were authenticated on the basis of the coincidence measurements. The properties of the levels are discussed, logft values and branching ratios deduced, spins and parities assigned and the lifetime for the first excited state of ¹⁶⁶Er was determined using the method of delayed coincidence between a plastic and a NaI(Tl) detector. Each established level scheme is compared with the theoretical predictions of current nuclear models, notably the interacting boson model (IBM). The Program-Package PHINT was run on the University of London CDC 7600 Computer in order to calculate energies and transition rates on the basis of this model. The nuclei investigated test the SU(5) limit for ¹¹⁰Cd, the O(6) limit for ¹⁹²Pt and the SU(3) --- O(6) transitional region for ¹⁹²Os and ¹⁶⁶Er.

The decay schemes of ⁷⁶As, ²⁰⁷Bi and ⁷⁵Se have been studied using Ge(Li) detectors and coincidence techniques with particular emphasis on the weaker modes of gamma decay. The feasibility of detecting weak modes of gamma decay is discussed and supporting electronic systems which have been developed to yield data suitable for reduction and analysis with computer programmes are described. Low energy gamma transitions in the decay of ⁷⁵Se were studied using an X-ray Ge(Li) detector. Two previouslyunconfirmed transitions at 24.4 keV and 80.8 keV have beendetected and their positions in the decay scheme of ⁷⁶As have been established. In the decay of ²⁰⁷Bi, an upper limit of 0.014 +/- 0.008 relative to the 570 keV transition as 100 has been placed on the intensity of the 'l-forbidden' gamma transition at 328 keV. The decay scheme of ⁷⁶As has been shown to include two previously unreported gamma-rays at 220 keV and 316 keV and coincidence experiments have indicated a new energy level at 2006 keV. Several gamma-rays and level energies suggested by previous authors were not confirmed by this work.