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In this thesis I study Quantum Chromodynamics on the lattice. This formulation of QCD allows for a first-principles calculation of the hadron mass spectrum. Comprehensive agreement with experiment has yet to be achieved, and this is due in part to the difficulties of isolating the ground state mass from the spectrum of excited states created using an interpolating field on the lattice. In the first chapter, after briefly introducing the standard Wilson action for lattice QCD, and the improved clover action with reduced discretisations errors, the standard techniques for extracting hadron masses are reviewed. In the second chapter I present two new methods for the extraction of hadron masses using a combination of two operators with the same quantum numbers to isolate the ground and first excited states. I apply these two methods to the low-lying hadron states and compare the results with existing methods for extracting the first excited state. Conventionally the Wilson and clover actions are assumed to be inappropriate for the simulation of hadrons containing one or more quarks with Compton wave-lengths shorter than twice the lattice spacing. The discretisation errors for both actions are expected to diverge in this limit. In chapter three I discuss a proposal that actions of this type are suitable for non-relativistic QCD. This proposal suggests a continuum non-relativistic dispersion relation for hadrons containing heavy quarks, parameterised by two mass scales. A dispersion relation of this form is tested against the finite-momentum behaviour of the pseudoscalar mesons containing one or more heavy quarks. The effects of using the different mass parameters to fix the physical quark mass on the predictions for the pseudoscalar and vector decay constants are studied, and this analysis is extended to the mass splittings in the mesons containing one or more heavy quarks in chapter four.

The question of a possible finite neutrino mass is one of the most investigated and controversial topics in particle physics and cosmology. The most promising direct ex periments for determining the neutrino mass are based on the study of the /-decay of molecular tritium. The mass of the neutrino is deduced by analysing the shape of the continuous energy spectrum of the electrons emitted in the /3-decay. In this thesis, the molecular physics issues facing these experiments are investigated. Theoretical final state probability distributions of the daughter molecule are calculated to satisfy the higher resolution requirements and increased sensitivity of the future ex periments. Transition probabilities to the six lowest electronically bound states of 3HeT+ are calculated. Rotational excitation of the daughter molecule is considered and probabilities obtained for the /-decay of T2 in the first four rotational states. Isotope contamination from DT and HT molecules is also investigated, and the probability distributions for 3HeD+ and 3HeH+ are calculated. The sensitivity of the initial temperature, ortho:para ratio and isotopic composition of the source is considered. Estimates of the error in the value of the neutrino mass deduced from fitting theoretical spectra, due to uncertainties in temperature, ortho:para ratio of T2 and percentage of DT molecules, are obtained. The R-matrix method is used to treat the electronic continuum of 3HeT+. Reso nances converging to the first eight excited target states are obtained, and the transition probabilities to these resonances and background continuum are calculated. Endpoint effects due to the decay of other possible species in the source - T_, T, T+, T2", Tg and T - are also investigated. It is hoped that this data will be used as part of the forthcoming KATRIN experi ment.

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The simulation of heavy hadrons using lattice field theory is outlined. Heavy Quark Effective Theory (HQET) is reviewed and is applied in determining an analytic expression for the mass of hadrons containing one heavy quark. The mass of the pseudoscalar and vector mesons and the heavy baryon Λ<I><SUB>Q</SUB></I> are determined for a number of heavy quark masses using lattice field theory. The behaviour of a number of linear combinations of these masses as a function of the heavy quark mass is examined and compared with its predicted behaviour from HQET. The branching ratio for some of the exclusive modes of the free quark decay <I>b</I> → <I>s</I>γ is calculated and compared with the recent experimental data for the decays <I>B</I> → <I>K</I>*γ and <I>B</I> → <I>X<SUB>s</SUB></I>γ.

Proton radioactivity from the highly neutron-deficient nuclide ¹³⁵Tb has been identified using a new double-sided silicon strip detector (DSSD) system at the Fragment Mass Analyser at Argonne National Laboratory. The decay occurs with an energy of Eρ=1179(7)keV and a half-life t_1/2=940⁺³²⁰-₂₂₀<i>μ</i>s. ¹³⁵Tb was produced via the bombardment of a ⁹²Mo target with a 315MeV ⁵⁰Cr beam, and is the first proton emitter to be detected from a (p6n) evaporation channel in heavy ion fusion-evaporation reactions. Proton decay rate calculations suggest that this nuclide has a large prolate deformation, in agreement with the predictions of the Möller-Nix mass model and the experimental observations of the neighbouring odd-even lanthanide proton emitters ¹³¹Eu and ¹⁴¹Ho. An unsuccessful search for the potential proton emitters ^125,126Pm, using the (p6n) and (p5n) evaporation channels respectively, is also reported. The non-observation of ¹²⁶Pm is consistent with mass model Q_Ppredictions, but the non-observation of proton emission from ¹²⁵Pm suggests a Q_P value significantly higher than predictions (so that the decay occurs too quickly to be observable) or significantly lower (so that proton emission is not competitive with β decay), or places an upper limit on the production cross-section of this nucleus. The Q_P predictions of the Möller-Nix and Liran-Zeldes mass models are compared with the currently available data set of experimentally-derived Q_P values for proton-unbound nuclei in the region of observed proton radioactivity (51≤Z≤83). Both models are found to perform reasonably well and provide useful predictions in this extremely neutron-deficient region.

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