This thesis is the report of a lattice calculation of the matrix element relevant to Leptonic and semi-leptonic decays of heavy mesons. The simulations were run in quenched lattice QCD, at two values of the coupling β, using a non-perturbatively improved action. The theoretical formalism of lattice QCD and heavy quark effective theory is introduced. Decay constants of B and D mesons are calculated. The form factors relevant to the B→D*ℓ_e decay are calculated and used to extract the slope parameter of the ISGUR-wise function and the parameter V_c6 of the CKM matrix.

NA48 is a fixed target experiment situated in the North Area High Intensity Facility at the CERN SPS. Its primary purpose is to study direct CP violation in the neutral kaon system, in particular ε'ε, the ratio of direct to indirect CP violation. This thesis presents a study of ε'ε using data taken by NA48 in a six week run in September-October 1997. A method for calculating ε'ε and possible systematic effects are discussed.

A series of six experiments was carried out to search for proton radioactivity in odd-odd drip line nuclei in the region Z = 61 - 73. The candidate nuclei were produced with 1p3n fusion evaporation reactions and separated from beam particles and other reaction products using the Daresbury Recoil Mass Separator. Recoiling evaporation residues were implanted in a double-sided silicon strip detector which recorded the energy, position and time of implantation events and subsequent proton or alpha decays. The position resolution of the detector (300μm on both axes) provided a high correlation efficiency between decay events and parent nuclei, resulting in a system which was capable of measuring proton transitions with half-lives π 1μs and cross sections π 1μb. A new proton line has been observed in the nucleus <SUP>156</SUP>Ta at energy of 1103±12keV, and half-life of 320±80ms. The transition is assigned to a ˜3% decay branch from a high spin h<SUB>11/2</SUB> isomeric state on the basis of systematics. Two transitions have been also observed in the new isotope <SUP>146</SUP>Tm at energies of 1119±5keV and 1189±5keV. The measured half-lives of 235±27ms and 72±23ms are well reproduced by simple WKB calculations assuming proton emission from h<SUB>11/2</SUB> orbitals and the transitions are assigned to a 10<SUP>+</SUP> isomeric state and a low lying 5<SUP>-</SUP> or 6<SUP>-</SUP> level. The proton separation energies have been used to assess the particular quality of the Möller-Nix and Liran-Zeldes mass models far from stability, and the measured partial half-lives are compared with WKB calculations based on different nuclear potentials. The subsequent implications for level ordering beyond the proton drip-line are also discussed. No evidence was found for proton radioactivity in the nuclei <SUP>128</SUP>Pm, <SUP>132</SUP>Eu, <SUP>138</SUP>Tb and <SUP>142</SUP>Ho. On the basis of mass model systematics it was concluded that the odd proton in these nuclei is not sufficiently unbound for proton emission to compete successfully with β-decay.

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Fast neutron elastic scattering has been studied for 2.9,16.1 and 14.2MeV energy from medium and heavy nuclei. Angular distributions of polarization and cross-section have been obtained for 2.9 MeV neutrons scattered from Fe, W, Tl, Pb, Bi and U. Simultaneous measurements of angular dependence of polarization and cross-section has also been done for 16.1 MeV neutrons from Fe, Cu, I, W, Bg, Pb and C by the pulsed beam time of flight technique. The angular ranges covered are from 20° to 160° at intervals of .1k. The experimental distributions have been corrected for the attenuation of the incident neutron flux in the scatterer, neutron multiple scattering and for the finite source-sample-detector geometry using a Monte Carlo computer progamme. Correction for relevant inelastic scattering has been done wherever possible with available experimental inelastic crosssections. The measurements are compared with the optical model calculations based on 'global-fit' parameters as well as parameters reported previously for particular nuclei. These parameters are found not to be very successful in fitting both differential cross-section and polarization for either 2.9 MeV or 16.1 Nev scattering. Much better fits to both cross-section and polarization are obtained by individual analyses for most of the nuclei. The calculations for 2.9MeV neutrons are combined with Hauser-Feshbach compound elastic calculations done with and without the Mol auer level width fluctuation correction. It has been observed that while for U both the calculations provide a similar fit to the expermental data, for W, T1, Pb and Bi calculations including the level width fluctuations correction provide a better fit. For the 16.1 Mev case the fit to the polarization with the optimum parameter set for heavier nuclei are poorer than for the lighter ones, with a marked discrepancy in the magnitude of polarization around 200 for most of the nuclei. The parameter sets which give the best fits to the data at 2.9 MeV and 16.1MeV are presented. A large spin-orbit potential is observed for the heavier nuclei at 2.9MeV while for the 16.1MeV case there is evidence for ? a volume imaginary term. °14.2MeV neutron double scattering measurements on Cu and Pb for 20° and 34 employing the associated particle time of flight technique resulted in a similarly large magnitude of polarization as observed for the present 16.1Mev scattering and also reported earlier. Optical model calculated polarization for 14.2MeV, based on global parameters shows a small magnitude around 20° as in the case of 16.1MeV neutrons. Attempts to modify conventional optical model parameters to account for such a discrepancy are made. It is observed that increasing the radius or the diffuseness of the spin-orbit term reproduces the large magnitude of polarization around 20° without affecting the polarization for the rest of the angles or the cross-section.

The charge excess and momentum spectrum of cosmic ray muons have been measured at 60 m above sea-level by means of the "Vertical Durham Spectrograph" which had been modi-fied in many respects (e.g. by the addition of a solid iron plug of thickness 45 cm) and re-aligned and calibrated. The effect of the multiple scattering in the magnet is found to be the most serious limitation of the instrument and methods of coping with it are investigated, among others a new statistical method. The values obtained for the charge ratio are 1.240 + 0.036 at 12 GeV/c, 1.262 + 0.031 at 23 GeV/c, 1.279 + 0.038 at 31 GeV/c, 1.208 + O.O69 at 47 GeV/c, 1.269 + u.085 at 66 GeV/c, and 1.324 + 0.111 at 102 GeV/c. These results have been combined with the results of previous workers. The best estimates thus obtained are compared with the theoretical expectations calculated by kacKeown et al. (1965a). The expectations are calculated for an empirical model of nuclear interactions including kaons, for the isobar model (Peters, 1963; Yash Pal, I963), and for the peripheral collision model (Narayan, 1964; Crossland and Powler, 1965), including the empirical low-energy pionization in the two latter models. A qualitative agreement is found between the experiments and theory in each case but quantitative conclusions cannot be drawn because of the statistical errors of the experimental results and because of uncertainty in the parameters of the models. The momentum spectrum observed agrees well with the spectrum given by Osborne et al. (1964) within the accuracy of the instrument. The underground muon spectrum observed by Vernov et al. (1965) and the spectrum of primary nuclei measured by the satellite Proton I (Grigorov et al., 1965; Vernov, 1965) disagree with the present results.

A phenomenological analysis of pion nucleon scattering at intermediate and high energies is presented. The intermediate energy range (2-5 GeV) is discussed in terms of a 'new' phase shift analysis which has been constructed from a series of single energy fits to an energy dependent model partial wave analysis. This 'new' phase shift solution exhibits a similar resonance structure to the energy dependent model but enjoys a much better fit to the scattering data, comparable with previous single energy analyses. We discuss the difficulties encountered in previous single energy analyses and illustrate the advantages and feasibility of the energy dependent analysis in which the partial waves satisfy the required smoothness criteria, by construction. The high energy scattering data is discussed with reference to the Regge pole model and we exploit the analytic properties of the scattering amplitudes by the use of the Continuous Moment Sum Rules (C.M.S,R,), The sum rules provide a set of ' consistency equations between the high energy Regge parameters and the low and intermediate energy data which is represented by the phase shifts. In previous analyses of the C.M.S.R., the energy at which they are evaluated has been taken as 2 GeV which corresponded to the maximum energy of available phase shift data. 2 GeV is a long way from the region where we expect the Regge representation to be valid and the saturation of the C.M.S.R. with only those trajectories identified in the high energy region is not obvious, since we may expect lower lying trajectories to be important at these energies. We construct the CM.S.R. at a higher cut off (5 GeV) from the 'new' phase shift solution and compare the results from a simultaneous analysis of the scattering data and C.M.S.R. at the two cut offs. Several differences are apparent between the two analysis in particular we show that it is not possible to construct the A’¯ and B+ atamplitudes at 2 GeV via the C.M.S.R without considering trajectories other than those identified in the high energy scattering region. We present evidence for a new vacuum trajectory which we associate with the n(_0+) (700) meson and this single vacuum trajectory alone constructs the amplitudes b+ at high energies. The total cross-section data is adequately described by the three trajectories P,P' and ρ in the energy range 5-20 GeV but the extrpolations of their contributions to the energy range (20-70 GeV) does not exhibit the energy dependence of the recent Serpukhov pio-nucleon total cross-section data. There have beenseveral models to account for this apparent change in behaviour at 20 GeV which involve the addition of further contributions to the conventional Regge pole term and all these models give an adequate description of the total cross-section data over the whole energy range, which is not surprising considering their increased parameter freedom. We consider two different possibilities of asymptopia which involve the addition of multi-pomeron cuts and dipole contributions respectively to the P,P', ρ Regge poles and we increase our information input to the analysis by the use of the F.E.S.R. as a series of constrait equations on the parameters of the fit. We show that the size of the multi-pomeron cuts identified from the scattering data and the C.M.S.R. are incompatible where as a dipole solution satisfies both the scattering data and C.M.S.R., we consider the possibility of pomeranchuk theorem violation by the inclusion of an odd-signature dipole like term in the amplitude A'¯ but we are unable to reach a decisive conclusion on the possible violation because of the large experimental errors on the Serpukhov data.

Birmingham Positron Imaging Centre has the only known Positron Camera dedicated solely for industrial processes. It has been successfully applied to numerous industrial processes as a non-invasive imaging method such as oil flow in engines, flow in rocks and extrusion processes. A novel technique of particle tracking has been developed at the University of Birmingham using a single radio nuclide labelled particle as a tracer. This technique allowed non-invasive monitoring of industrial processes such as mixing, gas fluidised beds and rotating drums. It provided important information about the effects that govern physical behaviour of the particle inside an industrial machine during its natural working cycle. This information can be used in designing and building more efficient, full scale industrial plants. However, if more than one particle could be traced simultaneously, more information such as interaction between the particles could be gathered and this could be used to identify the physical processes that are taking place. This study is about tracking multiple particles-particularly two particles. A number of methods such as positron emission holography, cluster analysis and tomography have been considered and related computer codes have been developed. The principals of Positron Emission Tomography (PET) and Positron Emission Particle Tracking Method (PEPT) have been explained in Chapter 2. The PEPT algorithm is discussed with some of the applications. Chapter 3 gives an overview of zone plate coded imaging technique that makes it possible to image incoherent radiation that would not be possible with reflective and refractive methods. It reviews some of the important zone plate designs and makes use of an ideal zone plate. Furthermore, a description of a reconstruction computer code that simulates diffraction is given. Chapter 4 gives the application of the zone plate encoded holography, Positron Emission Holography (PEH) technique, to the PET trajectories obtained experimentally for two particle tracking for the first time. The limitations of this technique have been evaluated for a different number of trajectories and resolution of the system was investigated. The trajectories obtained should ideally cross at the location of the particle. Since there are two particles, it is sometimes possible to group these trajectories into two groups of particles. The techniques of grouping are mainly found in the literature under the title of cluster analysis. It is for this reason, that Chapters gives a review of the principles and comparison of the different clustering techniques available in the literature. Chapter 6 describes a unique way of representing the trajectories. It is the midpoint of the closest distance between the trajectories. It also describes a clustering method that will cluster these midpoints into two clusters, rather than trajectories themselves,in order to locate the two particles. The advantages of this algorithm in comparison to the techniques given in Chapter 5 are illustrated with examples. Some of the difficult questions such as how well the objects are clustered or how many natural clusters can be formed by these objects that arise in cluster analysis are also investigated. The application of the clustering algorithm described in the above chapter is given for two stationary positron particles in Chapter 7. The application is repeated for different particle distances, for different particle orientations and a different number of trajectories. Chapter 8 describes another clustering method known as Multiple Location-Allocation method that is mainly used in economics or resource management. This technique is applied to the voxel reconstruction of the trajectories. A computer code for this technique was developed and wide range of techniques were considered from Digital Image Processing for thresholding. The application of the above technique to the experimental data for two stationary particles is given in Chapter 9. The initial allocation techniques were tested and a simple but very effective way of thresholding was described. In Chapter l0, all the above techniques were employed in tracking moving particles. One of the particles was placed on a rotating table which can be rotated at a constant angular speed. The other particle was fixed to a stationary position. The PEH algorithm does need a high number of trajectories but this puts limitations on the accuracy of the particle locations since during the time it takes to collect that number of trajectories, the particle might have moved to another position. However, the clustering algorithm developed in Chapter 6 provided very accurate results making it possible to track the particles for very short time periods. The algorithm developed in Chapter 8 also provides very accurate results but the PAM algorithm can work with a smaller number of trajectories. Finally Chapter l0 gives a summary of the conclusions and makes suggestions for possible future work.

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