The work presented in this thesis is dedicated to developing inexpensive quantum-chemical models that are able to produce smooth and physically correct potential energy curves for the dissociation of single covalent bonds. It is well known that the energies produced by many ab initio theories scaling as the fifth order with the system size (for instance, second-order Moller-Plesset (MP2) and Epstein-Nesbet perturbation theories) diverge at large interatomic separations. We show that the divergent behavior of such perturbation schemes is due to a small number of terms in the energy expressions. Then, we demonstrate that the self-consistent replacement of these terms by their analogs from the coupled cluster theory (such as CCSD) allows one to redress the erroneous behavior of the perturbation theories without the damage to the overall scaling. We also investigate the accuracy of these hybrid perturbation theory-coupled cluster theories near equilibrium geometry. Judging from the computed spectroscopic constants and shapes of the potential energy curves, one such model, denoted MP2-CCSD(II) in this work, performs consistently better than the MP2 theory at essentially the same computational cost.

Reactions of singlet (1S and 1D) and triplet (3P) carbon atoms with water, and 1D and 3P carbon atoms with methanol were studied computationally. In the water and methanol systems, the carbon vapor containing a mixture of C(1S), C(1D), and C(3P) atoms, is predicted to react by primarily interacting with the oxygen, OH bond and CH bond of the substrate mainly with the 1D state. While C(1S) was proven to be unreactive C(3P) can hardly be supported to be reactive, and can safely be defined as unreactive. The major product, CO forms as a result of oxygen abstraction, which is observed as a fast, energetically quite favorable process. The scheme of this oxygen abstraction is promising to be applicable to substrates with the general formula R1-O-R2 i.e. water, alcohols, and ethers. OH insertion, both for water and methanol, yields trappable carbenes / the carbene being a key species on the distribution of the end products. Water matrix trapping the carbene opens the path to the formation of formaldehyde / and exhibits a prototype reaction for the formation of dialkoxymethanes. Gas phase product spectrum from the reactions are broader, due to the accessibility of the routes originating from the otherwise trapped intermediates / and the excess energy of the reactions being carried by them. In the condensed phase the very early and rapid reactions seem to have chance, the subsequent rearrangements are hard to occur. The conclusions thus far apply to the reactions in the gas phase as well as in condensed phases involving inert matrices / and the experimental isolation of the species is highly dependent on the ability of the medium to trap the intermediates via effective transfer of excess energy. Due to the large excess energies of intermediates involved, subsequent reactions are fast / of the order 1013 s-1 from kinetic rate calculations. In the absence of efficient transfer of non-fixed energies to the surrounding medium, all of the reaction paths will conclude with irreversible dissociation reactions. Plausible mechanisms for all the experimentally observed products are predicted. The results are in agreement with the available experimental data.

The accurate calculation of atomic spectra, including radiative corrections, is one of the rather challenging tasks in theoretical physics. The entire formalism of quantum (gauge) field theory, augmented by the difficulties of the bound-state formalism, is needed for an accurate understanding of the relevant physics at the level of current high-precision spectroscopy. In this thesis, several calculations in this area are described in detail. Investigations on large-order perturbation-theory effects (and predictive limits of perturbation theory) supplement these investigations. In the context of applications, numerical algorithms for the acceleration of the convergence of series are discussed.

In 2007, the Department of Energy (DOE) declared the Advanced Test Reactor (ATR) a National Scientific User Facility (NSUF). This declaration expanded the focus of the ATR to include diversified classes of academic and industrial experiments. An essential part of the new suite of more accurate and flexible codes being deployed to support the NSUF is their ability to predict reactor behavior at startup, particularly the position of the outer shim control cylinders (OSCC). The current method used for calculating the OSCC positions during a cycle startup utilizes a heuristic trial and error approach that is impractical with the computationally intensive reactor physics tools, such as NEWT. It is therefore desirable that shim rotation prediction for startup be automated. Shim rotation prediction with perturbation theory was chosen to be investigated as one method for use with startup calculation automation. A modified form of first order perturbation theory, called phase space interpolated perturbation theory, was developed to more accurately model shim rotation prediction. Shim rotation prediction is just one application for this new modified form of perturbation theory. Phase space interpolated perturbation theory can be used on any application where the range of change to the system is known a priori, but the magnitude of change is not known. A cubic regression method was also developed to automate shim rotation prediction by using only forward solutions to the transport equation. / text

No description available.

Many contemporary experimental QCD results achieve greater accuracy in measurement than equivalent theoretical predictions calculated at leading order. Therefore it is necessary to consider next to leading order (NLO) predictions for many processes in order to compare experiment with theory. Accurate theoretical predictions are also important in order to reduce the uncertainty in QCD parameters such as the coupling constant a, and to test whether QCD is in fact the correct theory to describe the strong interaction. With NLO results it is also possible to separate different clustering algorithms and test non-perturbative effects. This thesis concentrates on the techniques necessary for the calculation of NLO observables from the processes e(^+)e(^-) → 4 jets and pp → γ + X. We formulate a new version of the hybrid subtraction scheme based on the colour antenna structure of the final state to evaluate the necessary phase space integrals for the 4 jet process. The scheme is universal and can be applied to any QCD processes. The general purpose Monte Carlo EERAD2 which incorporates this new technique is compared with both experimental data gathered by the DELPHI collaboration and other groups which have reported similar calculations. A Monte Carlo written for the process pp → γ + X requires a knowledge of the non- perturbative photon fragmentation function, D(_γ), and the second half of this thesis concentrates on a calculation of this process using the ALEPH measurement of D(_γ) based on a democratic algorithm. The Monte Carlo DPRAD incorporates these techniques and results from it are compared with data from the Tevatron.

The theory describing the scaling properties of quantum field theory is introduced. The symmetry principles behind scale and conformal transformations are reviewed together with the renormalisation group. A method for improving perturbative calculations of physical quantities in the infra-red limit is developed using general analyticity properties valid for all unitary quantum field theories. The infra-red limit of a physical quantity is shown to equal the limiting value of the Borel transform in a complex scale parameter, where the order of the Borel transform is related to the domain of analyticity. It is shown how this general result can be used to improve perturbative calculations in the infra-red limit. First, the infra-red central charge of a perturbed conformal field theory is considered, and for the unitary minimal models perturbed by ɸ(1,3) the developed approximation is shown to be very close to the exact results by improving only a one loop perturbation. The other example is the infra-red limit of the critical exponents of x(^4) theory in three dimensions, where our approximation is within the limits of other approximations. The exact renormalisation group equation is studied for a theory with exponential interactions and a background charge. It is shown how to incorporate the background charge, and using the operator product expansion together with the equivalence between the quantum group restricted sine-Gordon model and the unitary minimal models perturbed by ɸ(1,3), the equation obtained is argued to describe the flow between unitary minimal models. Finally, a semi-classical approximation of the low energy limit of a bosonic membrane is studied where the action is taken to be the world-volume together with an Einstein-Hilbert term. A solution to the linearized equations of motion is determined describing a membrane oscillating around a flat torus.

We develop the theory of parton distributions f(_a)(π, k(^t2), μ(^2), unintegrated with respect to transverse momentum k(_t), from a phenomenological standpoint. In particular, we demonstrate a convenient approximation in which the unintegrated functions are obtained by explicitly performing the last step of parton evolution in perturbative QCD, with single-scale functions a(π, Q(^2) as input. Results are presented in the context of DGLAP and combined BFKL-DGLAP evolution, but with angular ordering imposed in the last step of the evolution. We illustrate the application of these unintegrated distributions to predict cross sections for physical processes at lepton-hadron and hadron-hadron colliders. The use of partons with incoming transverse momentum, based on k(_t)-factorisation, is intended to replace phenomenological "smearing" in the perturbative region k(_t) > k(_o) (k(_o) ≈ 1 GeV), and enables the full kinematics of a process to be included even at leading order. We apply our framework to deep inelastic scattering and the fitting of F(_2)(π, Q(^2), to the transverse momentum spectra of prompt photons in hadroproduction and in photoproduction, and to the topical problem of bb production at HERA. Finally, we address the issue of parton-parton recombination (shadowing) at very low values of π, building on recent work by Kovchegov and others to make predictions for the likely magnitude of shadowing effects at the LHC.

The resummation of double-logarithmic perturbative contributions produced by soft- gluon radiation (Sudakov resummation) has proved to be an important tool for enlarging the applications of perturbative QCD to a wider range of kinematical regions. In particular, a complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large double logarithms that dominate the transverse momentum (p(_r)) distribution at small p(_r). This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) b space. The b space method succeeds in resumming all the leading and sub-leading logarithmic terms, but does not allow a smooth transition to fixed-order dominance at high transverse momenta. In contrast, the pr space approach experiences difficulties with resumming more sub-leading logarithms. This thesis concentrates on developing the p(_r) space formalism which completely resums the first four towers of logarithms. The number of fully resummed towers is the same as for the b space method. The results are compared, both analytically and numerically, with the original b space result as well as with results of other p(_r) space methods. Parametrization of the non-perturbative effects in p(_r) space is discussed. Given recent Tevatron data on Z boson production we find good agreement between the data and the theoretical predictions. Using the same formalism, the transverse momentum distributions are also calculated for W and Z boson production at the LHC. Finally, we discuss production of like-sign W pair production in the context of double parton scattering at the LHC.

In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schr&uml / odinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.