A energia não adiabática do estado fundamental para o átomo de hélio é obtida com o formalismo adiabático hiperesférico (HAA). Curvas de potencial, acoplamentos não adiabáticos e funções de canal são calculados por um procedimento numericamente exato baseado em uma expansão analítica das funções de canal. As equações radiais acopladas são resolvidas por técnicas usuais. A convergência do procedimento é investigada conforme os acoplamentos não adiabáticos são sistematicamente introduzidos. Com a inclusão, pela primeira vez, de onze curvas de potencial e funções de canal obtém-se uma energia para o estado fundamental que difere do melhor cálculo variacional por 0.1 partes por milhão. As forças de oscilador para as transições discretas do hélio na \"length-form\" e \"acceleration-form\" também são calculadas. Concluímos que o HAA não está mais obstruído pela falta de uma prescrição para se obter funções de onda de precisão arbitrária para sistemas coulombianos. / The nonadiabatic ground state for the helium atom is obtained with the hyperspherical adiabatic approach (HAA). Potential curves, nonadiabatic couplings, and channel functions are calculated by a numerically exact procedure based on the analytical expansion of the channel functions. The coupled radial equations are solved by standard techniques. The convergence of the procedure is investigated as nonadiabatic couplings are systematically introduced. The inclusion, for the first time, of eleven potential curves and channel functions gives a groundstate energy that differs from the best variational calculation by 0.1 parts per million. The oscillator strength for the discrete helium transitions in the length-form and acceleration-form are also presented. We conclude that the HAA is no longer hampered by the lack of prescription for the obtainment of arbitrary precision wave functions for Coulombic systems.

Research Doctorate - Doctor of Philosophy (PhD) / Helium has the highest ionization energy of any species and is as a consequence difficult to detect by conventional means. On the other hand, it is the ideal surface probe, having no net charge or spin, a low mass and a short de Broglie wavelength. Therefore, there exists a strong incentive to develop a microscopy technique based on helium atom scattering. The purpose of this thesis is to investigate in detail how an efficient helium detector might be developed using the phenomenon of field ionization, an ionization method that relies on quantum mechanical tunneling rather than the more conventional electron impact ionization techniques. In particular, the work focusses on the potential use of a novel nanomaterial, carbon nanotubes, as the source of the high electric fields required for field ionization detection. In Chapter 1 we review the history of field ionization research and the properties and synthesis methods for carbon nanotubes. Chapter 2 describes the experimental apparatus and procedures used for the present research, and Chapter 3 introduces the theoretical framework and background for field ionization. In Chapter 4, the prototypical field ionization system is considered from a detector viewpoint. The work demonstrates that existing theory is not sufficiently quantitative for describing a field ionization detector and therefore a semi-empirical theory is advanced for that purpose. Chapter 5 considers the problem of nanotube field enhancement in detail using computational methods, leading to a complete description of the maximum field enhancement of a nanotube array based on the four fundamental array parameters. Efforts to synthesize carbon nanotubes in the Newcastle plasma-enhanced chemical vapor deposition system are described in Chapter 6. Several procedures are developed for reproducible growth of nanotube films and the chemical vapor deposition system is characterized with single parameter studies. Chapter 7 presents the results of electron field emission and helium field ionization experiments carried out using the grown nanotube films. We demonstrate for the first time the field ionization of helium using a planar film of carbon nanotubes. Finally, we conclude the investigation of field ionization detection in Chapter 8 with a discussion on how such a detection method integrates into a helium microscope and in particular we detail the design and initial calculations for the planned Newcastle helium microscope.

In dieser Arbeit wird eine, zeitabhängige, nicht störungstheoretische numerische Methode entwickelt, welche Ionisation und Anregung von Atomen oder Molekülen in Stößen mit entweder PB oder P beschreibt und auf der impact-parameter Methode basiert. Es wird eine spektrale close-coupling Methode verwendet, um die zeitabhängige Schrödinger-Gleichung zu lösen, in welcher die Wellenfunktion in (effektive) Ein- oder Zwei-Elektronen-Eigenzustände des Targets entwickelt wird. Dies beinhaltet auch eine erstmalige volle Zwei-Elektronen-Beschreibung von H2 in PB-Stößen. Rechnungen werden für PB-Stöße mit H, H2+ und H2 sowie He und den Alkaliatomen Li, Na, K und Rb durchgeführt. Daten für P-Stöße werden für H2 und die Alkaliatomen Li, Na und K erzielt. Die Methode wird durch einen detaillierten Vergleich der erhaltenen Ergebnisse für P-Stöße und für PB + He mit Literaturdaten verifiziert. Andererseits ergänzen die totalen und differentiellen Wirkungsquerschnitte für Ionisation und Anregung der Targets in PB-Stößen die spärliche Literatur. Sowohl die Resultate für verschiedene Targets als auch für PB- und P-Stöße werden miteinander verglichen. Ein Schwerpunkt dieser Arbeit liegt auf der Untersuchung von PB + H2, welche die Abhängigkeit der Wirkungsquerschnitte vom Kernabstand und von der relativen Ausrichtung der molekularen Achse beinhaltet. Weiterhin werden Ergebnisse mit Ein-Elektronen-Modellpotentialen erzielt und mit der vollen Zwei-Elektronen-Beschreibung von H2 verglichen. Außerdem werden Energieverluste in PB-Stößen bestimmt. / In this work a nonperturbative, time-dependent numerical approach is developed which describes ionization and excitation of atoms or molecules by either PB or P impact based on the impact-parameter method. A spectral close-coupling method is employed for solving the time-dependent Schrödinger equation in which the scattering wave function is expanded in (effective) one- or two-electron eigenstates of the target. This includes for the first time a full two-electron, two-center description of the H2 molecule in PB collisions. The radial part of the one-electron eigenstates is expanded in B splines while the two-electron basis is obtained with a configuration-interaction approach. Calculations are performed for PB collisions with H, H2+, and H2 as well as with He and alkali-metal atoms Li, Na, K, and Rb. Additionally, data are obtained for P collisions with H2, Li, Na, and K. The developed method is tested and validated by detailed comparison of the present findings for P impacts and for PB + He collisions with literature data. On the other hand, total and differential cross sections for ionization and excitation of the targets by PB impact complement the sparse literature data of this kind. Results gained from different targets as well as from PB and P impact are compared with each other and assessed. Furthermore, results obtained with one-electron model potentials are compared to the full two-electron description of H2. Finally, stopping powers for PB impacts are determined.

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