Made available in DSpace on 2014-06-11T19:25:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-12-12Bitstream added on 2014-06-13T20:33:08Z : No. of bitstreams: 1 furtadoneto_a_me_guara.pdf: 575510 bytes, checksum: 6a1a49e71ce6fbc8113435f66d99a240 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O foco deste trabalho é o espectro de inversão da molécula de amônia, resultado do fenômeno do tunelamento quântico. Para isso, usamos um modelo simpli cado, uni- dimensional, suscetível a uma análise teórica rigorosa usando a mecânica quântica não- relativística. Dentre as diversas funções hamiltonianas já estudadas para este modelo, zemos uma rápida apreciação dos trabalhos de Cohen, Dennison-Uhlenbeck, Manning, Merzbacher e Rosen-Morse. Para um estudo mais profundo, usamos o potencial do poço duplo nito que, posteriormente, descobrimos já fora analisado por Peacock-López. Re- zemos a análise deste potencial usando um caminho diferente do realizado por aquele autor. Analisamos os casos limites para este potencial e notamos que realmente, nesses regimes, ele tende para um poço nito único ou dois poços nitos separados. Então, de- senvolvemos um software grá co centrado no pacote MINUIT, desenvolvido pelo CERN, para analisar e ajustar os parâmetros aos dados experimentais da amônia e, ao nal, comparamos os resultados obtidos com aqueles encontrados na literatura. No ajuste dos parâmetros à amônia, houve uma melhoria acentuada quando passamos de uma fórmula mais simples da massa reduzida para outra mais so sticada. No caso especí co do po- tencial de Peacock-López, a comparação revela que os nossos resultados, de uma maneira geral, são mais precisos. Nossa análise se soma àquelas que contêm uma discussão quan- titativa do potencial de poço duplo. Como parte integrante deste trabalho, uma versão unidimensional simétrica do potencial de Morse foi exatamente resolvida em termos de funções de Kummer e um par de equações transcendentes para as autoenergias. A tentativa de ajustar este resultado à molécula de amônia, porém, mostrou que os padrões de poço duplo deste potencial... / The focus of this work is the inversion spectrum of the ammonia molecule, a result of the phenomenon of quantum tunneling. For this, we use a simpli ed, one-dimensional model, amenable to a rigorous theoretical analysis using the non-relativistic quantum me- chanics. Among the various Hamiltonian functions previously studied for this model, we made a quick appraisal of the work of Cohen, Dennison-Uhlenbeck, Manning, Merzbacher and Rosen-Morse. For a deeper study, we used the nite double-well potential which, as we later discovered, had been considered by Peacock-López. We redid the analysis of this potential using a di¤erent path made by that author. We analyze the limiting cases for this potential and actually noticed that in these schemes, it tends to one nite well or two separate nite wells. So, we developed a graphical software centered on the MINUIT pack- age, developed by CERN, to analyze and adjust the parameters to the experimental data of ammonia and at the end, we compared the results with those found in the literature. In setting the parameters of ammonia, there was a marked improvement when we move from a simpler formula for the reduced mass to a more sophisticated one. In the speci c case of the potential of Peacock-López, the comparison shows that our results, in general, are more accurate and precise. Our analysis adds to those that contain a quantitative discussion of the double-well potential. As part of this work, a symmetric one-dimensional version of the Morse potential is exactly solved in terms of the Kummer functions and a pair of transcendental equations for the eigenenergies. Attempting to adjust this result to the ammonia molecule, however, showed that the double-well patterns of this potential well are irreconcilable with the energy spectrum of ammonia: Close pairs separated by long intervals

Orientador: Antonio Soares de Castro / Banca: Denis Dalmazi / Banca: Manuel Bastos Malheiro de Oliveira / Resumo: O foco deste trabalho é o espectro de inversão da molécula de amônia, resultado do fenômeno do tunelamento quântico. Para isso, usamos um modelo simpli…cado, uni- dimensional, suscetível a uma análise teórica rigorosa usando a mecânica quântica não- relativística. Dentre as diversas funções hamiltonianas já estudadas para este modelo, …zemos uma rápida apreciação dos trabalhos de Cohen, Dennison-Uhlenbeck, Manning, Merzbacher e Rosen-Morse. Para um estudo mais profundo, usamos o potencial do poço duplo …nito que, posteriormente, descobrimos já fora analisado por Peacock-López. Re- …zemos a análise deste potencial usando um caminho diferente do realizado por aquele autor. Analisamos os casos limites para este potencial e notamos que realmente, nesses regimes, ele tende para um poço …nito único ou dois poços …nitos separados. Então, de- senvolvemos um software grá…co centrado no pacote MINUIT, desenvolvido pelo CERN, para analisar e ajustar os parâmetros aos dados experimentais da amônia e, ao …nal, comparamos os resultados obtidos com aqueles encontrados na literatura. No ajuste dos parâmetros à amônia, houve uma melhoria acentuada quando passamos de uma fórmula mais simples da massa reduzida para outra mais so…sticada. No caso especí…co do po- tencial de Peacock-López, a comparação revela que os nossos resultados, de uma maneira geral, são mais precisos. Nossa análise se soma àquelas que contêm uma discussão quan- titativa do potencial de poço duplo. Como parte integrante deste trabalho, uma versão unidimensional simétrica do potencial de Morse foi exatamente resolvida em termos de funções de Kummer e um par de equações transcendentes para as autoenergias. A tentativa de ajustar este resultado à molécula de amônia, porém, mostrou que os padrões de poço duplo deste potencial... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract:The focus of this work is the inversion spectrum of the ammonia molecule, a result of the phenomenon of quantum tunneling. For this, we use a simpli…ed, one-dimensional model, amenable to a rigorous theoretical analysis using the non-relativistic quantum me- chanics. Among the various Hamiltonian functions previously studied for this model, we made a quick appraisal of the work of Cohen, Dennison-Uhlenbeck, Manning, Merzbacher and Rosen-Morse. For a deeper study, we used the …nite double-well potential which, as we later discovered, had been considered by Peacock-López. We redid the analysis of this potential using a di¤erent path made by that author. We analyze the limiting cases for this potential and actually noticed that in these schemes, it tends to one …nite well or two separate …nite wells. So, we developed a graphical software centered on the MINUIT pack- age, developed by CERN, to analyze and adjust the parameters to the experimental data of ammonia and at the end, we compared the results with those found in the literature. In setting the parameters of ammonia, there was a marked improvement when we move from a simpler formula for the reduced mass to a more sophisticated one. In the speci…c case of the potential of Peacock-López, the comparison shows that our results, in general, are more accurate and precise. Our analysis adds to those that contain a quantitative discussion of the double-well potential. As part of this work, a symmetric one-dimensional version of the Morse potential is exactly solved in terms of the Kummer functions and a pair of transcendental equations for the eigenenergies. Attempting to adjust this result to the ammonia molecule, however, showed that the double-well patterns of this potential well are irreconcilable with the energy spectrum of ammonia: Close pairs separated by long intervals / Mestre

Das Ionisierungsverhalten kleiner Moleküle (insbesondere H2 und NH3) in intensiven, ultrakurzen Laserfeldern wird theoretisch untersucht. Das Hauptaugenmerk liegt dabei auf dem Einfluss der Kerndynamik. Zunächst wird das Ionisierungsverhalten des H2-Moleküls bei eingefrorener Kernschwingung untersucht. Bereits im Rahmen dieser Näherung kann im Mehrphotonenregime ein zuvor beobachteter Zusammenbruch der Näherung im Gleichgewichtsabstand festgehaltener Kerne erklärt werden. Weiterhin wird der Übergang vom Mehrphotonen zum quasistatischen Ionisierungsregime für 800-nm-Laserfelder untersucht. Eine neuartige Methode zur Beschreibung der korrelierten Schwingungs- und Elektronendynamik des H2-Moleküls (7D) wird entwickelt. Mit dieser Methode wird schließlich der Einfluss der Kernbewegung während des Laserfeldes auf das Ionisierungsverhalten untersucht. Es wird ein sichtbarer Einfluss auf den zuvor diskutierten Zusammenbruch der Näherung festgehaltener Kerne beobachtet. Dies gilt ebenfalls für einen vor kurzem experimentell beobachteten Isotopeneffekt in der Ionisierung der Moleküle H2 vs. D2 untersucht. Im zweiten Teil der Arbeit wird das Ionisierungsverhalten des NH3-Moleküls untersucht. Die Möglichkeit, die Kerngeometrieabhängigkeit zur Erzeugung und Messung von Schwingungswellenpaketen im neutralen NH3-Molekül mittels Lochfraß auszunutzen, wird untersucht. Das erwartete Schwingungsverhalten und die dafür optimalen Laserparameter werden aufgezeigt. Zusätzlich wird die Möglichkeit des Filmens eines tunnelnden Kernwellenpakets im Doppelmuldenpotential entlang der Schwingungskoordinate untersucht. In der Tat sollte die Verwendung extrem kurzer Laserfelder das Drehen eines Echtzeit-Filmes dieses quantenmechanischen Tunnelprozesses ermöglichen. Abschließend werden die Winkelabhängigkeit der Ionisierungswahrscheinlichkeit von NH3 (ähnelt Orbitalgeometrie) sowie elliptisch polarisierte Laserfelder untersucht. / The ionization behavior of small molecules (especially H2 and NH3) exposed to intense, ultrashort laser fields is investigated theoretically. The focus lies on the influence of nuclear dynamics on this ionization behavior. The ionization behavior of the H2 molecule is first examined within the frozen-nuclei approximation. A previously reported pronounced breakdown of the fixed-nuclei approximation can be explained already within this level of approximation. Furthermore, the transition from the multiphoton to the quasistatic ionization regime is studied for 800 nm laser pulses. A novel approach for the correlated description of the electronic-vibrational motion of the H2 molecule (7D) is developed. The influence of vibrational dynamics during the laser field on the ionization behavior is investigated using this method. A pronounced difference on the previously discussed breakdown of the fixed-nuclei approximation is observed. The vibrational dynamics also lead to a notable change for a recently experimentally observed isotope effect in the ionization of the molecular isotopes H2 vs. D2. The ionization behavior of the NH3 molecule is studied in the second part of this thesis. The possibility to exploit the geometry dependence of the ionization yield in order to create and measure vibrational wave packets in the neutral NH3 molecule via Lochfraß is explored. The expected vibrational dynamics and the optimal laser parameters to observe this effect are demonstrated. Furthermore, the possibility to shoot a "movie" of a tunneling wave packet in the double-well potential along the vibrational coordinate is investigated. Indeed, extremely short laser fields should allow creating a real-time movie of the quantum-mechanical tunneling process. Finally, the orientation dependence of the ionization yield of the NH3 molecule (reflecting the orbital shape) and elliptically polarized laser fields are studied.