Laser Induced Thermal Lens Effect in Rhodamine B — Signature of Resonant Two Photon Absorption

Measurement of thermal lensing signal as a function of laser power made in Rhodamine B solutions in methanol give clear evidence of two photon absorption process within certain concentration ranges when 488 nm Ar+ laser beam is used as the pump source. Only one photon process is found to occur when 514 nm and 476 nm beams are used as the pump.

Synthesis and Photochemistry of a few Olefin appended Dibenzobarrelenes and Bisdibenzobarrelenes

The thesis entitled: ‘Synthesis and Photochemistry of a few Olefin appended Dibenzobarrelenes and Bisdibenzobarrelenes’ is divided into 5 chapters.In Chapter 1, the fundamental concepts of Diels-Alder reaction, di-r:methane rearrangement and energy transfer process in organic photochemistry is discussed.Chapter 2 presents the synthesis of 9-olefin appended anthracenes and bisanthracenes. The target of synthesising various bridgehead olefin appended dibenzobarrelenes and some novel bisdibenzobarrelenes, led us to the synthesis of the appropriate alkenylanthracenes and bisanthracenes as precursor molecules. Diels-Alder reaction was the synthetic tool for the preparation of the target olefin appended dibenzobarrelenes and bisdibenzobarrelenes. This chapter attempts to throw light on our endeavours in synthesising the various 9-alkenylanthracenes and bisanthracenes.Chapter 3 deals with the synthesis of olefin appended dibenzobarrelenes and bisdibenzobarrelenes. Ever since the discovery of di-It-methane rearrangement dibenzobarrelenes, tailored with dijferent substituents at various positions have always been a tool to photochemists in unravelling the mechanisms of light induced reactions. Our intention of analysing the role of a It-moiety at the bridgehead position of the dibenzobarrelene, was synthetically envisaged via the Diels-Alder reaction. Bisdibenzobarrelenes were synthesised through tandem Diels-Alder reaction. Various alkenylanthracenes and bisanthracenes were employed as dienes and the dienophiles used were dimethyl acetylenedicarboxylate and dibenzoylacetylene. In this chapter, we report our venture in synthesising the various olefin appended dibenzobarrelenes and bisdibenzobarrelenes. Chapter 4 describes the preliminary time-resolved fluorescence studies of some olefin appended dibenzobarrelenes and bisdibenzobarrelenes.To understand the primary and secondary physicochemical processes in a photochemical reaction it is necessary to characterise the excited states and the transient intermediates during their short lifetime. A number of methods developed on the basis of the physical properties of the transient species are available for their detection. Time-correlated single-photon counting technique has been utilised in the present study of the excited states of olefin appended dibenzobarrelenes and bisdibenzobarrelenes. To understand the primary and secondary physicochemical processes in a photochemical reaction it is necessary to characterise the excited states and the transient intermediates during their short lifetime. A number of methods developed on the basis of the physical properties of the transient species are available for their detection. Time-correlated single-photon counting technique has been utilised in the present study of the excited states of olefin appended dibenzobarrelenes and bisdibenzobarrelenes.Chapter 5 portrays the photochemistry of olefin appended dibenzobarrelenes and bisdibenzobarrelenes. Dibenzocyclooctatetraene and dibenzosemibullvalene are the photoproducts obtained respectively through the singlet excited state and the triplet excited state of dibenzobarrelenes. Chemical literature shows evidences of the photoreactivity of dibenzobarrelenes generating both the singlet and triplet mediated photoproducts, in a single photoreaction. Our research target in synthesising various bridgehead olefin appended dibenzobarrelenes and bisdibenzobarrelenes, was based on the perception that olefins are eflicient triplet quenchers, thereby quenching intramolecularly the triplet excited state of the barrelenes. A It-moiety at the bridgehead position of the dibenzobarrelene, creates a tetra tr-methane system, which similar to a 6li—7l' or tri-tr-methane systems, could be the fertile ground for interesting photochemical rearrangements. Our attempts in deciphering the photochemistry of the olefin appended dibenzobarrelenes and bisdibenzobarrelenes is the substance of this chapter.

Nd:Glass laser-induced damage to thin films, two-photon excited fluorescence and plasma studies

Laser-induced damage is the principal limiting constraint in the design and operation of high-power laser systems used in fusion and other high-energy laser applications. Therefore, an understanding of the mechanisms which cause the radiation damage to the components employed in building a laser and a knowledge of the damage threshold of these materials are of great importance in designing a laser system and to operate it without appreciable degradation in performance. This thesis, even though covers three distinct problems for investigations using a dye Q-switched multimode Nd:glass laser operating at 1062 nm and emitting 25 ns (FWHM) pulses, lays its main thrust on damage threshold studies on thin films. Using the same glass laser two-photon excited fluorescence in rhodamine 6G and generation and characterisation of a carbon plasma have also been carried out. The thesis is presented in seven chapters.

Theoretical modeling of photon and electron-stimulated Na and K desorption from SiO2

The mechanism of generation of atomic Na and K from SiO2 samples has been studied using explicitly correlated wave function and density functional theory cluster calculations. Possible pathways for the photon and electron stimulated desorption of Na and K atoms from silicates are proposed, thus providing new insight on the generation of the tenuous Na and K atmosphere of the Moon.

Two and three nucleon induced photon absorption

We have investigated the mechanisms leading to two and three body photon absorption in nuclei. At photon energies around the pion production threshold we obtain a fraction of three body absorption of less than 10% of the total, contradicting previous theoretical claims that it dominates the absorption process. The strength of the three body channel grows smoothly with the photon energy reaching a maximum of about 60% of the total direct absorption at energies of the photon around 400 MeV.

Nd:Glass Laser-Induced Damage To Thin Films, Two-Photon Excited Fluorescence And Plasma Studies

Laser-induced damage is the principal limiting constraint in the design and operation of high-power laser systems used in fusion and other high-energy laser applications. Therefore, an understanding of the mechanisms which cause the radiation damage to the components employed in building a laser and a knowledge of the damage threshold of these materials are of great importance in designing a laser system and to operate it without appreciable degradation in performance. This thesis, even though covers three distinct problems for investigations using a dye Q-switched multimode Nd:glass laser operating at 1062 nm and emitting 25 ns (FWHM) pulses, lays its main thrust on damage threshold studies on thin films. Using the same glass laser two-photon excited fluorescence in rhodamine 6G and generation and characterisation of a carbon plasma have also been carried out.

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Median graphs, the remoteness function, periphery transversals, and geodetic number two

A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed

Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

Two-photon ionization of atomic inner-shells

Die Summation ueber des vollstaendige Spektrum des Atoms, die in der Stoehrungstheorie zweiter Ordnung vorkommt, wurde mit Hilfe der Greenschen Funktion Methode berechnet. Die Methode der Greenschen Funktion verlangt die Berechnung der unterschiedlichen Greenschen Funktionen: eine Coulomb-Greensche-Funktion im Fall von wasserstoffaehnlichen Ionen und eine Zentral-feld-Greensche-Funktion im Fall des Vielelektronen-Atoms. Die entwickelte Greensche Funktion erlaubte uns die folgenden atomaren Systeme in die Zweiphotonenionisierung der folgenden atomaren Systeme zu untersuchen: - wasserstoffaehnliche Ionen, um relativistische und Multipol-Effekte aufzudecken, - die aeussere Schale des Lithium; Helium und Helium-aehnliches Neon im Grundzustand, um taugliche Modelle des atomaren Feldes zu erhalten, - K- und L-Schalen des Argon, um die Vielelektronen-Effekte abzuschaetzen. Zusammenfassend, die relativistische Effekte ergeben sich in einer allgemeinen Reduzierung der Zweiphotonen Wirkungsquerschnitte. Zum Beispiel, betraegt das Verhaeltnis zwischen den nichtrelativistischen und relativistischen Wirkungsquerschnitten einen Faktor zwei fuer wasserstoffaehnliches Uran. Ausser dieser relativistischen Kontraktion, ist auch die relativistische Aufspaltung der Zwischenzustaende fuer mittelschwere Ionen sichtbar. Im Gegensatz zu den relativistischen Effekten, beeinflussen die Multipol-Effekte die totalen Wirkungsquerschnitte sehr wenig, so dass die Langwellennaeherung mit der exakten Naeherung fuer schwere Ionen sogar innerhalb von 5 Prozent uebereinstimmt. Die winkelaufgeloesten Wirkungsquerschnitte werden durch die relativistischen Effekte auf eine beeindruckende Weise beeinflusst: die Form der differentiellen Wirkungsquerschnitte aendert sich (qualitativ) abhaengig von der Photonenenergie. Ausserdem kann die Beruecksichtigung der hoeheren Multipole die elektronische Ausbeute um einen Faktor drei aendern. Die Vielelektronen-Effekte in der Zweiphotonenionisierung wurden am Beispiel der K- und L-Schalen des Argon analysiert. Hiermit wurden die totalen Wirkungsquerschnitte in einer Ein-aktives-Elektron-Naeherung (single-active-electron approximation) berechnet. Es hat sich herausgestellt, dass die Elektron--Elektron-Wechselwirkung sehr wichtig fuer die L-Schale und vernachlaessigbar fuer die K-Schale ist. Das bedeutet, dass man die totalen Wirkungsquerschnitte mit wasserstoffaehnlichen Modellen im Fall der K-Schale beschreiben kann, aber fuer die L-Schale fortgeschrittene Modelle erforderlich sind. Die Ergebnisse fuer Vielelektronen-Atome wurden mittels einer Dirac-Zentral-feld-Greenschen Funktion erlangt. Ein numerischer Algorithmus wurde urspruenglich von McGuire (1981) fuer der Schroedinger-Zentral-feld-Greensche Funktion eingefuehrt. Der Algorithmus wurde in dieser Arbeit zum ersten Mal fuer die Dirac-Gleichung angewandt. Unser Algorithmus benutzt die Kummer- und Tricomi-Funktionen, die mit Hilfe eines zuverlaessigen, aber noch immer langsamen Programmes berechnet wurden. Die Langsamkeit des Programms begrenzt den Bereich der Aufgaben, die effizient geloest werden koennen. Die Zentral-feld-Greensche Funktion konnte bei den folgenden Problemen benutzt werden: - Berechnung der Zweiphotonen-Zerfallsraten, - Berechnung der Zweiphotonenanregung und -ionisierungs-Wirkungsquerschnitte, - Berechnung die Multiphotonenanregung und -ionisierungs-Wirkungsquerschnitte, - Berechnung einer atomaren Vielelektronen-Green-Funktion. Von diesen Aufgaben koennen nur die ersten beiden in angemessener Zeit geloest werden. Fuer die letzten beiden Aufgaben ist unsere Implementierung zu langsam und muss weiter verbessert werden.

On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Absolute Kr 4s-electron photoionization cross sections between 30 and 90 eV measured by photon-induced fluorescence spectroscopy (PIFS)

Absolute Kr 4s-electron photoionization cross sections as a function of the exciting-photon energy between 30 and 90 eV were measured by photon-induced fluorescence spectroscopy (PIFS). The measurements were compared with available experimental data and theoretical calculations.