Improvement of Energy Levels in Praseodymium-I by a Line Combination Approach
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Improvement of Energy Levels in Praseodymium-I by a Line Combination Approach Bachelor Thesis by Martin Nuss - 0630923 TU Graz - Institute of Experimental Physics under the supervision of Univ.-Prof. Dr. L. Windholz April, 2009 Contents 1 Abstract 3 2 Introduction 4 3 Fundamentals 5 3.1 Praseodymium - P r59 ..................................5 3.2 Atomicmodel.......................................6 3.3 Atomic fine structure . .8 3.4 Atomic hyperfine structure . 14 3.5 Selection Rules . 19 3.6 Complex Spectra . 20 3.7 Experimental Basis . 26 4 Improvement of Energy Levels 30 4.1 Energy Level correction approach . 30 4.2 Working Process . 32 5 Results 41 5.1 Results of the corrections . 41 5.2 Prospectives . 57 6 Appendix 58 6.1 Example of a data sheet . 58 6.2 Sourcecode . 65 Bibliography 68 List of figures 70 2 1 Abstract In this Bachelor's thesis the energy values of currently known Praseodymium-I energy levels in a range of 2000cm−1 from 9400cm−1 to 11400cm−1 were examined and corrected (improved). The goal when all work will be finished in the future is to reach a final uncertainty in level energy of about ±0:003cm−1 which is about 1 − 2 orders of magnitude lower than today. In the inspected energy region 29 even levels were examined and corrected as 'lower' levels using an averaging method. Resulting from the correction of these lower levels 114 odd 'upper' levels were corrected using well identifyable and assignable spectral lines. In addition several A-factors of magnetic hyperfine structure were improved. The correction process was done using high resolu- tion Fourier Spectrographic data as well as data from Laser Induced Fluorescence measurements. Furthermore a table of all known or suspected energy levels of Praseodymium-I was available. All this information was brought together in a program developed by Prof. L Windholz to handle this enourmous amount of entities in an easy way. In dieser Bakkelaureatsarbeit wurden die bis jetzt bekannten Energiewerte von Praseodym-I Energieniveaus in einem Bereich uber¨ 2000cm−1 von 9400cm−1 bis 11400cm−1 untersucht und korrigiert (verbessert). Das Ziel, wenn alle Arbeiten an den Energieniveaus abeschlossen sein wer- den, ist es, eine Unsicherheit der Energie von ±0:003cm−1 zu erreichen. Das ist ungef¨ahr 1 − 2 Gr¨ossenordnungen kleiner als die Unsicherheit heute ist. In dem untersuchten Energiebereich wurden 29 gerade Niveaus untersucht und mit einer Mittel- wertmethode als 'untere' korrigiert. Daraus resultierend wurden 114 ungerade 'obere' Niveaus auf- grund von gut identifizierbaren und zuordenbaren Spektrallinien korrigiert. Ebenso wurden einige A-Faktoren der magnetischen Hyperfeinstruktur verbessert. Die notwendigen Daten der Spek- trallinien stammen aus Messungen von Fouriertransformationsspektrographen und Laserinduzierter Fluoreszenz. Dazu kommt eine Tabelle mit daraus errechneten, bekannten oder vermuteten En- ergieniveaus von Praseodym-I. Die gesamte Information wurde in einem von Prof. L Windholz entwickelten Programm zusammengefuhrt,¨ welches die einfache Handhabung der riesigen Daten- mengen erm¨oglicht. 3 2 Introduction This work consists of a theoretical part giving an overview of the necessary fundamentals of atomic physics and a second part explaining the correction process in detail. While the first part may be of general interest, the second part may be of special interest for anybody who is going to work on the task of improving Pr-I energies. This may concern many students, because the work on the Pr-I energy levels will take a long time (there are simply too many). Abbreviations, phrases and conventions used throughout this thesis are: • hfs - hyperfine structure • FTS - Fourier Transformation Spectroscopy • LIF - Laser Induced Fluorescence • lower level - an energy level chosen to be the lower level of a transition is called lower level • upper level - an energy level chosen to be the upper level of a transition is called upper level • good spectral line - a spectral line which is clearly classified (i.e. matches perfectly in hfs and energy and may additionally be seen in fluorescence) • Pr-I - Prasodymium in its natural valence configuration. (Pr-II would be singly ionized Pr, and so on.) • The Energy is given in form of wave numbers (in units cm−1 (1cm−1= 1 Kayser = 1000mK)). 4 3 Fundamentals 3.1 Praseodymium - P r59 In this section the most important and relevant data and chracteristics of the element Praseodymium are stated. The data given here has been acquired from [11] and [1]. Praseodymium (Pr) is a (under normal conditions NC) soft, paramag- netic metal in solid phase (see fig. 3.1). It is easily oxidised at air and develops a greenish oxide layer. It's crystal structure is hcp (hexagonal close packed) (αPr). Praseodymium's 59 protons assign it to the Lan- thanoid group (rare earth metals) in the periodic table of the elements g (see fig. 3.2). The relative atomic mass Ar is 140; 907 mol at the only sta- ble isotope (see below). Furthermore Praseodymium has a mass density g of 6:48 cm3 , a melting point of 1204K and a boiling point of 3212K. On our planet earth Pr is very scarce with a mass fraction of 10−4 − 10−5% (in the form of minerals: Monazite, Cerite, ...). Figure 3.1: Praseodymium sample (from [11]) Figure 3.2: Periodic table of the elements - Praseodymium in Lanthanoid group (from http://www.dayah.com/periodic/ 07.04.2009) For the classification of spectral lines using hyperfine structure the nuclear spin quantum num- 5 ber I of 2 is very important. 141 Pr is a anisotope element, which means it occurs naturally in one stable isotope only: P r59 . There are 38 radioactive artificial isotopes but all of them (except for two) have half lives in the magnitude of seconds to minutes only. This fact simplifies the hyperfinstructure analysis signifi- cantly because the isotopic shift (see 3.4 A) does not occur. 5 kJ Praseodymium's first energy of ionization is 527 mol . The electronic configuration of the ground state is: [Xe]4f 36s2 [1s22s22p63s23p63d104s24p64d105s25p6]4f 36s2 The electronic configuration of the ground state in terms of electrons per principal quantum num- ber is: K(2) − L(8) − M(18) − N(21) − O(8) − P (2) Praseodymium like all Lanthanoids has an extraordinarily complex and line-rich spectrum due to its valence configuration. Praseodymium is used in combination with Cerium or Neodymium for the manufacturing of catalysts. Furthermore in alloys with Magnesium for the construction of high-strength met- als for aircraft engines and in alloys with Cobalt for permanent magnets. Another application of Praseodymium is in lighting industry where it is used in carbon arc- and projector lights. Praseodymium compounds give glasses a yellow color. Moreover Prasedymium is a component of didymium glass, which is used to make special welder's and glass blower's goggles. Like all rare earth metals, Praseodymium is of low toxicity. Praseodymium has no known biological role. 3.2 Atomic model In the early 20th century the nowadays used atomic model was established. An early atomic model was Thomson's plum pudding model which thought of atoms as lumps of positive charge with small negative point particles mounted on springs (see fig. 3.3 (left)). Lenard's Dynamiden model accounted for the transition of radiation through matter and described atoms as empty space with randomly placed small positively and negatively charged particles (see fig. 3.3 (right)). Figure 3.3: Evolution of the atomic model: (left) Thomson's Plum Pudding model, (right) Lenards Dynamiden model It was Rutherford's scattering experiment of α particles at thin gold foils which revealed the existence of a positively charged very small nucleus. He also introduced the model of electrons revoluting in circles around the nucleus (see fig.3.4 (left)). The enourmous difficulties the Rutherford atomic model had in explaining how electrons can rev- olute in stable orbits without radiating energy (and collapsing into the nucleus) as proposed by classical electrodynamics where taken on by Bohr. He used also Balmer's formula for the stable energies in the newly introduced Energy level scheme. Combining his postulates with Balmer's 6 formula he ended up with the Bohr atom model (the first semiclassical description of atoms) (see fig.3.4 (right)): 1. Electrons revolute on stable spherical orbits around the nucleus with enegy En. Electron orbits are only stable if the orbital angular momentum is a multiple of Planck's constant. p = n~ In contradiction to classical electrodynamics the electrons in such orbits do not radiate and thereby loose energy. Apart from these orbits classical electrodynamics is valid (coulomb force = centrifugal force). 2. The radius of revolution of an electron cannot be changed continously. It can only absorb a photon and climb up one energy level (increased radius) or emit a photon and climb one down. En − En0 = hν Figure 3.4: Evolution of the atomic model: (left) Rutherford's atomic model, (right) Bohr's atomic model Sommerfeld extended the Bohr theory to elliptical orbits and also introduced a second quantum number k accounting for the different axial ratios (see fig. 3.5 (left)). For Hydrogen the Bohr-Sommerfeld semi-classical theory reaches good agreement with the exper- iment up to fine-structure, but it is mathematically inconsistent and also lacks conviction in a physical understanding altought it is very vivid. The first mathematically consistent theory was developed by Schr¨odinger, Heisenberg, etc. and gives a totally different picture of atoms. In quantum mechanics every electron is described by a complex probability amplitude (see fig. 3.5 (right)). It should be remarked that the results of the Bohr-Sommerfeld theory agree with the results of the Schr¨odinger equation up to fine-structure for Hydrogen. In the 20th century the quantum theory was refined in several steps.