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Radiative Lifetime and Landé-Factor Measurements of the Se I 4P35s

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Radiative Lifetime and Landé-Factor Measurements of the Se I 4P35s Radiative lifetime and Landé-factor measurements 3 5 of the Se I 4p 5s S2 level using pulsed laser spectroscopy. Diploma paper by Raoul Zerne Contents Page ABSTRACT 1 1. INTRODUCTION 2 2. THEORY 5 2.1 Lifetime determinations 5 2.2 Quantum-beat through pulsed optical excitation 7 2.3 Optical double-resonance 9 3. EXPERIMENTS 13 3.1 The cell arrangement 13 3.2 Experiment setup 14 3.3 Lifetime measurements 16 3.4 Quantum-beat measurements 20 3.5 Cptical double-resonance measurements 22 4. CALIBRATION OF THE MAGNETIC FIELD 26 5. DISCUSSION 31 ACKNOWLEDGEMENTS 33 REFERENCES 34 Abstract This diploma project consists of spectroscopic examinations of atomic selenium. Natural selenium was thermally dissociated in a quartz resonance cell keeping the background pressure of selenium 3 5 molecules low by differential heating. The 4p 5s S2 level was excited by frequency-tripled pulsed dye-laser radiation at 207 nm. From time-resolved recordings of the fluorescence decay at 216 nm the natural radiative lifetime of the S level was determined to be 493(15) ns. Quantum-beat and optical double resonance measure- ments in an external magnetic field yielded g =2.0004(10) for the Lande factor. 1. INTRODUCTION Laser spectroscopy has revolutionized atomic and molecular spectroscopy. The use of tunable lasers have made completely new types of experiments possible, and investigations which were impossible with conventional light sources can now be performed. The great advantage of lasers is the very high intensities that can be obtained in a small frequency interval. The spatial properties of laser beams are also of great importance. In many cases it is necessary to have a very high power density per unit frequency I(i>). With lasers this can frequently be obtained. A continuous laser may have about 10 times higher power density per unit frequency than conventional light sources (e.g. radio frequency (rf) discharge lamps). Using pulsed lasers I(v) can be further increased by many orders of magnitude. Radiative lifetime measurements are of great importance in astrophysics and plasma physics. In astrophysics, transition probabilities and the related oscillator strengths are used to determine relative abundances of the elements in the sun and the stars. In plasma physics, the radiative properties of atoms and ions are used for temperature determinations and for calculations of the concentrations of different constituents. Laser spectroscopic studies of the selenium atom are complicated, since the resonance lines fall in the far ultra-violet and vacuum-ultra-violet spectral regions (demands vacuum since oxygen, water vapor and carbon dioxide in the air strongly absorb wavelengths below 200 nm). However, several studies of lifetimes and hyperfine structures with excitation around 200 nm have been performed in recent years (see Ref. [2-4]). In this diploma pro- ject lifetime and Lande g.-factor measurements for the 4p 5s S level of selenium, using 207 nm laser excitation is performed. The 3 5 result is compared with the corresponding state (5p 6s S2) of the heavier Group VIA atom tellurium that was investigated using reso- nance spectroscopy following rf lamp excitation about 20 years ago [5]. Elements such as selenium and tellurium are difficult to investigate by resonance spectroscopy since the the vapor mainly consist of polyatomic molecules. These molecules must be dis- sociated to make the atomic fraction large enough for spectro- scopy. This can be performed in different ways, we have chosen to use differential heating. Many applications of selenium have been found within semiconductor technology and xerography. Selenium is also known in biology and agriculture as a trace element. Some compounds of selenium are very toxic. Thus it is important to be able to detect small amounts of selenium from a technological as well as from an eco- logical point of view. It is also of interest to determine the abundance of selenium in astronomical objects. Presently the abun- dance of selenium in the sun is unknown. In order to assess selenium concentrations from emission measurements it is necessary to know transition probabilities of suitable selenium spectral lines. 2. THEORY 2.1 Lifetime determinations Excited atoms have different probabilities for decay into diffe- rent lower states. The spontaneous transition probability for an atom in level i to decay into level k is A-k, and is determined by the matrix element <*.|er|*.>, where er is the electric dipole operator (see Fig. 2.1.1). The total probability for an atom in level i to decay spontaneously, is given by (2.1.1) ik where the summation is over all levels, k, with energies less then E.. If N atoms are excited into level i at time t=0, the number of atoms remaining in this level will decrease exponentially with time N = Noexp(-t/x.) (2.1.2) with x.= I/A.. (2.1.3) Fig 2.1.1. Relations between radiative properties (From Ref. flj). Here we have assumed that the level i is not repopulated from higher levels. This is the bar for the use of emission spectro- scopy for lifetimes measurements. The time, on average the atoms remain in level f texp(-t/x )dt t= -H = T. (2.1.4) J exp(-t/x.)dt '0 and therefore x. is the mean lifetime for level i. The variance (At) is also easy to calculate f(t-x )2 exp(-t/x )dt J (At)2= 4o ' ' = x2 (2.1.5) J exp(-t/x.)dt Thus, the "uncertainty" in lifetime is also equal to x.. The uncertainty in energy AE must fulfill the Heisenberg uncertainty relation AE-Ateh/2, (2.1.6) and the minimum energy uncertainty is AE . = h/(4rcx). The uncertainty in frequency, Av= AE . /h, defines the natural radiation line width Ai>N= 2Ai; = l/2nx. (2.1.7) In many cases the individual transition probabilities A-k are of primary interest. There exist several methods for determination of the relative transition probabilities a.., for example emission spectroscopy (see Table 5.1). Absolute determinations are considerably more difficult. However, lifetime data can be used to determine the normalization constant c i k so that the absolute transition probabilities can be determined. Experimental transition probabilities, when compared with theore- tical values, provides sensitive testing of theoretical atomic wavefunctions. It is especially sensitive to the outer pan of the wavefunctions because of the r weighting. 22 Quantum-beat through pulsed optical excitation If the Fourier-limited spectral bandwidth Aw * 1/At (At pulse lenght) of the laser pulse is larger than the frequency separation of the sublevels v =(E-E2)/h of the excited state, then these sublevels can be populated simultaneously and coherently (see Fig. 2.2.1 a). By coherent we mean that a well-defined relation exists between the phase factors of the different eigenstates. The fluorescence intensity emitted from these coherently prepared sub- levels shows a modulated exponential decay. The modulation, or the quantum-beat phenomenon, is due to interference of the transition amplitudes between these different excited states. Fig. 2.2.1. Principle of quantum beat (From Ref. fl]), a) Level scheme illustrating coherent excitation of level 1 and 2 with a short broad-band pulse. b) Fluorescence intensity showing a modulation of the exponential decay. Assume that two closely spaced levels 1 and 2 of an atom or mole- cule are simultaneously excited by a short laser pulse from a common initial lower level i. If the pulsed excitation occurs at time t=0, the wavefunction of the excited state at this time can be written as a linear superposition of the eigenstates of the excited sublevels: (2.2.1) where the coefficients a. represents the probability amplitudes that the laser pulse has excited the atom into the eigenstate k. Because of the spontaneous decay into the final level f, the wavefunction at a later time t is given by t/2T l*(t)> = Eakl*k(O)>exp(-iEkt/h)e- . (2.2.2) The time-dependent intensity of the fluorescence light emitted from the excited levels is determined by the transition matrix element, 2 I(t) = C|<*f|eg-r|*(t)>| , (2.2.3) where e is the polarization vector of the emitted fluorescence photon. Inserting (2.2.2) in (2.2.3) yields t/T I(t) = Ce' (A + Bcos«12t) (2.2.4) with 2 2 2 2 A = a1 K0fleg-rl01>l + a2 l<0fleg-r|*2>| (2.2.5) B = 2a1a2K*fle-rl^lK^le T|*2>I, (2.2.6) u>n = (E2 - Ex)/h. (2.2.7) This shows that a modulation of the exponential decay is observed only if both matrix elements for the transition 1 -* f and 2 -» f are non zero at the same time. A measurement of the modulation frequency u allow determination of the energy separation of the two levels, even if their energy separation is less than the Doppler width. Quantum-beat spectroscopy therefore allows Doppler- free resolution. This quantum-beat interference effect is analogous to Young's double slit interference experiment. If it had been possible to detect the transitions separately, then the interference effect would have been lost. Zeeman quantum beats can also be explained semi-classically. The absorbing atoms can be considered as electric dipoles. The linearly polarized radiation from the laser will induce oscilla- tions of the electric dipoles. Oscillating dipoles will radiate in a sin e pattern, where e is the angle relative to the magnetic field. Thus no radiation can be observed in the field direction where the detector is. Since the atom has a magnetic dipole moment it will precess around the magnetic field and the radiation lobe will be turned in towards the detector twice every full revolu- tion.
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