Alexandra Fittante
Northern Michigan University


REU program - Summer 2011

University of Wisconsin - Madison
Madison, Wisconsin 53706

Research projects of other REU students

The Application of Experimental Methods to Determine Atomic Transition Probabilities

Introduction

This summer I assisted Dr. Jim Lawler and Dr. Betsy Den Hartog in their on-going effort to accurately measure transition probabilities for the elements in low stages of ionization using advanced experimental techniques. The accurate measurement of these probabilities has been one of the major problems of atomic spectroscopy. Better transition probabilities are helping to make atomic spectroscopy more quantitative for astrophysics as well as other fields.

Background Theory

The investigation of elemental abundances in stars continues to be an important part of astrophysics. Accurate knowledge of these abundances sheds light on the distribution and production of chemical elements in the Galaxy, thus unveiling some of the mystery surrounding the Galactic chemical evolution. Of specific interest in this study is a group of metal-poor Galactic halo stars. Halo stars are some of the oldest objects in our Galaxy and contain a chemical record of the Galaxy, making them perfect candidates for the investigation of the Galactic chemical evolution.

Elements that are heavier than iron cannot be produced through fusion but instead are produced by two other processes, the s-process (slow neutron capture) and the r-process (rapid neutron capture). The s-process produces an abundance of stable nuclei and is believed to occur mostly in AGB stars over a period of thousands of years. This process is far better understood than its counterpart, the r-process. Most astronomers believe the r-process occurs in core-collapse (Type II) supernovae, however it has also been proposed that it occurs in neutron star mergers. This elusive process has yet to be satisfactorily explained, thus providing scientists with the intriguing task of trying to understand it.

The project I have been working on this summer will hopefully be able to answer some of the questions about the r-process. A number of the metal-poor halo stars are very r-process-rich, and several studies have been done that confirm the existence of an r-process-only abundance pattern for these stars, at least for the Rare-Earth elements. By using advanced techniques, such as the laser-induced fluorescence experiment and the Fourier Transform Spectroscopy analysis that I assisted with this summer, to determine stellar elemental abundances, we can better define this abundance pattern. This well defined pattern will allow us to more accurately model, understand, and explain the r-process nucleosynthesis as well as the Galactic chemical evolution in general.

Transition Probabilities

Transition probabilities are crucial for the determination of elemental abundances in the observable universe. The type of transition probability that I've been helping to determine is defined as the probability per unit time of an atom in an upper energy level making a spontaneous transition to a lower energy level. This type of transition probability is also known as an Einstein A coefficient. Up until the recent introduction of laser techniques for radiative lifetime measurements, the uncertainty of atomic transition probabilities was usually rather high. Now with the application of these advanced techniques, lifetime measurements have become much more accurate. However, transition probabilities cannot be determined solely from radiative lifetime measurements except in the case where there is only one transition from an upper level. Usually there is more than one transition in the decay of an upper level, so radiative lifetime measurements are combined with relative intensity measurements, or branching fractions, to produce absolute transition probabilities. Conveniently, the improved techniques for lifetime measurements coincided with a major advancement in branching fraction measurements. The introduction of Fourier Transform spectrometers has significantly improved the accuracy of branching fractions. The combined efforts of new laser techniques and Fourier Transform spectroscopy are resulting in vast improvements in the investigation of atomic transition probabilities. The figure below illustrates the relationship between transition probabilities, radiative lifetimes, and branching fractions.

transition probability illustration
Figure 1. Illustration of upper level (u) transitions to different lower levels (1, 2, and 3). A1, A2, and A3 are the transition probabilities of transitions from the upper level to levels 1, 2, and 3 respectively. The sum of these transition probabilities is the inverse of the radiative lifetime of the upper level (τu).

Branching Fractions

A branching fraction is defined as the ratio of atoms that decay from a specific upper level to a specific lower level, to the total number of atoms that decay from that same upper level to any lower level. Branching fractions can be determined from relative intensity measurements of spectral emission lines. This involves measuring the intensity of the spectral emission line produced by the transition from a particular upper level to a specific lower level and dividing that value by the sum of the intensities of the lines produced by the transitions from the same upper level to any lower level.

Radiative Lifetimes

A radiative lifetime is the amount of time an electron spends in an upper "excited" energy level before it decays to a lower energy level. The lifetime of a given upper level is the same for every transition in that level. These lifetimes can be measured using time-resolved laser-induced fluorescence. Fluorescence is the emission light produced by the transition of an electron from an upper level to a lower level. The experiment I used can measure lifetimes from approximately two nanoseconds to two microseconds and produces data with accuracies of ± 5%. Most of the elements on the periodic table can be studied using this technique. Radiative lifetimes provide the absolute normalization for branching fractions.

Fourier Transform Spectroscopy Data Analysis

This summer I assisted Dr. Jim Lawler with his on-going analysis of Samarium I (Sm I) and Titanium II (Ti II) spectra recorded with the 1.0 meter Fourier Transform Spectrometer (FTS) at the National Solar Observatory at Kitt Peak, Arizona. The Kitt Peak FTS allows the simultaneous measurements of all spectral elements, offers Doppler limited resolution as small as 0.01 cm-1, a wavenumber accuracy of 1:108, and is capable of recording a million point spectra in ten minutes over a broad spectrum from UV to IR. This instrument collects a continual beam of light containing many different wavelengths and produces an interferogram with the raw data. The FTS then applies a Fourier transform, as its name implies, to the interferogram which transforms the raw data into the desired spectrum. An example of a spectrum produced by the FTS is shown in Figure 2 below. This method of data collection is critical for accurate branching fraction measurements because unlike a grating monochromator, which scans one spectral element at a time, the FTS takes simultaneous measurements of all spectral elements. This feature makes the FTS much less sensitive to drifts in the light source intensity.

sample FTS data
Figure 2. Example of spectra produced by FTS


In order to accurately determine branching fractions from the FTS data a relative intensity calibration is essential. This calibration is done using both standard lamp calibrations and the calibration of Argon I and II lines. A tungsten filament continuum lamp is often used because of its range over wavenumbers for which the FTS is less sensitive. However one must use caution when using continuum lamps to calibrate the FTS over wide ranges because they produce "ghost" continuums. This continuum lamp calibration is useful, but it provides an external calibration, so if they are not aligned precisely with the measured light source, significant errors may incur. Therefore an internal calibration using Argon I and II lines is necessary to mitigate this problem. This is done by comparing well-known branching fractions of Ar I and ArII lines with the measured intensities of the same lines. The combination of these calibrations result in the efficiency versus wavenumber curve for the FTS. Figure 3 below shows an efficiency versus wavenumber curve for the FTS.

efficiency vs. wavenumber curve
Figure 3. Efficiency vs. wavenumber curve

There are several potential errors that must be avoided when measuring branching fractions with the FTS, such as errors from blending of the line of interest with another metal atom or ion line or a buffer gas line, an error from the inability to measure weak lines, especially in the infra-red region, and the possibility of radiation trapping occuring when radiation emitted by one atom is absorbed by another. In order to determine accurate branching fractions, these possible complications are accounted for by recording spectra under various conditions. Spectra are recorded at several varying discharge currents to test for radiation trapping. Typically, conventional hollow cathode discharge lamps (HCD) are used with the FTS, but to distinguish possible ion blends with spectral elements an Electrodless Discharge Lamp (EDL) is used for a few recordings. Due to its well-known branching fractions, Argon is most often used as a buffer gas in the discharge lamps, however several recordings are taken using Neon as a buffer gas in order to identitfy any Argon blends with spectral elements.

As I mentioned earlier, I worked on the FTS analysis of Sm I and Ti II spectra this summer. Before analyzing a transition line, all possible transition wavenumbers between the known energy levels of Sm I and Ti II that satisfied both the parity change and the ΔJ ≤ 1 selection rules were computed and used during my analysis of the FTS data for those elements. Once a transition line had been identified, I numerically integrated it to determine its raw intensity, which was in turn converted to a branching fraction. Each transition comprised of spectra recorded under varying conditions (9 spectra for Sm I and 14 spectra for Ti II), which I have explained in detail above, and each variation was numerically integrated for every transition in every upper level. In addition to the integration of these lines, I had to estimate the signal-to-noise ratio for each, as well as include a comment describing the line, such as whether it was isolated, a doublet, to the left or right of center, or if it was possibly blended with other lines. The following images are a few of the transition lines of Sm I and Ti II I analyzed this summer.


Sm I Spectral Lines

Sm1 Spectrum, Upper Level 115, Transition 1, Spectra 1
Sm1 Spectrum, Upper Level 115, Transition 2, Spectra 1
Sm1 Spectrum, Upper Level 115, Transition 3, Spectra 1
Upper Level 115, Transition 1, Spectrum 1
Upper Level 115, Transition 2, Spectrum 1
Upper Level 115, Transition 3, Spectrum 1



Ti II Spectral Lines

Ti2 Spectrum, Upper Level 47, Transition 1, Spectra 1
Ti2 Spectrum, Upper Level 47, Transition 2, Spectra 1
Ti2 Spectrum, Upper Level 47, Transition 3, Spectra 1
Upper Level 47, Transition 1, Spectrum 1
Upper Level 47, Transition 2, Spectrum 1
Upper Level 47, Transition 3, Spectrum 1


Laser-Induced Fluorescence Experiment

In addition to the FTS data analysis, I also worked on measuring the radiative lifetimes of Neodymium I (Nd I) and Iron I (Fe I) with Dr. Betsy Den Hartog using time-resolved laser-induced fluorescence. The experiment consisted of three major components: the source, the laser, and the data collection equipment. Figure 4 below gives both top and side view schematics of the lifetime apparatus.

lifetime apparatus diagram
Figure 4. Lifetime apparatus diagram

The Source

In this experiment we use a hollow cathode discharge sputter source to produce an atomic/ionic beam of a desired element. The use of a hollow cathode source essentially eliminates the effects of collisional quenching in a beam environment. Collisional quenching is a decrease in fluorescence intensity caused by the collision of an excited atom with another atom, ion, or electron. The large-bore hollow cathode is lined with a thin foil of the metal being studied and is sealed on one end except for a 1.0 mm diameter hole. A pulsed Argon discharge, typically operating between 0.3 and 0.4 torr with 10 A pulses lasting ~10 µs, is used to sputter the metal foil lining the cathode. Sputtering is a process in which atoms are ejected from a target (the metal foil) due to the bombardment of the target by energetic particles (the pulsed Argon discharge). A diffusion pump is used to evacuate a low-pressure (10-4 torr) scattering chamber, which is connected to the end of the hollow cathode via a small hole. The sputtered atoms and ions of the metal being studied are extracted through the hole in the hollow cathode into the scattering chamber.

The Laser

We use a nitrogen-laser-pumped pulsed dye laser in our fluorescence studies. The dye laser consists of a mixture of solvent with an organic dye which is circulated through dye cells. The nitrogen laser is used to "pump" the dye solution in the dye cells past its lasing threshold, causing the dye to lase. This laser beam is then collimated and steered through an opening in the side of the scattering chamber using an intricate system of optics. The dye laser is very advantageous in this experiment because of its ability to be tuned to a specific wavelength. The use of frequency doubling crystals and diffraction gratings, as well as the ability to easily replace a dye used in the laser with another type of dye all contribute to the tunability range (205 nm to 720 nm) of the dye laser. Because of this narrow bandwidth, the laser can selectively excite the specific upper level desired to be studied. The dye laser pulses are delayed ~20 to 40 µs relative to the current pulses in the Argon discharge in the source. This delay allows for the transit of the sputtered metal ions and atoms from the hollow cathode into the scattering chamber before the laser pulse enters the scattering chamber. The laser has a pulse duration of ~3 ns and a bandwidth of nearly 0.2 cm-1. Then the pulse enters the scattering chamber and crosses orthogonally with the beam of sputtered metal atoms and ions one cm below the opening of the hollow cathode. The interaction of the two beams excites electrons in the metal atoms/ions to a desired upper level from which they then decay and produce the fluorescence measured in this experiment.

The Data Collection Equipment

The fluorescence signal is collected by a photomultiplier tube (PMT) through the use of a pair of fused silica lenses with an optical system of f/1. It is often necessary to use spectral filters, either broadband colored glass filters or narrowband multilayer dielectric filters, which are inserted between the two lenses to block scattered laser light and contributions from cascade fluorescence from lower levels. This occurs when the upper level of interest has an infrared branch to a near-lying level, which subsequently decays at a wavelength within the spectral bandpass of the PMT. Cascade from higher levels is no longer an issue due to the highly selective excitation of the dye laser. The region in the scattering chamber where the laser light and sputtered metal ions and atoms interact is imaged onto the photocathode of the PMT. When the fluorescence hits the photocathode, according to Einstein's photoelectric effect, electrons are produced. These electrons are then directed by a focusing electrode toward the electron multiplier, consisting of a series of electrodes called dynodes. When the electrons reach the electron multiplier they undergo secondary emission, which is when electrons in a vacuum tube cause the emission of additional electrons by striking an electrode. Finally, after the accumulation of many electrons, the electron pulse reaches the anode of the PMT, which results in a sharp current pulse. This pulse is then recorded by a transient digitizer, yielding the desired fluorescence exponential decay curve. A diagram of a PMT is shown below in Figure 5.

PMT diagram
Figure 5. Photomultiplier tube diagram

The Experiment

The elements we investigated this summer were Neodymium I (Nd I) and Iron I (FeI), as I previously stated. The first element we observed was Nd I, so the hollow cathode was equipped with a thin Nd I foil liner. Before collecting data, the source needed to "clean up" so any contiminates were eliminated from the cathode and the discharge. Also, the transient digitizer had to be warmed up and calibrated. So the source was turned on in the morning and run with an Argon pressure of ~0.36 torr, a DC current of 60 mA, and a pulser current of 5 A. Throughout the morning I would steadily increase the DC voltage until it reach 400 V and the pulser current was between 5 and 10 A. When the discharge had a nice, light purple color, it indicated that the source was clean and we could start the experiment. The next step was to warm up the nitrogen laser. Once that was warm we started circulating the dye in the dye cells, and then optimized and aligned the laser. From there we set up a monochromator on the wavenumber of a transition line in the Nd I upper level we desired to measure. Then we carefully tuned a diffraction grating along the laser path by adjusting its micrometer setting until the monochromator indicated we were in the viscinity of our desired line. After we found the line, we verified that the laser was still optimized and recorded a pressure scan of an area around the line ranging from ~5 to 10 Å. Then we tuned the laser onto the desired transition line and recorded the fluorescence decay curve with the digitizer, choosing an appropriate time window such that a minimum of three lifetimes were recorded. We then tuned the laser off the transition line and recorded a background. From this data, two segments (~1.5 lifetimes each) were extracted and a least-squares fit to a single exponential was performed on the background-subtracted decay data to determine the lifetime of the Nd I upper level. This procedure was repeated four more times resulting in five recorded decay curves for each measured transition line. Each Nd I upper level was measured twice, using different transition lines in the level whenever possible. This repitition helps us to ensure that the lines were identified correctly and were classified correctly to the desired upper level. This process was then repeated for other Nd I upper levels. Figure 6 shows a sample pressure scan and sample fluorescence decay curves for Nd I transition lines.

Nd I pressure scan
Nd I fluorescence decay curve
Figure 6. Left: Pressure scan of transition lines of Nd I levels. Right: Fluorescence decay curves of transition line of Nd I level.

After we had finished measuring the lifetimes of the Nd I levels, we measured several very well known radiative lifetimes in order to help determine the accuracy of the experiment. These "benchmark" lifetimes that we measured included lifetimes of levels in Beryllium I (Be I), Beryllium II (Be II), and Iron II (Fe II), which cover the range of lifetimes from 1.8 to 8.8 ns. We also measured lifetimes for several Helium I (He I) levels covering the range from 95 to 220 ns. As there are no convenient "benchmark" lifetimes to measure on the interval from 8 to 95 ns, highly accurate measurements of relative absorption oscillator strengths of Chromium I (Cr I) and Iron I (Fe I) are used to calculate accurate lifetime ratios, which help to fill this gap. This procedure is performed periodically in order to determine the systematic uncertainty of the experiment.

Once we finished measuring these lifetimes, we began measuring Iron I (Fe I) lifetimes, so the Nd I foil lining the cathode was replaced with an Fe I foil. We then decided to begin measuring Fe I lifetimes starting with transition lines in the UV range, so we needed to introduce a frequency doubling crystal to the system of optics the laser passed through. To use these crystals, we needed to tune the laser to twice the desired wavelength. Then when the laser light passed through the crystal its frequency was doubled, thus its wavelength was halved, resulting in laser light tuned to the original wavelength of interest. Once the crystal was installed, we continued to measure the lifetimes of Fe I levels using the same procedure I described for Nd I. Figure 7 shows a sample pressure scan and sample fluorescence decay curves for Fe I transition lines.

Fe I pressure scan
Fe I fluorescence decay curve
Figure 7. Left: Pressure scan of transition lines of Fe I levels. Right: Fluorescence decay curves of transition line of Fe I level.

Results

The determination of atomic transition probabilities is an on-going project. This summer, I helped complete the FTS analysis of Sm I spectral lines and successfully analyzed many Ti II lines, though the analysis of the Ti II FTS data is not yet finished. I also worked with Dr. Den Hartog to finish the second set of radiative lifetime measurements of the Nd I levels, and I aided her in measuring the "benchmark" lifetimes necessary to determine the systematic uncertainty of the time-resolved laser-induced fluorescence experiment. We also began measuring lifetimes of Fe I levels, though we did not have time to get through all of the upper levels.


References

Den Hartog, E. A., M. E. Wickliffe, and J. E. Lawler. "Radiative Lifetimes of Eu I, II, and III and Transition Probabilities of Eu I." Astrophysical Journal (2002). Web. http://iopscience.iop.org/0067-0049/141/1/255/55379.text.html.

Fleming, Karen. "Introduction to Fluorescence Theory and Methods." Lecture. Web. http://vohweb.chem.ucla.edu/voh/classes%5CSpring08%5C156ID35%5Cfluoresence.pdf.

"Fluorescence Spectroscopy." Wikipedia. Web. 29 July 2011. http://wikipedia.org.

Lawler, J. E., C. Sneden, J. J. Cowan, I. I. Ivans, and E. A. Den Hartog. "Improved Laboratory Transition Probabilities for Ce II, Application to the Cerium Abundances of the Sun and Five R-Process-Rich, Metal-Poor Stars, and Rare Earth Lab Data Summary." The Astrophysical Journal Supplement Series 182.1 (2009): 51-79. Print.

Lawler, J. E. "Laser and Fourier Transform Techniques for the Measurement of Atomic Transition Probabilities." Print.

Thompson, Lee. "PHY320 - Teaching - Physics and Astronomy." Department of Physics and Astronomy. The University of Sheffield. Web. 29 July 2011. http://www.sheffield.ac.uk/physics/teaching/phy320.

Thorne, Anne P. Spectrophysics. Second ed. London: Chapman and Hall, 1974. Print.