H C J Mulders
email: h.c.j.mulders@tue.nl

M Haverlag

G M W Kroesen

Determination of Spectroscopic Properties of Indium Bromide

To develop a more efficient plasma light source, molecules are considered as the prime source of radiation, because they can potentially avoid the conversion losses of the low pressure mercury lamp as well as the thermal losses of the high pressure mercury lamps. A candidate to serve as the prime radiator in such a lamp could be Indium Bromide, but spectroscopic data to assess its aptitude is largely unavailable.

To increase the knowledge of the spectroscopic properties of these molecules and InBr in particular, an experiment was designed to acquire this information. Laser Induced Fluorescence was used to study the radiative properties of InBr for lighting purposes. Using an innovative method to interpret the measured data, detex plots, more information can be obtained from the spectra. Also the effect of a background gas and plasma was investigated for both a capacitive and an inductive plasma.

Mainly the electronic A-state of InBr was investigated. Results include newly identified rotational transitions, vibrational constants, rotational constants for different vibrational levels, band head wave numbers and Franck-Condon factors for various vibrational transitions.

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1. Introduction Some of the most efficient light sources -lamps-we know are the fluorescent lamps and the high intensity discharge lamps. The fluorescent lamp has a very efficient efficient mercury discharge that produces UV radiation with an efficiency of around 75% in practical configurations [START_REF] Lister | The physics of discharge lamps[END_REF], [START_REF] Waymouth | Electric discharge lamps. Monographs in modern electrical technology[END_REF]. This radiation is then converted to visible light using fluorescent powders with a relatively poor efficiency caused by the Stokes losses [START_REF] Ronda | Luminescence[END_REF], yielding a total efficiency of around 30%.

The high intensity discharge lamps work rather differently. These lamps produce visible light directly from a mercury discharge enriched with some metals, usually in the form of metal halides. The combination of a 5000 K LTE plasma with a relatively cool wall (1200 K), leads to thermal losses and moreover many lines radiate in the IR region. The overall efficiency of these lamps is also around 30-35%.

To try to avoid the losses incurred in the two lamp types described above, a new lamp type is suggested. Basically, the goal is a lighting system that has the best of both worlds: no conversion losses and no IR and heat losses. In reality though, such a lamp will have a bit of both worlds. The discharge will probably produce radiation with a more desirable spectrum than a low pressure mercury discharge, though probably not quite as good as the discharge in a high pressure lamp. Therefore it may well need some limited conversion of the spectrum in phosphors, but then the hope is that the Stokes losses can at least be significantly reduced. The same holds for the heat losses of such a lamp: much better than for a high pressure discharge, but probably not quite as good as for a low pressure discharge. All in all though, this approach can open up possibilities for a more efficient discharge lamp [START_REF] Stoffels | Discharges for lighting[END_REF], [START_REF] Scholl | Low pressure gas discharge lamp with a mercury-free gas filling[END_REF], [START_REF] Scholl | Low pressure gas discharge lamp with gas filling containing tin[END_REF], [START_REF] Hilbig | Low-pressure gas discharge lamp with an alkaline eart chalcogenides as electron emitter material[END_REF], [START_REF] Hildenbrand | Low pressure vapor discharge lamp with a mercury-free gas filling[END_REF].

A promising candidate to serve as the prime radiator in such a lamp is Indium Bromide, but spectroscopic data to assess its aptitude is largely unavailable. To increase the knowledge of the spectroscopic properties of these molecules and InBr in particular, an experiment was designed to acquire this information. Laser Induced Fluorescence was used to study the radiative properties of InBr for lighting purposes. Results include the temperature dependence of the fluorescence decay time, spectroscopic constants and rotational temperature determination from a LIF spectrum.

InBr has interesting properties for plasma lighting applications [START_REF] Hastie | High temperature vapors : science and technology. Materials science and technology[END_REF]. It has a high vapor pressure at low temperatures [START_REF] Schnedler | The calculation of complex chemical equilibria[END_REF], and significant part of the emitted light is emitted in the (near) visible part of the spectrum [START_REF] Bruchhausen | Resonant coherent anti-stokes raman scattering applied to vapor phase ini[END_REF], [START_REF] Hilbig | Molecular discharges as light sources[END_REF], [START_REF] Hilbig | Investigations on low pressure indium mono-halide discharges[END_REF], [START_REF] Flesch | Light and Light Sources[END_REF], [START_REF] Stoffels | Discharges for lighting[END_REF]. In this article, spectrally resolved laser induced fluorescence measurements on indium bromide will be discussed. First we will discuss some theoretical aspects, such as the general properties of the InBr spectrum and the Franck-Condon factors. Then we will describe the method used to carry out the measurements presented later in this article. Finally we will present the results of the measurements and some conclusions.

Theory

Indium Bromide Spectrum

Here, features of the Indium-Bromide spectrum will be discussed [START_REF] Papoušek | Vibration-rotational spectroscopy and molecular dynamics: advances in quantum chemical and spectroscopical studies of molecular structures and dynamics[END_REF], [START_REF] Griffiths | Introudction to Quantume Mechanics[END_REF], [START_REF] Alonso | Quantumfysica. Fundamentele Natuurkunde[END_REF], [START_REF] Kovacs | Rotational structure in the spectra of diatomic molecules[END_REF], [START_REF] Whiting | Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra[END_REF]. The ground state of InBr is a 1 Σ + 0 state. The first exited state, (A) is a 3 Π + 0 state. There is also a B-state, this is a 3 Π 1 state [START_REF] Herzberg | Molecular Spectra and Molecular Structure[END_REF], [START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF], [START_REF] Yang | Experimental and theoretical study on the electronic states and spectra of inbr[END_REF], [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF]. Together with the metastable 3 Π - 0 and 3 Π 2 states, they form a triplet state ‡ which is split due to spin-orbit coupling. The C state is a 1 Π state. A schematic drawing (not to scale) of the energy levels is shown in figure [START_REF] Lister | The physics of discharge lamps[END_REF]. The wave number of the photons that can be emitted or

X 1 Σ + 3 Π 0 (0 -) A 3 Π 0 (0 + )
26 597.9 cm -1

B 3 Π 1 (1) 27 381.3 cm -1 3 Π 2 C 1 Π(1)
34 955 cm -1

Figure 1. A schematic view of the energy levels of InBr freely after [START_REF] Mishra | Spectroscopic studies of diatomic indium halides[END_REF]. The electronic states of InBr are shown with three vibration levels each. For the electronic ground state X (vibrational state 0) a schematic drawing of the rotational structure is shown in an inset. All vibrational states of all electronic states of InBr have a rotational structure similar to this one. The dotted lines represent metastable states. The arrows indicate vibrational transitions between the ground state (X) and the A-state with ∆v = 0 absorbed is determined by the difference in energy between the upper and the lower state involved in the transition. In the InBr spectrum, the difference in wave number between ‡ It may seem strange that this triplet state consist of four states, however the A ( 3 Π + 0 ) state and the metastable 3 Π - 0 are in fact one level split in two states.

transitions that have the same ∆v is small §. Therefore, they are grouped together in the spectrum in so called ∆v bands. Three of the vibrational transitions that belong to the ∆v = 0 band are shown in figure [START_REF] Lister | The physics of discharge lamps[END_REF]. An example of the spectrum of an InBr-Argon plasma is shown in figure [START_REF] Waymouth | Electric discharge lamps. Monographs in modern electrical technology[END_REF]. In this spectrum, the rovibrational structure of the transitions between the electronic A-state and the ground state (X), alongside transitions between the electronic B-state and the ground state (X) can be seen. In this article, mainly transitions between the electronic A-state and the ground state are studied. The focus is on the rotational structure of vibrational transitions in the ∆v = 0 band. However, measurements on the ∆v = +1 and ∆v = -1 bands have also been performed. The rotational structure consists of a P-branch, and an R-branch. The P-branch forms a band head. An example of a laser absorption spectrum of the ∆v = 0 band is given in figures [START_REF] Ronda | Luminescence[END_REF] and [START_REF] Stoffels | Discharges for lighting[END_REF]. In figure [START_REF] Ronda | Luminescence[END_REF] the band heads of the P-branch of the 0-0 and the 1-1 level are indicated. A more detailed view, with the rotational quantum numbers of the levels indicated is shown in figure [START_REF] Stoffels | Discharges for lighting[END_REF].

Two different stable isotopes of Bromine exist, which are approximately equally naturally abundant: 79 Br and 81 Br. Therefore, different isotopes of the InBr molecule exist. They are indicated as InBr 79 and InBr 81 . For different isotopes, the same general formulae hold, however, the spectroscopic constants such as B v are (slightly) different. Wavenumber (cm -1 ) (0,0)

(1,1)

Figure 3. An absorption spectrum of the ∆v = 0 band of the electronic transition between the A-state and the ground state. The band head of the 0-0 and the 1-1 transition are visible on the left. Rotational transitions with higher J are visible to the right. This graph was calculated from a ∆v = 0 detex plot by integrating all the fluorescence emission per excitation wavenumber, which corresponds to the absorbtion at that wavenumber.

Franck-Condon Factors & Branching Ratios

The vibrational structure of an electronic transition is explained by the Franck-Condon [START_REF] Franck | Elementary processes of photochemical reactions[END_REF] [26] principle as paraphrased by [START_REF] Atkins | Physical Chemistry[END_REF]:

Because the nuclei are so much more massive than the electrons, an electronic transition takes place very much faster than the nuclei can respond.

During a transition, e.g. from the ground state, the electronic configuration of the molecule is rapidly changed. The nuclei are subjected to a new force field due to the new constellation of electrons around them. They respond by starting to vibrate from their original positions, which was so far unchanged during the rapid electronic transition.

In the quantum mechanical formulation of the Franck-Condon principle, the molecule undergoes a transition to the upper vibrational level that most closely resembles the vibrational wave function of the lower vibrational level of the electronic ground state.

The intensity of a vibronic transition is proportional to the square of the overlap integral between the vibrational wave functions of the two states that are involved in the transition. This is known as the Franck-Condon factor for the transition. To obtain the rotational quantum number of the exited A-state add one, since for the R-branch J ′ = J ′′ + 1 holds. In this region of the spectrum the rotational quantum number of the R-branch peaks of InBr 81 is one higher than that of InBr 79 , these peaks coincide.

Rotational Redistribution Broadening

When the InBr molecules collide with Argon atoms, the rotational quantum number can change. It has been observed that for the typical Argon pressures in our experiments, this process can be as fast as the optical decay. The rotational redistribution process becomes faster at higher temperatures, due to the increased collision frequency. Evidence for the redistribution can be found in the measurements presented further on in this paper. The spectra with Argon as a background gas look distinctly broader than the spectra without background gas. The various aspects of these measurements will be discussed in more detail in section 5.

Experimental Setup

Introduction

A setup was built to perform LIF experiments [START_REF] Demtröder | Laser Spectroscopy[END_REF] to determine various fundamental properties of Indium Bromide as well as some operating properties of the lamps under investigation. The gas temperature of these plasmas was one of the most important properties to be measured, as it carries a lot of information about the state of the discharge.

Furthermore, the Franck Condon factors of various vibrational transitions and the corresponding transition energies were determined. Also the transition energies of some rotational transitions were measured.

General

In this section we will give a general description of the setup. The setup is built around an oven with inside it a quartz tube containing Indium Bromide. The tube containing the InBr is heated to the desired temperature to evaporate the InBr. A laser system is used to excite the molecules. An elaborate detection system containing an iCCD camera and photon counting equipment is used to detect the fluorescence.

Oven

For the experiment on InBr vapor, the quartz tube with InBr vapor is placed in an oven. In this oven the sample can be heated up to approximately 633 K. However, most of the measurements were done at a temperature of about 513 K to reach the optimal InBr vapor pressure (∼1 Pa) for the determination of spectroscopic constants in our setup. A higher temperature quickly leads to a much higher pressure causing undesirable broadening of the spectra and at a lower temperature the intensity of the fluorescence quickly drops below the detectable level.

The oven is mounted on two rails that allow for horizontal movement, perpendicular to the axis of the quartz tube inside it. The position is adjusted by moving the micrometer adjuster screw (1 in figure 5). To prevent turbulence in the optical path accessing the oven, two 20 cm long tubes (2 in figure 5) are mounted on both ends of the oven.

Around the oven a heat shield is mounted (3 in figure 5). It also serves as a radiation shield, since the discharge inside can produce UV-radiation. The oven is suspended from 3 rods (4 in figure 5) that connect it to the baseframe. The rods are connected to the quartz part of the oven. The purpose of this construction is to reduce heat conduction losses to the base and optical table.

The oven is heated by six infrared radiators (5 in figure 5): three mounted above the quartz tube and three mounted below the quartz tube. Each group of three heaters is controlled by a separate 2132 Eurotherm PID controller. Each controller is fed with temperature data from a K-thermocouple strategically placed above or below the quartz tube.

The front and back ends of the oven are also heated to create a temperature profile that is as homogeneous as possible. The edge heaters are controlled by one Eurotherm 2116 PID controller. This controllor receives temperature data from 2 K-thermocouples attached to the ends of the oven.

After enough stabilization time, the temperature of the oven is within 1 K of the requested temperature. The cold spot of the tube is within 1 K of the oven temperature. 6 steel rings (6 in figure 5) hold the quartz tube (7 in figure 5),that will be described in the following section, in place by clamping it firmly. They are flexible, to allow for variation of the tube diameter.

Quartz Tube

The quartz tube used in this experiment is mounted inside the oven described in section 3.3 as can be seen in figure 5. The tube is about 30 cm long and has a diameter of 3 cm. A small protrusion can be seen at about 1 4 of the length. This is the pipe that was used to fill the tube with the desired dose and seal it. On the ends of the tube, Tantalum electrodes are used to increase the RF coupling efficiency.

Excitation

The excitation in this setup is performed by a tunable dye laser pumped by a high repetition rate, frequency tripled Nd:Yag laser, built by EdgeWave GmbH. The laser beam is not focussed into the plasma.

The dye laser used in these experiments is a Cobra Stretch high repetition rate laser, manufactured by Sirah GmbH.

The laser dye used in the experiments is Exalite 376, which can emit in the 370-380 nm wavelength range (≈ 27.0 • 10 3 cm -1 -26.3 • 10 3 cm -1 ). The laser is used to excite the InBr at various wave numbers. In table [START_REF] Lister | The physics of discharge lamps[END_REF] the specifications of the Nd:Yag laser and of the dye laser are summarized.

The absolute wavelength error of ≤ 0.03 nm at 570 nm scales to an absolute error of about 1.5 cm -1 at 26600 cm -1 . The reproducibility of ≤ 0.005 nm at 570 nm scales to an error of about 0.2 cm -1 at 26600 cm -1 . These specifications indicate the direct tuning to a specific wave number will likely not be very accurate. This is why a laser scan is used. The starting wave number has an offset, but from a starting wave number, the subsequent steps of a scan are reproducible. The shape of the spectrum can be used to calibrate the wave number axis. The high repetition rate is vital for these experiments, due to the easily saturated transitions in this study. To prevent saturation, only very small amounts of energy per shot can be used to induce the fluorescence. This yields very small amounts of fluorescence. In order to detect these signals, the experiment has to be repeated many times. To do this in a reasonable amount of time, a high repetition rate is needed. Experiments were performed to confirm the absence of saturation. The typical modus operandi of these tests was to repeat a measurement with only half the laser power as in the first measurement, then a quarter of the laser power and so on. Without exception, all these tests showed that the signal scaled linearly with the laser power, confirming the absence of saturation.

Detection

The fluorescence emitted by the excited InBr-molecules is collected with a lens and directed to either a photomultiplier tube (PMT) or an intensified CCD camera (iCCD). A monochromator is used to select the bands for study. Alternatively, a UG11 filter is used to allow light from all A→X and B→X transitions to reach the PMT at once. Using this filter, light from all possible decay paths of the excited level can be detected. The PMT is used to perform the time resolved (tr)-LIF measurements. The iCCD camera is used to perform the spectrally resolved (sr)-LIF measurements.

The monochromator used in this experiment is a Jobin-Yvon HR1000. One of the issues that we encountered with the monochromator was due to temperature stability. The wavelength calibration of the monochromator varied with ambient temperature. This caused undesirable intensity fluctuations in measurements with the PMT resulting in unreliable intensity profiles. The temperature of the lab could vary by more than 10 ℃ due to the large south facing windows.

To suppress these fluctuations, a system was built to isolate the monochromator from ambient temperature fluctuations. The system was made of an insulating box, a heating device and a feedback control system. This system stabilized the temperature of the monochromator at 40 ℃. With this system in place the fluctuations are reduced to an acceptable level of ±1 pixel from ±15 pixels. 1 pixel roughly corresponds to 15 pm. Fluctuations up to about 75 pm are acceptable, but anything beyond that creates serious intensity fluctuations in measurements with the PMT.

Observing the LIF signal is not easy because of the low intensity of the light. An iCCD camera was used because it is much more sensitive than a classic CCD camera. The camera used in these experiments is a 4 QuickE iCCD camera made by Stanford Computer Optics. The 4 Quick E camera is fast: it can switch the intensifier on or off in 1.2 ns, making short gating times possible. This is combined with a very high repetition rate (3.3 MHz in burst mode). The spatial resolution of the CCD is 768 × 494 pixels.

The background level increased problematically during long measurements. This was caused by the increasing temperature of the lab during these measurements.

To decrease the influence of ambient air temperature fluctuations, a water cooled Peltier element is used. It is attached to a heat sink that is directly attached to the CCD matrix. With this cooling system, a constant temperature of -3 ℃ is maintained in the iCCD camera. In this way, the background is reduced by a factor ∼ 6, which is essential to make the LIF signal detectable against the background.

The light from the spectrometer is detected with a photomultiplier (PMT) (Hamamatsu H6780) tube to capture and count single photons of one distinct wavelength with good time resolution.

The PMT is connected via an amplifier (Ortec 9306) to an Ortec 9353 multichannel scaler (MCS) to obtain time resolved signals. The MCS has a burst sampling rate of 1 GHz.

A multichannel scaler reacts to a start and a signal pulse. The start pulse starts an internal clock of the MCS that runs from 0 to a preset end time for the experiment. In our experiments, the preset end time is typically of the order of 10 µs: the time after which the LIF signal has decayed below the noise level. The detection interval is divided into smaller intervals called bins. The binwidth in our case is typically 1.2 ns.

The signal pulse -sometimes called stop pulse in the instrument jargon-is in our case an amplified pulse from a PMT. If the voltage on the signal port of the MCS increases above an adjustable discriminator level, the MCS detects a pulse. It responds to that by increasing the counter of the appropriate bin by 1. After detecting a pulse, an MCS typically is unable to respond to pulses for some time: the dead time.

By repeating an experiment multiple times, a time evolution of a signal can be gradually acquired this way.

Plasma

In a number of experiments, a plasma is ignited in the tubes for these experiments. To do this, various RF amplifiers have been used, such as the KALMUS 122C, the Amplifier Research 75A250 and the Electronics & Innovation AB-250. To measure the power going into the plasma, a system of directional couplers was used, made by Amplifier Research. To read out the data from the couplers, the Amplifier Research PM2002 was used.

Method: detex Plots

The spectrally resolved LIF (sr-LIF) measurements have been performed using the iCCD camera (as described in section 3) to collect the emitted light. Also for these measurements, the dye laser (as described in section 3) is scanned over a preset wave number range. Typically 1000 lasershots are accumulated to produce a camera image. The sr-LIF measurements are time integrated. The time integration frame is 1 µs. This means that the first 1 µs of the fluorescence emission is collected on the iCCD. For each step of the scan, an iCCD image is obtained. The spectral range of one iCCD image is typically about 700 cm -1 . The camera images from all steps in the dye laser scan are combined into a detection-excitation plot (detex plot). This portmanteau was introduced to abbreviate this word, but also because this is a new diagram to be used in the interpretation of laser induced fluorescence. Similar diagrams have been used for Raman scattering on carbon nanotubes [START_REF] Hirana | Strong microdielectric environment effect on the band gaps of (n,m)single-walled carbon nanotubes[END_REF].

In these detex plots, the excitation wave number is put on the vertical axis. The detection wave number is put on the horizontal axis. The intensity of the detected signal is plotted color coded in this frame, so the color at an x-y coördinate gives the intensity of the emission at the detection wave number (on the horizontal axis) after absorption at the excitation wave number (displayed on the vertical axis). In figure 6 the color coding process is schematically shown. Figure 7 shows a complete detex plot.

Putting the detection wave number on the horizontal axis may seem counter intuitive, but it is helpful, because then every horizontal line in the detex plot represents a fluorescence spectrum taken at the wave number indicated on the vertical axis.

Results

In this section the results of the measurements will be shown and discussed. First, results for the InBr vapor without buffer gas and without a plasma will be shown, followed by results for the vapor with the buffer gas without plasma. Finally results for the plasma will be shown, both for a capacitively coupled plasma and an inductively coupled plasma.

InBr Vapor detex Plots

Figure 8 shows the detex plot of the measurement carried out in InBr vapor without background gas and without plasma. In these plots, the sr-LIF signal is shown with the detection wave number on the horizontal axis, for different laser wave numbers (vertical axis). The vertical bands are the various ∆v bands. For the InBr measurement, each of them consists of three smaller branches. For these measurements, the laser excitation was in the ∆v = 0 band. The vibration bands of the detex plots of the InBr measurement show three branches. When the branches are studied carefully, one can see a spot in the central branch for every spot in the left branch, as well as one for every spot in the right branch. This is shown in figure 9. This phenomenon is explained by the following. When the laser is tuned to a wave number that matches absorption in the P-branch (∆J = -1) -e.g. between the ground state vibration level 0, J=130 to the exited A-state, vibration level 0, J=129-, there are two possibilities to go back to the electronic ground state vibrational level 0: to J=130, P-branch emission and to J=128, R-branch (∆J = +1) emission. Because the energy difference between (A,0,129) and (X,0,130) is smaller than the energy difference between (A,0,129) and (X,0,128), this emission appears on the high wave number side.

Near these lines, there is also excitation via the R-branch, e.g. from electronic ground state vibrational level 0, J=86 to the exited A-state, vibration level 0 J=87. Also for this exited level, there are two possibilities to go back to the electronic ground state vibrational level 0: to J=86, R-branch emission and to J=88, P-branch emission. Because the energy difference between (A,0,87) and (X,0,86) is bigger than the energy difference between (A,0,87) and (X,0,88), this emission appears on the low wave number side.

The central branch consists of emissions from relaxation transitions from upper to lower level that take place through the same path as the excitation. The left branch is emission in the R-branch after absorption in the P-branch. The right branch is emission in the P-branch after absorption in the R-branch. In figure [START_REF] Schnedler | The calculation of complex chemical equilibria[END_REF] an energy level diagram is shown to illustrate this process. In terms similar to the terminology used for selection This is an ad hoc abbreviation for electronic A-state, vibrational level 0, rotational level 129. Left: Excitation via the R-branch. Relaxation is possible through two paths, in the R-branch, with the same wave number as the excitation, and in the P-branch, with a lower wave number than the excitation.

n n-1 n-2 n-3 n+2 n+1 n+3 n n-1 n-2 n-3 n+2 n+1 n+3 m m-1 m-2 m-3 m+1 m+2 m+3 m m-1 m-2 m-3 m+1 m+2 m+3 A A C L C R J'' J' J' J'' A state,
Right: Excitation via the P-branch. Relaxation is possible through two paths, in the P-branch, with the same wave number as the excitation and in the R-branch, with a higher wave number.

rules, ∆J ′′ = +2, 0, -2 can be used to indicate the left (lower detection wave number) central and right (higher detection wave number) branch respectively. From this explanation it can be concluded that the distance between the left branch and the central branch can be calculated from F (J ′′ + 2) -F (J ′′ ). The distance between the right branch and the central branch follows from F (J ′′ ) -F (J ′′ -2). Also, the other way around, if the rotational constants of the lower level are known e.g. from microwave studies, the distance between the branches can be used to determine the rotational quantum number of the level, though this would require a greater resolution than what is available in our setup.

When the rotational quantum numbers of the upper level and their peak positions are known, the rotational constants of the upper level can be determined from the distance between them. This is done as follows; two peaks with the same lower level are searched, the distance between them is now determined by the rotational constants of the upper level by a formula analogous to the previously mentioned ones.

Determining wave numbers of rotational transitions of the P-branch ∆v = 0

The sr-LIF measurements can be used to determine the rotational quantum number and the wave number of the transitions. For the electronic A-state vibration 0 to the electronic X-state vibration 0 a list of the wave numbers at which different rotations of the P and R-branch appear has been produced by [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF]. For high wave numbers, the rotational quantum number of a P-branch transition is approximately 40 higher than the rotational quantum number of an R-branch transition that appears near the same wave number. This is due to fact that the P-branch forms a band head. Because the rotational quantum number of the R-branch is lower, the transitions are more intense. It is therefore difficult to determine the locations of the P-branch transitions for high wave numbers.

From the discussion in the previous section it is concluded that in the detex plots, the left rotation branch is light that is emitted in the R-branch after absorption in the Pbranch. In this branch, there is no emission from absorption in the R-branch. Therefore, the left rotation branch can be used to determine the wave number of transitions of the P-branch.

To do this, the range of data corresponding to the P-branch under investigation has to be identified and isolated. This is done by carefully selecting the part of the detex plot (generally 9 data points wide) and creating a graph of the fluorescence emission of the v = 0 P-branch emission of the electronic A-state versus the excitation wavelength. Typically, such a graph looks like an absorption spectrum such as in figure 3, but it exclusively contains emission from the P-branch. After this, the job of identifying peaks and noting their wave number begins (see figure 4). This procedure, produces a list of wave numbers of a sequence of peaks. To find the corresponding rotation quantum number J, it has to be matched with the list produced by [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] -in this case-and for any additional lines, the numbering is continued.

In this article the wave numbers of P-branch transitions have been determined up to J=174, which extends the list produced by [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] that goes up to J=140. The results are listed in table 2. In the ∆v = 0 band, the rotational transitions of the electronic A-state vibration 1 to the electronic X-state vibration 1 appear. Because the transition probability of this transition is smaller [START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF] (see also table 3), and because the population of vibration level 1 is smaller than that of vibration level 0, the intensity of this transition is lower than the intensity of the 0-0 transition. It is difficult to identify the wave numbers of the 1-1 transition in the ∆v = 0 band. However, after excitation in the ∆v = 0 band, the fluorescence signal in the ∆v = 1 band can be evaluated to determine the wave numbers of the rotations of the 1-1 vibrational transition as a function of the rotational quantum number. These values can then be used to determine the rotational constants of vibration 1 of the electronic A-state.

At T = 500 K, the expected relative intensities of emission in the ∆v = 1 band after excitation in the ∆v = 0 band for a LIF measurement are displayed in table 3 for the different upper levels.

To determine the rotational constants of vibrational state 1 of the electronic Astate from a normal absorption or emission spectrum, the ∆v = 1 band is evaluated. At T = 500 K, the expected relative intensities of emission in the ∆v = 1 band are displayed in table [START_REF] Stoffels | Discharges for lighting[END_REF].

By comparing tables 3 and 4, it can be concluded that in a detex plot with excitation in the ∆v = 0 band, the fluorescence signal in the ∆v = 1 band will have less interference from rotations of other upper levels than in an ordinary absorption or emission spectrum of the ∆v = 1 band. Therefore, it will be easier to determine the wave numbers of the transitions from such a LIF experiment. This same procedure can be used to isolate rotational spectra from different upper levels by choosing the right combination of excitation and detection band. It can be concluded that detex plots resulting from LIF measurements are an accurate method to determine the wave numbers of rotational transitions of various upper levels. This is particularly helpful in dense spectra such as the InBr spectrum.

5.1.2. Determining B A0 from the R-branch data of the ∆v = 0 transition In the same way as described in the previous section, the wave numbers of transitions in the R-branch of the transition from the A-state, vibrational level 0 to the ground state, vibrational level 0, have been determined. The results are listed in table 5.

Table 5: Wave numbers of the R-branch rotational transitions of the transition between the electronic Astate vibration 0 and the ground state vibration 0 for InBr 79 according to the measurement in this report and according to [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] J, R-branch InBr 79 (cm -1 ) [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] (cm -1 ) J, R-branch InBr 79 (cm -1 ) [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] Using this information, one can make a graph of J versus wave number for this specific transition. It can then be fitted with a formula describing the relationship between J and the wave number for the R-branch:

ν(J) = ν 0 + J 4 (D ′′ -D ′ ) + J 3 (2D ′′ -6D ′ ) + J 2 (-B ′′ + B ′ + D ′′ -13D ′ ) (1)
+ J(-B ′′ + 3B ′ -12D ′ ) + 2B ′ -4D ′ .
In this equation, ν(J) denotes the wave number of the R-branch transition for that particular rotational quantum number J. ν 0 is the wave number of the vibronic transition (incorporating the electronic and vibrational transition energy). B is the rotational constant where a single prime denotes the upper state and a double prime the lower state. This aforementioned graph for the most comprehensive data set we have, which is from [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] up to J = 76 and data from our own measurement up to J = 130, is presented in figure 11. The R-branch data is fitted with equation 1. From microwave measurements [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] it is known that the ground state rotational constant B ′′ = 0.0557099 cm -1 and the ground state anharmonicity D ′′ = 1.42 • 10 -8 cm -1 . From the fit various constants were determined: the rotational constant of the lowest vibrational level of the Astate B ′ = B A0 = 0.058410 ± 0.000002 cm -1 and the anharmonicity D ′ = D A0 = 1.59 • 10 -8 ± 1 • 10 -10 cm -1 .

To check the consistency, also the P-branch data was fitted. The values found were B ′ = B A0 = 0.05842 ± 0.00001 cm -1 and D ′ = D A0 = 1.55 • 10 -8 ± 5 • 10 -10 cm -1 . These results are consistent with the data presented above, however less accurate, due to the smaller and noisier data set. After isolating the R-branch of the ∆v = +1 in the data set, a graph of the relative intensity of the R-branch signal versus the wave number is obtained, as is shown in figure 13.

From this graph, the wave numbers of the peaks were obtained, resulting in a sequence of identified peaks which are listed in table 6. Due to the noise levels, it can be quite difficult to identify and follow sequences of peaks and in this case the confidence in the accuracy of the first column (Isotope 1) of peaks is higher. Therefore, this column will be used to calculate B A1 and D A1 . Of course a major obstacle in achieving this goal is the assignment of the rotational quantum number (or lack thereof). To make a best guess -because that is what it will be-the fit with formula 1 is performed for various values of i. The various fitted parameters are evaluated and compared to the values that are expected. This is shown for the wave number of ν(0), as is shown in figure 14. The same is done for the rotational constant B A1 and for D A1 . The best value for Ji is determined by assuming that the value found for the fitted ν(0) should be close to the measured value. For the values of B A1 and D A1 it is assumed that they are probably close to the values found for B A0 and D A0 .

The best fit (for J = i + 38) is shown in figure 15. It leads to B A1 = 0.05809 ± 0.00005 cm -1 and D A1 = 1.8 • 10 -8 ± 0.2 • 10 -8 cm -1 . In this case the assignment for J is J = i + 38. The uncertainty band of these numbers is determined by the change as a consequence of a mis-assignment of J of ±1. This would lead to a relatively small change in B A1 , but it would lead to a significant change in D A1 of the order of 10%. 5.1.4. Determining B X1 from the R-branch data of the ∆v = -1 transition To determine B X1 , the first method to be tried was by looking at the detex plot obtained by exciting via the ∆v = -1 transition. This plot is shown in figure 16. The problem with this approach is that there are simply too many different vibrational transitions with a high intensity in this particular ∆v-branch. This fact makes it virtually impossible to distinguish the individual rotational transitions on close inspection, because there are simply too many sets of lines that are mixed together. What would have been nice about this method is that it couples the v = 1 level of the electronic ground state with the v = 0 level of the A-state, of which the rotational constants are known to a high degree of accuracy. Another option to obtain B X1 is to use the ∆v = 0 detex plot as was shown in figure 8. Since B A1 was already determined in the previous section, we can use this plot to couple the v = 1 level of the ground state with the v = 1 level of the A-state.

Just like in the previous section, the applicable set of data is isolated. A graph of the relative intensity of the R-branch signal versus the wavelength is obtained, as is shown in figure 17.

From this graph, the peaks were identified, resulting in a sequence of identified peaks which are tabulated in table 7. To make a best guess the fit with formula 1 is performed for various values of i. The various fitted parameters are evaluated and compared to the values that are expected for them. This is done for the wave number of ν(0), the rotational constant B X1 and for D X1 .

The best value for Ji is determined by assuming that the value found for the fitted ν(0) should be close to the measured value. For the values of B X1 and D X1 it is assumed that they are probably close to the values found for B X0 and D X0 .

The best fit (for J = i + 56) is shown in figure 18. It leads to B X1 = 0.056677 ± 0.00002 cm -1 and D X1 = 2.83 • 10 -8 ± 0.01 • 10 -8 cm -1 . In this case the assignment for J is J = i + 56. The uncertainty band of these numbers is determined by the change as a consequence of a mis-assignment of J of ±1. This would lead to a relatively small change in B X1 and in D X1 . The value of D X1 is surprising, because it differs significantly from D X0 . By looking for an excitation wave number that only excites from a single vibrational level of the ground state and therefore to a single vibrational level of the A-state, it is possible to find a very direct representation of the Franck-Condon factors in the detex plots.

For the v ′ = 0 vibrational level of the A-state this was done by looking at the fluorescence spectrum after excitation at 26600 cm -1 . At this energy, only excitation from v ′′ = 0 in the ground state to v = 0 in the A-state is possible, so all excited molecules are in the v ′ = 0 level of the A-state. By evaluating the fluorescence spectrum taken from the ∆v = 0 detex plot (figure 8) as shown in figure 19, it is possible to determine the relative intensities of the different decay paths, which correspond directly to the probability of that specific decay path. This probability is the Franck-Condon factor.

Franck-Condon factor [21]

A(v = 0) → X(v = 0) 0.602 0.6030 A(v = 0) → X(v = 1) 0.289 0.2841 A(v = 0) → X(v = 2) 0.088 0.0861 A(v = 0) → X(v = 3) 0.018 0.0211 A(v = 0) → X(v = 4) 0.0046
The error in these values is estimated to be 2%. That brings the measured values very close to -but not exactly in-agreement with the values found in [START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF].

The same procedure was followed for the v ′ = 1 level of the A-state. The resulting graph taken at 26825 cm -1 from the ∆v = 1 excitation detex plot is shown in figure 20. . The integrated intensities of these peaks are listed in table 10. An interesting observation is the fact that there is emission visible in the ∆v = +2band, since photons emitted in that band can not originate from molecules in the v ′ = 1 level of the A-state. This is caused by higher vibrational transitions, such as the 3-4 and 4-5 transition. This means that a small part of the emission recorded in figure 20 does not originate from the desired v ′ = 1 level. This has consequences for the accuracy of the Franck-Condon factors determined from this data. Since about 5.6% of the emission

Franck-Condon factor [21]

A(v = 1) → X(v = 0) 0.375 0.3273 A(v = 1) → X(v = 1) 0.118 0.1538 A(v = 1) → X(v = 2) 0.244 0.2863 A(v = 1) → X(v = 3) 0.150 0.1562 A(v = 1) → X(v = 4)
0.057 0.0555 5.1.6. Determination of Band Head Wave Numbers In most measurements various band heads are superimposed on eachother. This makes it difficult to accurately determine their respective wave numbers. This problem makes it more difficult to accurately simulate spectra. In detex plots, more band heads are separately visible because of the resolution of both the excitation and detection wave number. One can simply choose the most suitable ∆v-band to determine its wave number. Different detection bands can be used to determine wave numbers of band heads with low intensity that are super positioned on the rotational structure of a transition with high intensity. In this section the wave numbers of the 4-4, 5-5 and 6-6 band heads will be determined. Often, absorption or emission spectra are evaluated to determine the wave number of transitions. In these spectra the rotation band heads of the different vibrational levels may overlap. This is the case for InBr. In [START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF] the locations of the band heads of vibrational transitions have been determined. From these evaluations it follows that in the ∆v = 0 band, the 4-4, 5-5 and 6-6 transitions are superimposed on other strong transitions such as the 0-0 transition. Therefore it is difficult to determine the exact locations of these band heads. For the determination of band heads involved in superpositions, an sr-LIF experiment can be analyzed to more accurately determine the location of the band heads.

The procedure is based on evaluating the detex plots. The band head identification will be based on the following two factors. One is the wave number where the band head is expected according to literature. The other is the relative theoretical intensity of the emission in different ∆v bands. This last aspect is used to determine in which ∆v band to search. In the case of examining the 4-4, 5-5 and 6-6 transition of InBr this is the ∆v = 2 band. The relative intensity of the different bands is also used to identify peaks. The intensity detected in ∆v band depends on the population of the upper level and the Franck-Condon factor of the transition. The population of the upper level is created by absorption. The population of the upper level therefore depends on the Franck-Condon factor for the excitation and on the population of the lower level. An illustration of the basic principles behind the method is presented in figure [START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF]. The fluorescence from upper level vibration 0 to lower level vibration 0 is more intense than the fluorescence from upper level 1 to lower level 1. In the spectrum, these transitions are superimposed in the ∆v = 0 band, and therefore it is difficult to identify the properties of the 1-1 transition. In the ∆v = 1 band, there is no emission from the upper level vibration 0, therefore it is easier to identify emission from upper level vibration 1 in this band.

N ′′ 0 N ′′ 1 N ′ 0 N ′ 1 Excitation Excitation Detection Detection ∆v = -1 ∆v = 0 ∆v = 0 ∆v = 0 ∆v = 0 ∆v =
Vibrational level 0 as well as vibrational level 1 of the excited A-state have no emission in the ∆v = 2 band. Therefore, after excitation in ∆v = 0, the emission in the ∆v = 2 band is evaluated. Upper level 4 has emission in this band; the 4-2 transition does emit in this band. Vibration levels 2 and 3 of the A-state may also have emission in the ∆v = 2 band, however the Franck-Condon factors of the 2-2 and 3-3 transitions are very small. This means that the vibration levels 2 and 3 of the A-state will have a very small population, therefore the 2-0 and 3-1 transition in the ∆v = 2 band are not expected to be strong.

Although on the detection axis, the wave number of the 4-2 transition is shown, the wave number on the excitation axis is the wave number at which the 4-4 excitation has taken place, hence the band head of the 4-4 transition can be determined without being troubled by light from the 0 and 1 upper vibration level. The 4-2 transition can also be determined from a normal absorption or emission experiment, but in normal absorption or emission experiments it does not yield information about the 4-4 transition. Also for the 5-5 and the 6-6 transition, the ∆v = 2 band can be evaluated.

In table [START_REF] Bruchhausen | Resonant coherent anti-stokes raman scattering applied to vapor phase ini[END_REF], the predicted relative intensities of the peaks ¶ detected in the the ∆v = 2 band are listed. Although all the information on intensities is available from Table 11. The relative intensities of emission in the ∆v = 2 band depending on the upper level v ′ , after excitation in the ∆v = 0 band. The data is scaled to a value of 1 for the emission of upper level 0 in the ∆v = 0 band.

transition relative intensity

v ′ = 0 → v ′′ = -2 - v ′ = 1 → v ′′ = -1 - v ′ = 2 → v ′′ = 0 0.001 v ′ = 3 → v ′′ = 1 0.001 v ′ = 4 → v ′′ = 2 0.007 v ′ = 5 → v ′′ = 3 0.014 v ′ = 6 → v ′′ = 4 0.016 v ′ = 7 → v ′′ = 5 0.014 v ′ = 8 → v ′′ = 6
0.011 the detex plots, it is difficult to visualize the intensity profile from them. Therefore, the part of the detex plot that shows the ∆v = 2 band is spectrally integrated. The resulting partial spectrum shows the intensity of emission in the ∆v = 2 band after absorption in the ∆v = 0 band as a function of the wave number of absorption. The result is shown in figure 22. In table 12 the wave number of the identified band heads is displayed. When sr-LIF measurements are partially integrated, they give spectra like the ones in figure [START_REF] Yang | Experimental and theoretical study on the electronic states and spectra of inbr[END_REF]. This type of spectra can be made for detection in different ∆v bands.

By making the right choice of excitation and detection bands, the signal from the desired upper level can be found with as little as possible interference from other transitions. Therefore the wave numbers of the transitions involved in superposition in ¶ scaled to an intensity of 1 for the emission of upper level 0 in the ∆v = 0 band

(5) (4) The other way around, this principle can be used to calculate Franck-Condon factors based on the relative intensities of the different upper levels in integrated spectra of the different ∆v bands. This is because by comparing the shape of the different integrated spectra insight can be gained on the contributions of other upper levels and the effect of redistribution.

InBr Vapor with Background Gas

Spectrally resolved measurements were also performed for the ∆v = 0 excitation transition in InBr vapor with 2.5 mbar as a background gas, but without plasma. Figure 23 shows the detex plot obtained from measurements. Comparing this detex plot with the detex plot of the tube without the background gas, it is observed that the vibrational bands look very different when the background gas is present. The rotational branches are not visible anymore; each vibrational band is now represented by a very wide, unresolved spectrum.

From this it is concluded that the rotational redistribution processes + are much faster than the optical decay processes. The overall species density in the tube is higher due to the presence of the Argon. The rotational redistribution visible in figure 23 is caused by the collisions with Argon.

Rotational branches are not visible anymore, but vibrational bands are still clearly visible. The intensity ratios of these vibrational bands appear about the same as in the detex plot of the tube without the background gas. To confirm this, the relative intensities of the different vibrational bands were determined, in exactly the same way as in the previous section and they confirm that no vibrational redistribution has occurred.

The relative intensities of the various ∆v-bands at 26600 cm -1 for the determination of the Franck-Condon factors are listed in table 13.

Capacitively Coupled Plasma

The measurements discussed in this section were performed with the same tube as in the previous section, containing InBr powder and Argon at a pressure of 2.5 mbar. To make a plasma, the RF amplifier discussed in section 3 was used at 13.56 MHz. It was connected to the tube via an L-type matching network. The measurements were performed with the RF power set to 15 W. The effect of the plasma on the cold spot temperature was negligible.

To allow the plasma to stabilize, measurements were started at least 1 hour after the start of the plasma. All other settings of the trigger system, the laser and the camera used to perform these experiments were identical to the experiment in the previous section.

The detex plot obtained from a burning plasma is shown in figure 24.

Comparing figure 24 and figure 23 reveals no significant differences. From this it is concluded that for these conditions, the impact of the plasma on the fluorescence processes is very small, i.e. below the detection limit of our setup.

Inductively Coupled Plasma

For studies of the InBr plasma lamp, the first step was to find out at what locations in the lamp LIF-experiments are possible.

The most suitable location was picked and a detex plot was made for this location. No LIF-signal could be observed in the center of the lamp, but in other sections of the lamp the LIF-signal could be observed. These sections were just outside the bright center of the lamp, at the point where the white color faded to blue. This fact that no LIF signal could be observed in the center of the lamp leads to the question whether the LIF-signal was actually not there, or just not visible because the lamp masked the fluorescence by its own emissions. To gain insight in this matter, the intensity fluctuations of the plasma emission in the center of the lamp was compared to the intensity of the fluorescence signal at the sections where it could be observed. This comparison gave rise to the conclusion that the LIF signal is in fact not present at the center of the lamp. If it were there, it would have been observed, since the fluorescence signal elsewhere in the lamp exceeds the fluctuations of the plasma by a factor ∼ 5.

From this the conclusion is drawn that all the InBr in the center of the lamp is completely dissociated, so all molecular contributions to the spectrum originate from the edge of the plasma, where (3-particle) association processes can compete with the dissociation process, due to the lower plasma density. This also explains the strong atomic character of an inductive InBr lamp.

A detex plot was created for the section of the lamp where the LIF signal could be observed. Figure 25 shows this plot.

The uninterrupted diagonal line in the detex plot is an interesting artefact. It is caused by scattered light from the laser and therefore this line indicates the position where the detection wave number is equal to the excitation wave number. Another striking feature of this detex plot is the diagonal line that runs through the ∆v = 0 band of the A-state. This is scattered light from the laser. Its presence means that it is difficult to get accurate intensity data from this plot, however it is unavoidable and gives a good visual reference for the excitation frequency.

Another important observation is that all transitions, both A-X and B-X transitions, start at the same excitation wave number. This is different from what was observed in all other measurements. It indicates that in this situation, vibrational redistribution plays an important role. Furthermore, it is noted that the A-X emission at ∆v = +1 is more intense than the emission at ∆v = 0. This is an unexpected result as well, because the excitation of the laser produces population in v ′ = 0. Somehow, more fluorescence appears at photon energies higher than the energy of the photons supplied for excitation by the laser.

Similar to the measurements with the background gas, the rotational splitting is no longer visible, which is unsurprising.

The most important observation though, is that emission from the B-state occurs when excitation is to the A-state. This means that somehow, molecules are transferred from the A-state to the B-state. The emission seen in the B-bands is not just plasma emission, as it is not present when the laser energy is lower than ∼26600 cm -1 -and thus no laser excitation of the A-state takes place-but it is also clear that just the presence of the laser beam itself is not enough to create the emission from the B-state from the same observation.

It cannot be determined exactly how population is transferred to the B-state. Direct collisional transfer cannot be ruled out and neither can increased plasma emission due to increased population of the A-state.

Conclusions

For the correct assignment and interpretation of rovibronic spectra, sr-LIF measurements have a great advantage compared to normal emission or absorption spectra. This advantage is that there is a wave number axis for both the emission wave number as well as for the absorption wave number in the resulting detex plot. Normal emission or absorption spectra only have one of the two. The newly introduced detex plot is a very insightful way of representing the data found with this measuring technique. It also enables exploration of finer details of molecular spectra.

In a detex plot, transitions that interfere with each other in a normal absorption or emission spectrum can be separated. This splitting may occur for rotational transitions as well as for vibration transitions. Due to this splitting, in a detex plot, transitions with a low intensity can be studied with less interference from other transitions with higher intensity.

In this article, the splitting of rotational branches has been used to extend a list produced by [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF], containing the wave numbers at which the rotational transition of the electronic A-state vibrational level 0 to the ground state vibrational level 0 of InBr occurs. Almost 30 extra P-branch transitions have been identified.

The list of wave numbers of rotational transitions that was found to expand the list in [START_REF] Vempatie | Rotational analysis of the A0 + -X0 + systems of indium bromide[END_REF] has been used to determine the rotational constant of v = 0 of the A-state and its anharmonicity, B A0 .

For the transition from v = 1 of the A-state to v = 0 of the ground state, a list of wave numbers of rotational transitions was also produced by looking at the detex plot for excitation via the ∆v = +1 band. This list is incomplete, i.e. the beginning is missing. To still assign the correct rotational quantum number J to the transitions found, comparisons to the known values of such as B A0 were made. After this assignment, the value of the rotational constant B A1 of the v = 1 level of the A-state and its anharmonicity were determined. Similarly, B X1 and its anharmonicity were determined. The constants determined from all these experiments are listed in table [START_REF] Flesch | Light and Light Sources[END_REF]. The values found and the branch that has the band head are in agreement with the fact that B ′ > B ′′ as was expected in section 2.

Franck-Condon factors for vibrational transitions from v = 0 and v = 1 of the A-state of InBr to the ground state were determined by comparing the intensities of the various vibrational bands in the appropriate detex plots. In this work, the splitting of vibrational transitions has been used to determine the wave number at which the band heads of the 4-4, 5-5 and 6-6 vibrational transition between the electronic A-state and the ground state of InBr occur. In a normal absorption or emission spectrum the much stronger 0-0 transition is located in the same wave number range. This makes the determination of the location of the 4-4, 5-5 and 6-6 band head nearly impossible or inaccurate at best without the detex plots.

In the detex plot, the ∆v = +2 band emission has been used to determine at which wave number emission from vibrational levels 4, 5 and 6 of the electronic A-state occur. Since the excitation of InBr has been in the ∆v = 0 band, the wave number on the excitation axis can be used to determine the band heads of the 4-4, 5-5 and 6-6 vibrational transitions.

Also, detex plots were made of not just the InBr vapor, but vapor in combination with a background gas, of 2.5 mbar of Argon. In this situation, rotational redistribution due to the increased collision rate was shown to be significant compared to optical relaxation. This redistribution obscured the rotational branches, transforming each ∆v band into a single smeared out shape.

Additionally, a capacitively coupled plasma was produced in the tube with InBr and Argon at a power of ∼10 W. The capacitively couples plasma yielded similar data in a detex plot.

When a LIF experiment was attempted for an inductively coupled plasma, no LIF signal was visible in the center of the discharge. From this observation, the conclusion is that all the InBr in the center of the lamp is completely dissociated. All molecular contributions to the spectrum originate from the edge of the plasma, where association processes can compete with the dissociation process, due to the lower plasma density. The high degree of dissociation also explains the strong atomic character of an inductive InBr lamp. It was, however, possible to detect the LIF signal on the edge of the plasma in an inductively coupled discharge.

Figure 2 .

 2 Figure 2. The emission spectrum of an InBr-Argon plasma. The various ∆v bands of the electronic A-state and of the electronic B-state are indicated in the figure.

Figure 4 .

 4 Figure 4. A closer view of the spectrum of figure[START_REF] Ronda | Luminescence[END_REF]. The big peaks are rotation transitions of the R-branch. In this wave number range the peaks of the P-branch are much less intense. The numbers indicate the rotational quantum number of the ground state of the InBr 79 . To obtain the rotational quantum number of the exited A-state add one, since for the R-branch J ′ = J ′′ + 1 holds. In this region of the spectrum the rotational quantum number of the R-branch peaks of InBr 81 is one higher than that of InBr 79 , these peaks coincide.

Figure 5 .

 5 Figure 5. A drawing of the oven with the quartz tube visible inside. 1. Micrometer adjuster screw. 2. Anti-turbulence tubes. 3. Heat shield. 4. Suspension rods. 5. Infrared radiators. 6. Clamping rings. 7. Quartz tube.

Figure 6 .

 6 Figure 6. Schematic representation of step 1 in constructing a detex plot. For each scan, the energy collected by the camera is plotted as is shown on the bottom of this figure; the detection wave number is put on the horizontal axis. The intensity of the signal is color coded in this frame.

Figure 7 .

 7 Figure 7. Example of a detex plot. The intensity of the measured spectrum is color coded for each x-y-coördinate.

Figure 8 .

 8 Figure 8. The detex plot of the sr-LIF measurement on InBr. Excitation was in the ∆v = 0 band. From left to right the bands ∆v = -3 through ∆v = +2 are shown. Each vibration band consists of three different branches that are explained by the different combinations of rotational transitions in the P-branch and R-branch for excitation and detection.

Figure 9 .

 9 Figure 9. A close up of the detex plot of the sr-LIF measurement on InBr. On further inspection of the dots visible in this plot, one can see that the left and right dots do not coincide completely, although they do overlap largely.

Figure 10 .

 10 Figure 10. Illustration of the three branches. The letter A stands for absorption, the letters L, C, R indicate that the emitted light is detected in the left, center or right branch of the detex plot.Left: Excitation via the R-branch. Relaxation is possible through two paths, in the R-branch, with the same wave number as the excitation, and in the P-branch, with a lower wave number than the excitation.Right: Excitation via the P-branch. Relaxation is possible through two paths, in the P-branch, with the same wave number as the excitation and in the R-branch, with a higher wave number.

Figure 11 . 1 . 5 . 1 . 3 .

 111513 Figure 11. Graph of wave number versus rotational quantum number for the R-branch of the 0-0 transition from the A-state to the ground state. The red line running through the data points is a fit based on 1 .

Figure 12 .

 12 Figure 12. The detex plot of the sr-LIF measurement on InBr. Excitation was in the ∆v = +1 band. From left to right the bands ∆v = -3 through ∆v = +2 are shown. Each vibration band consists of three different branches that are explained by the different combinations of rotational transitions in the P-branch and R-branch for excitation and detection.

Figure 13 .

 13 Figure 13. Graph of the intensity of the R-branch of the ∆v = +1 vibrational transition versus the wave number versus at which it occurred.

Figure 14 .

 14 Figure 14. Graph of the wave number of ν(0) as determined from the fit based on 1 versus various values for Ji. The red line running through the data points is the actual ν(0) as directly measured from the data. The position of the bandhead suggests that J = i + 38 provided the best fit.

Figure 15 .

 15 Figure[START_REF] Papoušek | Vibration-rotational spectroscopy and molecular dynamics: advances in quantum chemical and spectroscopical studies of molecular structures and dynamics[END_REF]. Graph of wave number versus rotational quantum number for the R-branch of the transition from the A-state vibrational level 1 to the ground state vibrational level 0. The red line running through the data points is a fit based on equation 1.

Figure 16 .

 16 Figure 16. The detex plot of the sr-LIF measurement on InBr. Excitation was in the ∆v = -1 band. From left to right the bands ∆v = -3 through ∆v = +2 are shown. Each vibration band consists of three different branches that are explained by the different combinations of rotational transitions in the P-branch and R-branch for excitation and detection.

Figure 17 .

 17 Figure 17. Graph of the intensity of the R-branch of the ∆v = +1 vibrational transition versus the wave number of the fluorescence.

Figure 18 .. 5 . 1 . 5 .

 18515 Figure 18. Graph of wave number versus rotational quantum number for the R-branch of the transition from the A-state vibrational level 1 to the ground state vibrational level 1. The red line running through the data points is a fit based on equation1.

Figure 19 .

 19 Figure 19. Graph of the fluorescence recorded after excitation at 26600 cm -1 . At this wave number, all excited molecules are at v ′ = 0 in the A-state.

.

  The relative intensities are determined from figure19by calculating the total fluorescence emission for each ∆v-band by integrating the area under each emission peak and dividing it by the total emission from all ∆v-bands. The Franck-Condon factors found this way are listed in table 8.

Figure 20 .

 20 Figure 20. Graph of the fluorescence recorded after excitation at 26825 cm -1 . At this wave number, most excited molecules are at v ′ = 1 in the A-state.

Figure 21 .

 21 Figure 21. The intensity detected in ∆v band depends on the population of the upper level and the Franck-Condon factor of the transition, indicated in the figure as FC xy , where x denotes v upper and y v lower . The population of the upper level depends on the Franck-Condon factor in the excitation and the population of the lower level.The fluorescence from upper level vibration 0 to lower level vibration 0 is more intense than the fluorescence from upper level 1 to lower level 1. In the spectrum, these transitions are superimposed in the ∆v = 0 band, and therefore it is difficult to identify the properties of the 1-1 transition. In the ∆v = 1 band, there is no emission from the upper level vibration 0, therefore it is easier to identify emission from upper level vibration 1 in this band.

Figure 22 .

 22 Figure 22. The intensity of emission in the ∆v = 2 band after absorption in the ∆v = 0 band, as a function of the wave number of absorption. The number indicates the vibration level of the upper state.

Figure 23 .

 23 Figure 23. The detex plot of the sr-LIF measurement on InBr with 2.5 mbar of Argon as a background gas. Excitation was in the ∆v = 0 band. From left to right the bands ∆v = -3 through ∆v = +2 are shown. The vibrational bands do not show a separation into rotational branches as opposed to the detex plot obtained without the background gas.

Figure 24 .

 24 Figure 24. The detex plot of the sr-LIF measurement on a tube with a plasma of InBr with 2.5 mbar of Argon as a background gas. Excitation was in the ∆v = 0 band. From left to right the bands ∆v = -3 through ∆v = +2 are shown. The vibrational bands do not show a separation into rotational branches as opposed to the detex plot obtained without the background gas.

Figure 25 .

 25 Figure 25. The detex plot for the the edge of the InBr inductively coupled plasma lamp. From left to right the ∆v = -1 through ∆v = +2 vibrational bands of the A-state are visible and some (faint) B-state bands. They are marked in the graph where e.g. A -2 stands for the ∆v = -2 band of the A-state.Another striking feature of this detex plot is the diagonal line that runs through the ∆v = 0 band of the A-state. This is scattered light from the laser. Its presence means that it is difficult to get accurate intensity data from this plot, however it is unavoidable and gives a good visual reference for the excitation frequency.

Table 1 .

 1 Properties of the Nd:Yag laser which is used to seed the dye laser

	Nd:Yag laser
	wavelength	355 nm
	operating current	20 -40 A
	output power	0 -4 W
	pulse duration	5 -7 ns
	repetition rate	1 kHz
	dye laser
	grating	3600 lines/mm 90mm
	resolution	3 • 10 6
	absolute wavelength error ≤ 0.03 nm @ 570 nm
	wavelength reproducibility ≤ 0.005 nm @ 570 nm
	laser dye
	dye	Exalite 376
	range	370-380 nm
	dye peak efficiency	13%

Table 2 :

 2 Identification of the P-branch rotational transitions of the transition between the electronic Astate vibration 0 and the ground state vibration 0 for InBr 79 and InBr 81

	J	InBr 79 (cm -1 ) [23] (cm -1 ) InBr 81 (cm -1 ) [23] (cm -1 )
	121	26625.62	26625.59	26625.25	26625.23
	122	26.16	26.12	25.77	25.75
	123	26.72	26.65	26.30	26.29
	124	27.25	27.19	26.84	26.80
	125	27.79	27.73	27.38	27.32
	126	28.35	28.28	27.93	27.88

Table 3 .

 3 The relative intensities calculated from the data in[START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF] in the ∆v = 1 band in a detex plot, after excitation in the ∆v = 0 band at T = 500 K, scaled to an intensity of 1 for v ′ = 1.

		v ′ relative intensity
		0	-
		1	1.00
		2	0.08
		3	0.02
		4	0.10
		5	0.10
	167	55.34	54.59
	168	56.10	55.34
	169	56.83	56.10
	170	57.63	56.83
	171	58.44	57.63
	172	59.20	58.44
	173	59.99	59.20
	174	60.76	59.99

Table 4 .

 4 The relative intensities of emission in the ∆v = 1 at T = 500 K for a regular emission or absorption spectrum, scaled to an intensity of 1 for v ′ = 1, based on[START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF].

	v ′ relative intensity
	0	-
	1	1.00
	2	0.741
	3	0.382
	4	0.154
	5	0.047

Table 6 :

 6 Isotope 1 (cm -1 ) Isotope 2 (cm -1 ) i Isotope 1 (cm -1 ) Isotope 2 (cm -1 )

	J = 0	26827.78	26827.78 41	51.5223	52.7039
	i = 1	36.1160	36.1160 42	51.9656	53.2332
	2	36.4109	36.4109 43	52.4500	53.7391
	3	36.6844	36.6844 44	52.9148	54.2879
	4	36.9793	36.9793 45	53.4012	54.7742
	5	37.2742	37.2742 46	53.8875	55.3875
	6	37.5906	37.5906 47	54.3934	55.9363
	7	37.9285	37.9285 48	54.9227	56.4656
	8	38.2449	38.2449 49	55.3875	57.0144
	9	38.5613	38.5613 50	55.9363	57.5223
	10	38.8367	38.9617 51	56.4656	58.0281
	11	39.1531	39.3211 52	57.0144	58.5789
	12	39.4891	39.6805 53	57.5223	59.2977
	13	39.8055	40.0594 54	58.0281	59.825
	14	40.1434	40.4188 55	58.5789	60.4598
	15	40.4188	40.9871 56	59.1492	61.0301
	16	40.8406	41.368 57	59.7195	61.6219
	17	41.1766	41.6199 58	60.2898	62.2137
	18	41.5574	42.0418 59	60.7406	62.8269
	19	41.9168	42.4441 60	61.4539	63.5477
	20	42.3172	42.866 61	61.9813	64.1394
	21	42.6336	43.2879 62	62.5535	64.6883
	22	43.0125	43.7098 63	63.1238	65.0477
	23	43.3934	44.1531 64	63.7156	65.6609
	24	43.8777	44.575 65	64.3289	66.2547
	25	44.3426	44.9754 66	64.6883	66.8680
	26	44.7859	45.4671 67	65.2820	67.5242
	27	45.2078	45.9051 68	65.8953	68.0105
	28	45.6297	46.3699 69	66.4871	68.5184
	29	46.0516	46.8133 70	67.1434	69.1316
	30	46.5164	47.2762 71	67.6512	69.7664
	31	46.9598	47.7195 72	68.1375	70.3797
	32	47.4246	48.2273 73	68.8992	71.0144
	33	47.8680	48.7762 74	69.4285	71.6492
	34	48.3113	49.2625 75	70.0633	72.3484
	35	48.7762	49.7254 76	70.7195
	36	49.2625	50.1902 77	71.3738
	37	49.6629	50.6766 78	72.0105
	38	50.1063	51.2039 79	72.6668

Wave numbers of the R-branch rotational transitions of the transition between the electronic Astate vibration 1 and the ground state vibration 0 for InBr, for both isotopes. Since the assignment of these levels is unknown, they are simply numbered with index i. Note that in the first entry in the table the wave number i

Table 7 :

 7

	i	Isotope 1 (cm -1 ) Isotope 2 (cm -1 )	i	Isotope 1 (cm -1 ) Isotope 2 (cm -1 )
	J = 0	26683.9200	26683.9200 57	38.0059	61.6219
	i = 1	17.7441	36.1160 58	38.459	62.2137
	2	17.9707	36.4109 59	39.0176	62.8269
	3	18.1563	36.6844 60	39.4922	63.5477
	4	18.4023	36.9793 61	39.9668	64.1394
	5	18.6289	37.2742 62	40.5449	64.6883
	6	18.8770	37.5906 63	41.0605	65.0477
	7	19.1855	37.9285 64	41.6387	65.6609
	8	19.3906	38.2449 65	42.1953	66.2547
	9	19.6797	38.5613 66	42.6914	66.8680
	10	19.9258	38.9617 67	43.2695	67.5242
	11	20.2148	39.3211 68	43.8477	68.0105
	12	20.4414	39.6805 69	44.3848	68.5184
	13	20.7305	40.0594 70	44.9213	69.1316
	14	21.0176	40.4188 71	45.5410	69.7664
	15	21.2852	40.9871 72	46.1191	70.3797
	16	21.5742	41.3680 73	46.6758	71.0144
	17	21.8828	41.6199 74	47.2754	71.6492
	18	22.1914	42.0418 75	47.8750	72.3484
	19	22.5020	42.4441 76	48.4746
	20	22.8105	42.8660 77	49.1348
	21	23.1191	43.2879 78	49.6504
	22	23.4492	43.7098 79	50.3340
	23	23.7578	44.1531 80	50.9121
	24	24.0879	44.5750 81	51.5313
	25	24.4375	44.9754 82	52.1934
	26	24.7676	45.4671 83	52.7930
	27	25.1387	45.9051 84	53.4531
	28	25.4883	46.3699 85	54.0313
	29	25.8398	46.8133 86	54.7344
	30	26.1895	47.2762 87	55.2520
	31	26.5605	47.7195 88	55.9961
	32	26.7512	48.2273 89	56.6777
	33	27.3223	48.7762 90	57.3184
	34	27.7344	49.2625 91	58.0430
	35	28.1055	49.7254 92	58.7461
	36	28.4766	50.1902 93	59.4082
	37	28.8906	50.6766 94	60.0703
	38	29.3027	51.2039 95	60.7520

Wave numbers of the R-branch rotational transitions of the transition between the electronic Astate vibration 1 and the ground state vibration 1 for InBr, for both isotopes. Since the assignment of these levels is unknown, they are simply numbered with index i. Note that in the first entry of the table is the wave

Table 8 .

 8 Franck-Condon factors determined from the detex plots with excitation via ∆v = 0. Theoretical values from Singh[START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF] are given for comparison.

Table 9 .

 9 Relative intensities of each ∆v-band as determined from 20. the ∆v = +2-band, the margin of error for the Franck-Condon factors found is estimated at 10%. The Franck-Condon factors determined from this data are listed in table10. Again, the values found in these experiments are close to, but not in exact agreement with the values found in[START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF].

	Fluorescence band Relative emission
	∆v = +2	0.056
	∆v = 0	0.118
	∆v = -1	0.244
	∆v = -2	0.150
	∆v = -3	0.057
	is visible in

Table 10 .

 10 Franck-Condon factors determined from the detex plots with excitation via ∆v = +1. Theoretical values from Singh[START_REF] Singh | Studies in the A-X and B-X system of InBr[END_REF] are given for comparison.

Table 12 .

 12 The wave number of the band heads of the ∆v = 0 absorption spectrum. A systematic error resulting from a shift of the excitation axis as a whole should be taken into account on top of the error indicated in the table. In this section a calculation has been made to calculate the intensities emitted by the different upper levels in the different ∆v bands based on the Franck-Condon factors.

	v ′ wavenumber (cm -1 ) [21] (cm -1 ) difference (cm -1 )
	4	26605.77 ± 0.07	26605.47	0.30
	5	26603.59 ± 0.06	26603.78	-0.19
	6	26599.70 ± 0.04	26599.66	0.04
	7	26593.65 ± 0.06	26593.61	0.04
	0	26599.00 ± 0.04	26599.00	0.00
	a normal absorption or emission experiment, can be more accurately determined from
	a sr-LIF experiment.

Table 13 .

 13 Franck-Condon factors determined from the detex plots compared with the relative intensities in the presence of a buffergas.

		InBr vapor InBr vapor + Argon
	∆v = +2	0.001	0.000
	∆v = +1	0.003	0.009
	∆v = 0	0.602	0.621
	∆v = -1	0.289	0.267
	∆v = -2	0.088	0.084
	∆v = -3	0.018	0.019

Table 14 .

 14 Rotational constants and anharmonicities determined in this work.constant value B A0 0.058410 ± 0.000002 cm -1 D A0 1.59 • 10 -8 ± 0.01 • 10 -8 cm -1 B A1 0.05809 ± 0.00005 cm -1 D A1 1.8 • 10 -8 ± 0.2 • 10 -8 cm -1 B X1 0.056677 ± 0.00002 cm -1 D X12.83 • 10 -8 ± 0.01 • 10 -8 cm -1

§ difference in vibrational quantum number (∆v = v ′v ′′ , where v ′ denotes the upper and v ′′ the lower vibrational quantum number.)

+ i.e. the processes that redistribute the excited molecules over all the rotational levels in the excitation space of InBr. In other words, the processes that thermalize the distribution over all rotational states.