Microsoft Word - fluo_manuscript_rev_S.Lantz.doc
Absolute measurement of the nitrogen fluorescence 
yield in air between 300 and 430 nm. 
G. Lefeuvrea1, P. Gorodetzkya2, J. Dolbeaua, T. Patzaka, P. Salina 
a APC - AstroParticule et Cosmologie, CNRS : UMR7164 – CEA – IN2P3 – Observatoire de Paris, Université 
Denis Diderot - Paris VII, 10, rue Alice Domon et Léonie Duquet 75205 Paris Cedex 13, France 
Abstract 
The nitrogen fluorescence induced in air is used to detect ultra-high energy cosmic rays and to measure their 
energy. The precise knowledge of the absolute fluorescence yield is the key quantity to improve the accuracy on 
the cosmic ray energy. The total yield has been measured in dry air using a 90Sr source and a [300-430 nm] filter. 
The fluorescence yield in air is  
4.23 ± 0.20 photons per meter  
when normalized to 760 mmHg, 15°C and with an electron energy of 0.85 MeV. This result is consistent with 
previous experiments made at various energies, but with an accuracy improved by a factor of about 3. For the 
first time, the absolute continuous spectrum of nitrogen excited by 90Sr electrons has also been measured with a 
spectrometer. Details of this experiment are given in one of the author's PhD thesis [32]. 
Keywords: nitrogen fluorescence, air fluorescence, extensive air showers, ultra-high energy cosmic rays.  
PACS: 29.30.Dn ;  98.70.Sa 
                                                
1 Actual address: Department of Physics, Syracuse University, Syracuse, NY 13244, USA 
2 Corresponding author: E-mail address: philippe.gorodetzky@cern.ch 
Introduction 
 One of the current challenges in high energy particle physics is to find the origin and nature of 
Ultra-High Energy Cosmic Rays (UHECR, E > 1018 eV). The measurement of their energy spectrum 
could confirm their interaction with the cosmological background (GZK theory). But this is a difficult 
task: the UHECR are not detectable themselves, but only the air shower they induce while going 
through the atmosphere. 
 Experiments which have tried to solve this problem still have non consistent results for 
E > 5•1019 eV. They use different detecting techniques. On one hand, AGASA [1, 2] has an array of 
ground detectors separated by about 0.7 km. Muons and electrons of the showers arriving at the 
ground are sampled. The energy reconstruction is difficult because of the lack of knowledge on 
hadronic cross sections. This method relays on Monte-Carlo particle distributions in the shower 
approximation to find the energy of the incoming particle. On the other hand, HiRes [3] uses 
fluorescence telescopes to detect the continuous development of the shower. The accuracy of this 
method can still be improved if the uncertainties on the fluorescence itself are lowered. Today, the 
Auger experiment uses both methods but still calibrates energy extracted from the ground detectors by 
the fluorescence (also on the ground, [4]). In the future, space-based experiments like JEM-EUSO will 
look for the fluorescence signal from above [5]. 
 Since 1964, several authors [6, 7, 8] have measured the fluorescence yield of each emission 
band of nitrogen (see the spectrum in fig. 5). The fluorescence yield is defined as the number of 
photons produced when an electron goes through one meter of air. In 2002, the cosmic ray community 
[9, 10, 11] decided to start an active campaign of fluorescence measurements for cosmic ray physics. 
Some were made at high energy in electron accelerators, the energy ranging from 80 MeV to 28 GeV 
[12, 13]. Others were made at low energy, around 1 MeV with a 90Sr radioactive source, or much 
lower with electron guns ([14, 15, 18, 21]). These experiments confirmed the hypothesis that the 
fluorescence yield, up to some tens of MeV, is proportional to the energy deposit of the particle, 
dE/dX. The difference between energy loss and energy deposit is of no importance from 0.1 to 
10 MeV [16, 17], which includes our range. Therefore, the absolute scale of the yield can be set with a 
measurement performed with electrons from a 90Sr source. 
 Now, the relative variation of the fluorescence yield with altitude is generally considered as 
quite well known [18]. The parameterization of the yield as a function of altitude is deduced from the 
relationship between pressure and altitude in an atmospheric model [19, 20]. These parameterizations 
are fairly consistent with one another, but can only give the variation of the yield with altitude and not 
the absolute value of the yield. Moreover, measurements of the absolute fluorescence yield have never 
reached a precision better than 13 to 20 % [13, 21]. 
 The experiment presented in this paper has been realized with a double purpose:  
• to improve significantly the precision on the fluorescence yield: it is now 5 % ; 
• to achieve a first continuous measurement of the fluorescence spectrum in the range from 300 to 
430 nm, which had never been done before with a radioactive source. 
1. Experiment 
1.1. Principle 
 Two measurements have been carried out, named “integral” and “spectral” measurements. 
Electrons from a strontium source are used to excite nitrogen. Three detectors are needed, all of them 
based on Photonis photomultiplier tubes (PMT). One detects the electrons (electron-PMT), the other 
two, the photons (photon-PMTs). 
 On one hand, the nitrogen emits fluorescence light through bands emitting lines from 300 to 
430 nm. Thus cosmic ray experiments like HiRes and Auger use band pass filters of that range in front 
of their detectors. This is what is done here in the integral measurement. 
 On the other hand, fluorescence yield experiments generally use narrow filters to separate the 
lines. But the overlap between some spectral filter bandwidth and the close proximity of some 
nitrogen bands make the separation difficult in reality. For this reason, the spectral measurement has 
been performed with an optical grating spectrometer, allowing a continuous check and a good 
separation of the lines.  
1.2. Description of the setup 
This setup has been conceived with the aim of improving the measurement accuracy. The 
fluorescence chamber is a cross-shaped stainless steel chamber (a 6-ports accelerator pipe cross). It is 
schematically shown in fig. 1. Electrons are emitted by a strong 90Sr source (370 MBq) which is 
placed on the top part of the cross. On the bottom part, a plastic scintillator (truncated cone, 20 and 
28 mm diameters, 20 mm thick and its angle is the same that the one made by the electron trajectories 
at the cone periphery). The electrons path is hence defined as the inside of a cone (100 mm height), 
with the source at its top. To homogenize the light between the scintillator and the PMT, a 
kaleidoscopic hexagonal light guide is used to carry the light. The phototube is a Photonis XP2262 
[22] equipped with an active voltage divider (the rate is high, of the order of 2.5 MHz, and very 
stable). 
Figure 1. Schematic view of the fluorescence chamber. The strontium source and the scintillator are inside the 
lead shield. The internal structure of the lead is shown in fig. 2 (side view). 
The consequence of the high counting rate is a high X-ray noise level, due to the interacting 
electrons with the surrounding matter, including the PMT. To shield to a maximum these X-rays, a 
10 cm diameter lead cylinder has been placed inside the chamber with the 90Sr source at its centre. A 
vertical cone is dug in the lead so the electrons can reach the scintillator. This cone is 30 mm diameter 
at its base, slightly wider than the electrons cone defined by the scintillator. Such a cone minimises the 
number of interactions between electrons and the lead: either they are totally stopped (around the 
source), or they touch in a grazing way the cone in their way to the scintillator. A GEANT Monte-
Carlo simulation shows that half of the useful electrons do reach the scintillator without an interaction 
with the lead, the other half touching only once. 
Figure 2. Internal structure of the lead shield. Inside the hollow cone is the smaller cone of the path of the useful 
electrons defined by the source and the scintillator (thick dotted line). 
An horizontal cylinder (40 mm diameter) is also dug in the lead, centred on the optical axis, to 
let the photons go to the photon-PMTs. This structure is represented in fig. 2. 
The effective fluorescence volume is thus, on a first approximation, the intersection of the 
vertical cone with the horizontal cylinder. In a more precise way, all geometrical efficiencies have 
been determined with Monte-Carlo simulations. They take into account all possible interactions 
between electrons and their surroundings and give the exact photon solid angles as well as the exact 
useful electron path length (the length used in the yield expressed in photons per meter). 
 Two kinds of interactions can occur: with the gas and with the lead. First, part of the energy of 
the source electrons is lost by ionization, i.e. creation of secondary electrons. If the secondaries go too 
far away from the useful fluorescence volume, they can either reach the lead or enter the horizontal 
cylinder. Both modify the detection efficiencies (geometry wise) of the photon-PMTs calculated. But 
99 % of these secondaries have an energy smaller than 5 keV. Their range in air at atmospheric 
pressure is less than 2 mm. This has been checked through a geometrical simulation not to be enough 
to have an influence on the solid angles. The effect of these δ rays on the yield expressed in photons 
per deposited energy is explained later in paragraph 3.1 
 The second type of interaction concerns the electrons from the source that do not reach 
directly the scintillator. Some of them are scattered by the lead and then bounce back to the 
scintillator. This has three consequences, studied by a GEANT Monte-Carlo simulation. The first is 
the increase in the electron counting rate, due to the larger solid angle available for the electrons: it is 
doubled by this effect. The second is a modification in the electron energy spectrum, which contains 
more low energy electrons. This has been taken into account in the calculation of the electrons average 
energies. The third is a slight change in the useful electron path length, also taken into account. 
 Some electrons can also bounce from the scintillator back into the fluorescence volume. This 
has been simulated to be a 10-9 effect on the photon detection, hence totally negligible.  
Figure 3. Schematic view of the optical components for the spectral measurement. 
For the integral measurement, fluorescence photons are detected and counted by a Photonis 
XP2020Q (2 in. diameter) placed on the left hand-side of the setup [23]. This PMT will be named 
integral-PMT and it is equipped with a fused silica window. As the fluorescence efficiency is known 
to be low (around 4 photons per meter), it has to work in single photoelectron mode, meaning at a very 
high gain. It is polarized positively (photocathode at ground) in order to reduce its own noise level to 
around 300 Hz (instead of 3 kHz with a negative polarity). This effectively removes the tiny 
discharges in the silica between the photocathode and the outside world. The optical filter on the 
entrance window is a Schott-Desag BG3 (2 mm thick, 34 mm diameter) [24]. It is the same as JEM-
EUSO intends to use, and very similar to those used by Auger. It is glued with Epotec 301-2 [25] 
which has the same refraction index than both the window and the filter.  
Figure 4. Absolute efficiency of the integral-PMT (dashed line) and spectral-PMT (bold line) as a function of the 
size of the effective detecting surface size. A 20 mm diameter diaphragm is used to limit the effective detecting 
area of the integral-PMT to the flattest region of the photocathode. Using a diaphragm of 20 mm diameter (314 
mm2), the efficiency is 18.7%. The spectral-PMT is used in its central region (~ 10×18 mm) where the efficiency 
including the filter is 19.3%. The uncertainty is 1.7% of the efficiency values. Note that the zero suppression on 
the vertical axis. 
For the spectral measurement, photons are analyzed by an optical grating spectrometer (Jobin-
Yvon H25) and counted by another Photonis  XP2020Q, attached to the spectrometer. This PMT will 
be named spectral-PMT. The light rays incoming the spectrometer have to be inside its numerical 
aperture (f = 250 mm, NA = f/4), so a silica converging lens of 150 mm focal length and 46 mm 
diameter [26] is inserted at the right place between the fluorescence volume and the entrance slit of the 
spectrometer. The optical image of this volume is thus on the latter. The optical magnification is 1/7. 
Entrance and exit slits of the spectrometer have the same dimensions: 2 x 7 mm, the maximum size 
available, inducing a resolution (measured with lasers) of 6 nm FWHM. This part of the setup is 
shown in fig. 3. 
The main uncertainty in this kind of experiments, where very few photons are counted, arises from the 
absolute efficiency of the photon-PMTs themselves. The manufacturers provides this value with an 
uncertainty of 15 to 20 % (at 1σ), which is not precise enough. For this reason, we designed a new 
way to measure the absolute efficiency of the photon-PMTs in the single photoelectron mode very 
accurately, based on the comparison with a NIST photodiode.  
The relative efficiency map of the photocathodes of the PMTs working in single photoelectron mode 
was measured with a 377 nm LED every 3 mm in X and Y with a relative precision better than 0.5%. 
This precision was needed to be better than the point to point variations in efficiency (about 2%), in 
order to control these variations. A measurement of the absolute efficiency of one of the map points 
with an accuracy of 1.7%, transforms that relative efficiency map in an absolute efficiency map. A 
dedicated paper, following a patent, will present this measurement. This result was used to determine 
the flattest region of the photocathode (see fig. 4). The effective detecting area of the integral-PMT 
was limited by a 20 mm diameter diaphragm where the efficiency stays roughly constant when the 
diaphragm size is increased. That way, a small error on the diaphragm diameter has a negligible 
consequence on the PMT efficiency (it has however on the solid angle, but this is easy to control). 
Figure 5. Fluorescence spectrum (vertical lines) with relative intensities and absolute response of the photon 
detector (PMT + filter + diaphragm, dashed curve) (source of the fluorescence spectrum : [14]). The integral-
PMT efficiency for this spectrum is 17.8%. 
The absolute spectral efficiency of the detector {PMT + filter + diaphragm} is the dashed line 
superimposed on the fluorescence spectrum in fig. 5. Its value for photons at 377 nm is (18.9 ± 0.3)%, 
and, when convoluted with the fluorescence bands [14] and the relative variations given by Photonis 
[22], is (17.8± 0.4)%. The spectral-PMT is illuminated on a 10 x 18 mm area (smaller area than the 20 
mm circle for the integral PMT, hence all photons at the exit slit of the spectrometer reaching different 
parts of this area would here also have roughly the same probability to produce photoelectrons).  
On their way from the fluorescence chamber to any of the photon-PMTs, integral or spectral-PMT, 
the 20 cm long tubes are baffled to prevent reflected photons to reach the photocathode. 
1.3. Gas 
The gas used is either nitrogen for the adjustments or Messer dry air for the measurements. Fig. 6 
shows the gas setup. It is possible to mix gases and to introduce controlled quantities of different 
impurities and water vapour. Those measurements including pressure variations are planned for the 
future. 
The gas circulates at a rate of 1 L.h-1 through the chamber to avoid impurities build-up and 
degassing of the walls. This circulation is controlled by a precise flow meter [27], followed by a 
pressure controller [28] and an ultra-clean primary pump with an ultimate vacuum of 50 mbar [29]. 
Internal and external pressures and temperatures are regularly monitored during data taking. 
Figure 6. The gas circulation scheme. 
1.4. Data acquisition 
Hardware data acquisition is basically the same that for other authors, but had to be adapted to 
high counting rates. Fig. 7 shows its principle. 
 The lifetimes of excited levels of nitrogen molecules at atmospheric pressure are of the order 
of a few nanoseconds [8, 14, 15, 18, 21]. A measurement based on the time coincidence between an 
electron and a photon is made to discriminate fluorescence from background photons.  
Figure 7. The data acquisition principle 
Basically, an electron in the scintillator is the trigger for the photon measurements. An 
electron produces about 0.16 photon in the 4 cm long fluorescence volume. Geometrical efficiencies 
toward each photon-PMT are very small: 3.69·10-4 for the integral-PMT and 7.48·10-6 for the spectral-
PMT. As a consequence, only 5.9·10-5 and 1.2·10-6 photon respectively reach the PMTs. So, both 
photon-PMTs work in single photoelectron mode. Their spectra are very “pure” in “1 photo-electron”, 
with a negligible amount of “2”. So a discriminator is enough to select the “1 photoelectron” peak. 
This can be seen in fig. 8. 
 ADCs (LRS 2249A, 0.25 pC per channel) record the electron and photon spectra. They are 
used only to check the gain stability of all PMTs during data taking. The “detection inefficiency”, D, 
defined as the proportion of lost fluorescence counts due to the mandatory discriminator threshold on 
the single photoelectron spectrum (see fig. 8), has also been measured and been found to be 3.76 % of 
the measured single photoelectron peak. 
Figure 8. Single photoelectron spectrum, with and without the pedestal. 
Time to Digital Converters (TDCs) (LRS 2228A, 0.3 ps per channel, monohit) are used to 
record the time difference spectra between electrons and photons.  
 Both ADCs and TDCs could be triggered by the electron signal, but this would produce a very 
high random rate. We cleaned up the trigger by replacing it by an electron-photon coincidence. 
 This coincidence is performed by a fast NIM coincidence unit. The photon pulse is 10 ns 
wide. The electron pulse is 100 ns wide to take into account the delay in photon emission (lifetimes of 
the levels). This was set to prepare acquisitions at low pressure, where the lifetimes are longer than at 
atmospheric pressure. Even at very low pressure, 100 ns ensures the loss due to that effect will be 
negligible. In other terms, a coincidence occurs when the photon arrives with less than 100 ns delay 
after the electron. 
 The TDC is stopped by the same electron (see fig. 7), this time as a 10 ns wide pulse and 
delayed by 150 ns. Therefore, the start has a rate much lower than the stop and this inverts the time 
axis. Results can be seen in fig. 9. The useful signal is the peak in the spectrum. It can be easily 
separated from the flat background. The effect on the peak left slope due to the lifetimes of the 
nitrogen levels cannot be seen on this figure because it has been measured in air at atmospheric 
pressure. The narrow peak on the far right-hand side is due to random photons arriving some 
nanoseconds before electrons. These spectra suffer from an important dead time. But the ratio of the 
peak to total spectrum is not affected. The real number of counts is extracted from scalers measuring 
the total spectrum with a small and well corrected dead time. These fast scalers (CAMAC 
CERNSPEC NE003, 25 MHz, and VME V560E, 100 MHz) count all electron, photon and 
coincidence pulses.  
Two thresholds, creating two triggers, are set on the 90Sr spectrum to study the possible 
dependence of the fluorescence yield with the electron energy even if it is difficult to imagine an 
influence other than energy deposit. One is set at ~ 600 keV and another at ~ 1.2 MeV. The 
corresponding average energies are 1.1 and 1.5 MeV. There are around 1 000 photon pulses per 
second counted by the integral-PMT (with a background of 300 Hz) and 40 by the spectral-PMT on at 
the top of the 337 nm line (with a background of 30 Hz). Moreover, the dead times, TM, of both 
electron scalers have been specifically measured and found to be 1.2 % (scaler rate 2·106 Hz) and 
0.7 % (scaler rate 6·105 Hz). 
2. Results 
2.1. Integral measurement 
Figure 9. Example of TDC spectrum for the integral measurement 
The photon yield per unit length, Y, is derived from the signal portion of the TDC spectrum 
through the following formula:  
where: 
• Π is the number of signal counts in the TDC spectrum (see fig. 9) ; 
• H is the integral of this spectrum ; 
• C is the number of coincidences sent to the TDC measured by a scaler. Only H coincidences have 
effectively started the TDC due to its dead time ; 
• 1 + D is the correction to the detection inefficiency ; 
• Ne is the number of electrons according to the scaler ; 
• 1 + TM  is the correction to the dead time of the scaler itself ; 
• Lmoy is the mean length of the electrons path in the fluorescence volume ; 
• εPMT is the efficiency of the integral-PMT ; 
• Tw is  the transmission of the fused silica window closing the fluorescence chamber ; 
• εgeo is the geometrical efficiency. 
 Systematic errors are presented in table 1. The main uncertainty of this experiment is due to 
the high counting rate of the electrons, leading to a non-linear dead time dependence in the TDC 
module. This effect, which varies from channel to channel, depends on the internal TDC time 
constants and is not fully understood. It has been evaluated by using all the module’s channels, and 
another TDC module (CAEN V1290N, multihit) to compare their results. All values are found equal 
within 4% (at 1σ) and this uncertainty has been chosen in a conservative way. In the future, to further 
reduce this uncertainty, fast flash ADCs will be used, allowing to discriminate pulses with and without 
pile-up on an event per event basis. 
On the contrary, the uncertainty on the efficiency of the integral-PMT is very low. This is due 
to the photomultiplier efficiency measurement made especially for the fluorescence measurement by 
the patented method.  
Table 1. Systematic uncertainties of the experiment. 
An example of typical data sample is presented in tab. 2. The low (1.1 MeV) and high (1.5 MeV) 
energy measurements give respectively 3.95 and 4.34 photons per meter. Statistical uncertainties are 
0.2 % and 0.8 %.  
 The energy normalization is made at 0.85 MeV using the dE/dX ratios with values 
interpolated from NIST data [30] and yields respectively 4.05 and 4.41 photons per meter.  
Table 2. Data sample for the low energy measurement. 
The pressure and temperature normalizations are then applied. Each excited level has its own lifetime, 
and the yield can be written with respect to pressure and temperature using the kinetic theory [6]. Thus 
this normalization has been made for each band using previous parameterizations (which give the 
same variations for the first kilometers above the ground [20]). Here, Nagano's model [21], who uses 
the different bands yields is used. The normalized pressure and temperature are those of the US-
Standard 1976 model [19] at sea level: 760 mmHg and 15°C. In this model, for an electron energy of 
0.85 MeV, one finds that the ratio of the yield at 753.8 mmHg and 295.95° K (the 1.1 MeV 
conditions) to the yield at 760.0 mmHg and 288.15° K (the US Standard conditions), is 0.9863, and 
the similar ratio for the 1.5 MeV conditions which are 751.8 mmHg and 296.05° K is 0.9860. These 
ratios are then used to normalize the measured values.  
 Finally, the two normalized values are 4.05 and 4.42 ph/m and have, due to this normalization, 
an added uncertainty of 0.6 %, setting the total relative uncertainty to 5.0 %. They are separated by 
8.5%, inside an error bar (± 1σ). Hence, these are averaged to get the fluorescence yield, at 
760 mmHg, 15°C and for 0.85 MeV electrons:  
4.23 ± 0.21 photons / m. 
This yield per meter is that of the primary particle, therefore it takes into account its 
production of δ rays and their fluorescence. This number can also be written in units of photons per 
deposited energy. For a given energy, these two quantities are strictly proportional, since: 
where Φν is the fluorescence efficiency at the wavelength corresponding to the frequency ν, with the 
yield per deposited energy being [31]: 
The energy of the δ rays is naturally included in the dE/dX of the initial electron. 
Nevertheless, in the context of this experiment, a special care must be taken for the δ rays. A Monte-
Carlo simulation has been performed and shows that here, with the geometry described earlier and at 
atmospheric pressure, only 1 % of the δ rays have more than 5 keV and some of these could be lost in 
the lead before having produced any fluorescence. The effective dE/dX should thus be reduced. This 
simulation shows then that almost 67 % of these δ rays with 5keV or more will produce detectable 
fluorescence. Therefore only 33 % of them are effectively lost and contribute to the reduction of the 
dE/dX. Finally, this reduction, hence the reduction in yield, is 0.4 %. The central value is shifted from 
0.4 % (we measured 4.21 photons/m before applying this correction). The uncertainty stays the same 
at 5 %. This would be very different at lower pressures, where a more extensive Monte-Carlo 
simulation would be required and the correction would be increased. 
The energy deposited by a 0.85 MeV electron in a meter of the US Standard air is 0.2059 MeV  
[30]. The fluorescence yield per deposited energy is thus 20.38 ± 0.98 photons per MeV. 
 The nitrogen yield to air yield ratio has also been measured, (at one electron energy only: 
1.1 MeV), and found to be 4.90 ± 0.01, where the low uncertainty is only statistical: all systematic 
errors compensate, the gas being the only element changed from one measurement to the other. This 
ratio is compatible with what has been measured at different energies : 6 ± 2 at 28.5 GeV [13], 
5.5 ± 0.3 at 1 MeV [21] 
2.2. Spectral measurement 
Spectral measurements are interesting for many purposes. The gas kinetic theory is valid for 
individual bands. Is the sum of the different bands yield equal to the integrated yield used by the 
majority of cosmic ray experiments using fluorescence? How do the different bands change yield 
when temperature and pressure are modified? Up to now, the different bands have been observed 
either with a grating spectrometer [6, 7, 14] in a first method, the electrons being produced by an 
electron gun. Their energy (around 10 keV) is so small that the electron scattering in the gas prevents 
any measurement of path length, hence cannot give a yield in photons per meter. The second method 
[8,15, 18, 21] uses narrow interference filters to analyze the bands. Here, the electrons, as in this work, 
come from a 90Sr source. Fig. 1 of [21] illustrates the method complexity. It is difficult to separate 
overlapping bands in some filters. The only solution to have a good resolution on the bands is to use a 
grating spectrometer, and the easiest way to have electrons with an energy large enough to know their 
path is to use a 90Sr source. The acceptance of a spectrometer is roughly an order of magnitude smaller 
than that of a filter. So the very first step is to prove the feasibility of such a method. This is what is 
done here. 
Hence, in this experiment, a 90Sr source 10 times stronger than in [8,15, 18, 21] was used, The 
counterpart of the high number of incident electrons is that a very special attention has to be given to 
pile-up effects and to the lead shield geometry to avoid the introduction of a large X-ray background. 
Results of the spectral measurements are represented in fig. 10. The whole fluorescence spectrum has 
been measured, from 300 to 436 nm, in dry air at room temperature and normal pressure, with 
electrons of average energy of 1.1 MeV. The time allowed to measure this spectrum was short and the 
spectrometer equipped with an output slit can measure only one wavelength at a time. So it was 
decided to open the slits at their maximum, setting the 1σ resolution to 3 nm. Thus measurements 
were made with steps of 3 nm. But even with 2·106 electrons detected every second, only 
0.16 fluorescence photons per second are recorded in the signal part of the TDC spectrum for the most 
intense line (337 nm). This is the reason why this spectrum has only been made for the “low” energy 
threshold, as defined above. 
 Fluorescence lines are much narrower than the resolution set for the spectrometer as is seen in 
[14]. The absolute yield is thus given by the height of the curve at a given wavelength, and not by the 
area integrated over a bandwidth dλ. The sum of the yields of all lines indicated in fig. 10 is 
3.9 ± 0.8 photons per meter. This value is in close agreement with the result of the integral 
measurement. The 20% uncertainty is due most entirely to the bad knowledge of the spectrometer 
absolute efficiency, especially in the UV.  
 Superimposed on this spectrum is Ulrich’s spectrum [14], convoluted with a 3 nm 
resolution. As it is a relative yield spectrum, it is shown here normalized to the 337 nm line. Our 
spectrum is well compatible with what would measure [14] with such a resolution. 
Figure 10. Spectrum of the absolute fluorescence yield of nitrogen in air between 300 and 436 nm. The bold line 
is the result of the present experiment, and the dashed line is Ulrich's spectrum [14] as if analyzed by our 
spectrometer. Discrepancies could be explained by the ageing of our spectrometer. 
The first observation is the confirmation of the feasibility of this measurement: all the main 
lines are indeed observed. Evidence is given that an absolute spectrum can be measured with a basic 
apparatus, and taking care of reducing the PMT background as explained earlier. The sum of the lines 
yield is consistent with the previous integral measurement. Moreover, its uncertainty is 20 %, when 
previous experiments do not give better than 15 %.  
 The second observation concerns the discrepancies, around 316 nm and beyond 375 nm. The 
extraction of the absolute yield involves the efficiency of the spectrometer. Its spectral efficiency 
curve is provided by the manufacturer with a low accuracy in the UV (which is true also for Ulrich's 
results). Furthermore two effects induce a very important loss in our spectrometer:  
• the ageing of each optical element (mirrors and grating). The spectrometer efficiency can be 
reduced to a value around 15 % after ten years of use ; 
• the extensive use with intense UV light before this experiment. 
At 400 nm, the absolute efficiency of the spectrometer was measured with an accuracy of 
about 2% to be only 15 %, instead of the 61 % given by the manufacturer (who confirms in a private 
communication such a low value compatible with ageing). The method used is very similar to that 
taken to determine the absolute efficiency of the photon-PMTs (comparison to a NIST photodiode). 
This value of 15 % has been used to calculate the absolute yields in the entire spectral range. But there 
is no reason that this loss is constant with respect to wavelength. The 20% uncertainty on the yield 
arises from this unknown but limited variation. The question of getting the absolute efficiency of 
spectrometers in the UV is quite challenging and is the object of specific attentions by the community 
of atomic / spectral physics.  
It is unfortunate that this spectrometer method does not yield yet an accuracy better than the 
"integrated yield" method. It will if the spectrometer resolution can be made high enough to totally 
separate the bands, which is possible if it is equipped with a CCD readout to minimize the experiment 
duration. Then, the absolute efficiency of the spectrometer will have to be determined with a high 
accuracy in the UV, not an easy task according to Ulrich, but possible through our patented method. 
In the future, two measurements will be done: 
• calibrate in an absolute way the old Jobin-Yvon; 
• use the new spectrometer able to measure the full spectrum at once with a 0.1 nm resolution and 
equipped with a light intensifier to measure the fluorescence yield. 
3. Conclusion 
The absolute fluorescence yield of nitrogen in dry air at atmospheric pressure has been 
measured. The precision of the measurement is improved by a factor of three, which has an immediate 
impact on the cosmic ray energies found by HiRes which uses Bunner's [6] yield. Their energies are 
increased by 22%, hence their spectrum is much closer to AGASA’s (which incidentally have been 
recently lowered the energy of their points by 10% [33]).  
The first continuous fluorescence spectrum of nitrogen excited by electrons from a 90Sr source 
was also measured. 
 Next steps are to introduce impurities in the gas, such as argon, water vapour and pollutants. A 
pressure study of the total yield will be made. On another hand, the spectral measurement will be 
improved thanks to a new spectrometer. Papers will follow to account for these measurements, which 
will provide an overall and realistic view of the fluorescence phenomenon. 
Acknowledgements 
 We would like to thank Bernard LEFIEVRE for his help with GEANT simulation of the setup, 
and François LELONG and Jean-Paul RENY for their help in building the bench. 
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[5] http://www.euso-mission.org/docs/RedBookEUSO_21apr04.pdf 
[6] A.N. Bunner, Ph.D. thesis, Cornell University, 1967. 
[7] G. Davidson, R. O'Neil, J. Chem. Phys. 41 (1964) 3946. 
[8] F. Kakimoto et al., NIM A 372 (1996) 527. 
[9] http://www.auger.de/events/air-light-03/ 
[10] http://lappweb.in2p3.fr/IWFM05/index.html 
[11] http://www.particle.cz/conferences/floret2006/ 
[12] F. Arciprete et al., Nucl. Phys. B Proc. Supp. 150 (2006) 186-189 
[13] J.W. Belz et al., Astropart. Phys. 25 (2006) 129. 
[14] A. Ulrich, private communication, and in [9], [10] and [11]  
[15] T. Waldenmaier, PhD thesis, Forschunzentrum Karlsruhe, 2006 
[16] F. Arqueros et al., Astropart. Phys. 26 (2006) 231  
[17] F. Blanco and F. Arqueros, Phys. Lett. A 345 (2005) 355 
[18] M. Nagano, K. Kobayakawa, N. Sakaki, K. Ando, Astropart. Phys. 20 (2003) 293. 
[19] http://www.pdas.com/atmos.htm 
[20] B. Keilhauer et al., Astropart. Phys. 25 (2006) 259. 
[21] M. Nagano, K. Kobayakawa, N. Sakaki, K. Ando, Astropart. Phys. 22 (2004) 235. 
[22] http://www.photonis.com/data/cms-resources/File/Photomultiplier_tubes/spec/XP2262.pdf 
[23] http://www.photonis.com/data/cms-resources/File/Photomultiplier_tubes/spec/XP2020Q.PDF 
[24] Optical filters/Band Pass filter/BG3 in http://www.schott.com/optics_devices/english/download/index.html 
[25] http://www.epotek.com/SSCDocs/datasheets/301-2.PDF 
[26] Edmund Optics C46278 
[27] http://www.bronkhorst.fr/fr/produits/débitmètres_et_régulateurs_gaz/lowdpflow 
[28] http://www.laa.fr/upload/44-4700-Fr-TESCOM.pdf?PHPSESSID=9ae88e24346e03c9765b5350ac7930af 
[29] http://www.knf.fr/images_messages/image1/61.dat 
[30] http://physics.nist.gov/PhysRefData/Star/Text/contents.html 
[31] B. Keilhauer, Ph. D. thesis, Universität Karlsruhe, 2003 
[32] G. Lefeuvre, Ph. D. thesis, Paris 7 University, 2006 (ref : APC-26-06). 
[33] M. Teshima, Ultra High Energy Cosmic Rays Observed by AGASA, XXXIII International Conf. On High 
Energy Phys (ICHEP'06), July 26, 2006, Moscow, Russia.

  The nitrogen fluorescence induced in air is used to detect ultra-high energy
cosmic rays and to measure their energy. The precise knowledge of the absolute
fluorescence yield is the key quantity to improve the accuracy on the cosmic
ray energy. The total yield has been measured in dry air using a 90Sr source
and a [300-430 nm] filter. The fluorescence yield in air is 4.23 $\pm$ 0.20
photons per meter when normalized to 760 mmHg, 15 degrees C and with an
electron energy of 0.85 MeV. This result is consistent with previous
experiments made at various energies, but with an accuracy improved by a factor
of about 3. For the first time, the absolute continuous spectrum of nitrogen
excited by 90Sr electrons has also been measured with a spectrometer. Details
of this experiment are given in one of the author's PhD thesis [32].

Introduction 
 One of the current challenges in high energy particle physics is to find the origin and nature of 
Ultra-High Energy Cosmic Rays (UHECR, E > 1018 eV). The measurement of their energy spectrum 
could confirm their interaction with the cosmological background (GZK theory). But this is a difficult 
task: the UHECR are not detectable themselves, but only the air shower they induce while going 
through the atmosphere. 
 Experiments which have tried to solve this problem still have non consistent results for 
E > 5•1019 eV. They use different detecting techniques. On one hand, AGASA [1, 2] has an array of 
ground detectors separated by about 0.7 km. Muons and electrons of the showers arriving at the 
ground are sampled. The energy reconstruction is difficult because of the lack of knowledge on 
hadronic cross sections. This method relays on Monte-Carlo particle distributions in the shower 
approximation to find the energy of the incoming particle. On the other hand, HiRes [3] uses 
fluorescence telescopes to detect the continuous development of the shower. The accuracy of this 
method can still be improved if the uncertainties on the fluorescence itself are lowered. Today, the 
Auger experiment uses both methods but still calibrates energy extracted from the ground detectors by 
the fluorescence (also on the ground, [4]). In the future, space-based experiments like JEM-EUSO will 
look for the fluorescence signal from above [5]. 
 Since 1964, several authors [6, 7, 8] have measured the fluorescence yield of each emission 
band of nitrogen (see the spectrum in fig. 5). The fluorescence yield is defined as the number of 
photons produced when an electron goes through one meter of air. In 2002, the cosmic ray community 
[9, 10, 11] decided to start an active campaign of fluorescence measurements for cosmic ray physics. 
Some were made at high energy in electron accelerators, the energy ranging from 80 MeV to 28 GeV 
[12, 13]. Others were made at low energy, around 1 MeV with a 90Sr radioactive source, or much 
lower with electron guns ([14, 15, 18, 21]). These experiments confirmed the hypothesis that the 
fluorescence yield, up to some tens of MeV, is proportional to the energy deposit of the particle, 
dE/dX. The difference between energy loss and energy deposit is of no importance from 0.1 to 
10 MeV [16, 17], which includes our range. Therefore, the absolute scale of the yield can be set with a 
measurement performed with electrons from a 90Sr source. 
 Now, the relative variation of the fluorescence yield with altitude is generally considered as 
quite well known [18]. The parameterization of the yield as a function of altitude is deduced from the 
relationship between pressure and altitude in an atmospheric model [19, 20]. These parameterizations 
are fairly consistent with one another, but can only give the variation of the yield with altitude and not 
the absolute value of the yield. Moreover, measurements of the absolute fluorescence yield have never 
reached a precision better than 13 to 20 % [13, 21]. 
 The experiment presented in this paper has been realized with a double purpose:  
• to improve significantly the precision on the fluorescence yield: it is now 5 % ; 
• to achieve a first continuous measurement of the fluorescence spectrum in the range from 300 to 
430 nm, which had never been done before with a radioactive source. 
1. Experiment 
1.1. Principle 
 Two measurements have been carried out, named “integral” and “spectral” measurements. 
Electrons from a strontium source are used to excite nitrogen. Three detectors are needed, all of them 
based on Photonis photomultiplier tubes (PMT). One detects the electrons (electron-PMT), the other 
two, the photons (photon-PMTs). 
 On one hand, the nitrogen emits fluorescence light through bands emitting lines from 300 to 
430 nm. Thus cosmic ray experiments like HiRes and Auger use band pass filters of that range in front 
of their detectors. This is what is done here in the integral measurement. 
 On the other hand, fluorescence yield experiments generally use narrow filters to separate the 
lines. But the overlap between some spectral filter bandwidth and the close proximity of some 
nitrogen bands make the separation difficult in reality. For this reason, the spectral measurement has 
been performed with an optical grating spectrometer, allowing a continuous check and a good 
separation of the lines.  
1.2. Description of the setup 
This setup has been conceived with the aim of improving the measurement accuracy. The 
fluorescence chamber is a cross-shaped stainless steel chamber (a 6-ports accelerator pipe cross). It is 
schematically shown in fig. 1. Electrons are emitted by a strong 90Sr source (370 MBq) which is 
placed on the top part of the cross. On the bottom part, a plastic scintillator (truncated cone, 20 and 
28 mm diameters, 20 mm thick and its angle is the same that the one made by the electron trajectories 
at the cone periphery). The electrons path is hence defined as the inside of a cone (100 mm height), 
with the source at its top. To homogenize the light between the scintillator and the PMT, a 
kaleidoscopic hexagonal light guide is used to carry the light. The phototube is a Photonis XP2262 
[22] equipped with an active voltage divider (the rate is high, of the order of 2.5 MHz, and very 
stable). 
Figure 1. Schematic view of the fluorescence chamber. The strontium source and the scintillator are inside the 
lead shield. The internal structure of the lead is shown in fig. 2 (side view). 
The consequence of the high counting rate is a high X-ray noise level, due to the interacting 
electrons with the surrounding matter, including the PMT. To shield to a maximum these X-rays, a 
10 cm diameter lead cylinder has been placed inside the chamber with the 90Sr source at its centre. A 
vertical cone is dug in the lead so the electrons can reach the scintillator. This cone is 30 mm diameter 
at its base, slightly wider than the electrons cone defined by the scintillator. Such a cone minimises the 
number of interactions between electrons and the lead: either they are totally stopped (around the 
source), or they touch in a grazing way the cone in their way to the scintillator. A GEANT Monte-
Carlo simulation shows that half of the useful electrons do reach the scintillator without an interaction 
with the lead, the other half touching only once. 
Figure 2. Internal structure of the lead shield. Inside the hollow cone is the smaller cone of the path of the useful 
electrons defined by the source and the scintillator (thick dotted line). 
An horizontal cylinder (40 mm diameter) is also dug in the lead, centred on the optical axis, to 
let the photons go to the photon-PMTs. This structure is represented in fig. 2. 
The effective fluorescence volume is thus, on a first approximation, the intersection of the 
vertical cone with the horizontal cylinder. In a more precise way, all geometrical efficiencies have 
been determined with Monte-Carlo simulations. They take into account all possible interactions 
between electrons and their surroundings and give the exact photon solid angles as well as the exact 
useful electron path length (the length used in the yield expressed in photons per meter). 
 Two kinds of interactions can occur: with the gas and with the lead. First, part of the energy of 
the source electrons is lost by ionization, i.e. creation of secondary electrons. If the secondaries go too 
far away from the useful fluorescence volume, they can either reach the lead or enter the horizontal 
cylinder. Both modify the detection efficiencies (geometry wise) of the photon-PMTs calculated. But 
99 % of these secondaries have an energy smaller than 5 keV. Their range in air at atmospheric 
pressure is less than 2 mm. This has been checked through a geometrical simulation not to be enough 
to have an influence on the solid angles. The effect of these δ rays on the yield expressed in photons 
per deposited energy is explained later in paragraph 3.1 
 The second type of interaction concerns the electrons from the source that do not reach 
directly the scintillator. Some of them are scattered by the lead and then bounce back to the 
scintillator. This has three consequences, studied by a GEANT Monte-Carlo simulation. The first is 
the increase in the electron counting rate, due to the larger solid angle available for the electrons: it is 
doubled by this effect. The second is a modification in the electron energy spectrum, which contains 
more low energy electrons. This has been taken into account in the calculation of the electrons average 
energies. The third is a slight change in the useful electron path length, also taken into account. 
 Some electrons can also bounce from the scintillator back into the fluorescence volume. This 
has been simulated to be a 10-9 effect on the photon detection, hence totally negligible.  
Figure 3. Schematic view of the optical components for the spectral measurement. 
For the integral measurement, fluorescence photons are detected and counted by a Photonis 
XP2020Q (2 in. diameter) placed on the left hand-side of the setup [23]. This PMT will be named 
integral-PMT and it is equipped with a fused silica window. As the fluorescence efficiency is known 
to be low (around 4 photons per meter), it has to work in single photoelectron mode, meaning at a very 
high gain. It is polarized positively (photocathode at ground) in order to reduce its own noise level to 
around 300 Hz (instead of 3 kHz with a negative polarity). This effectively removes the tiny 
discharges in the silica between the photocathode and the outside world. The optical filter on the 
entrance window is a Schott-Desag BG3 (2 mm thick, 34 mm diameter) [24]. It is the same as JEM-
EUSO intends to use, and very similar to those used by Auger. It is glued with Epotec 301-2 [25] 
which has the same refraction index than both the window and the filter.  
Figure 4. Absolute efficiency of the integral-PMT (dashed line) and spectral-PMT (bold line) as a function of the 
size of the effective detecting surface size. A 20 mm diameter diaphragm is used to limit the effective detecting 
area of the integral-PMT to the flattest region of the photocathode. Using a diaphragm of 20 mm diameter (314 
mm2), the efficiency is 18.7%. The spectral-PMT is used in its central region (~ 10×18 mm) where the efficiency 
including the filter is 19.3%. The uncertainty is 1.7% of the efficiency values. Note that the zero suppression on 
the vertical axis. 
For the spectral measurement, photons are analyzed by an optical grating spectrometer (Jobin-
Yvon H25) and counted by another Photonis  XP2020Q, attached to the spectrometer. This PMT will 
be named spectral-PMT. The light rays incoming the spectrometer have to be inside its numerical 
aperture (f = 250 mm, NA = f/4), so a silica converging lens of 150 mm focal length and 46 mm 
diameter [26] is inserted at the right place between the fluorescence volume and the entrance slit of the 
spectrometer. The optical image of this volume is thus on the latter. The optical magnification is 1/7. 
Entrance and exit slits of the spectrometer have the same dimensions: 2 x 7 mm, the maximum size 
available, inducing a resolution (measured with lasers) of 6 nm FWHM. This part of the setup is 
shown in fig. 3. 
The main uncertainty in this kind of experiments, where very few photons are counted, arises from the 
absolute efficiency of the photon-PMTs themselves. The manufacturers provides this value with an 
uncertainty of 15 to 20 % (at 1σ), which is not precise enough. For this reason, we designed a new 
way to measure the absolute efficiency of the photon-PMTs in the single photoelectron mode very 
accurately, based on the comparison with a NIST photodiode.  
The relative efficiency map of the photocathodes of the PMTs working in single photoelectron mode 
was measured with a 377 nm LED every 3 mm in X and Y with a relative precision better than 0.5%. 
This precision was needed to be better than the point to point variations in efficiency (about 2%), in 
order to control these variations. A measurement of the absolute efficiency of one of the map points 
with an accuracy of 1.7%, transforms that relative efficiency map in an absolute efficiency map. A 
dedicated paper, following a patent, will present this measurement. This result was used to determine 
the flattest region of the photocathode (see fig. 4). The effective detecting area of the integral-PMT 
was limited by a 20 mm diameter diaphragm where the efficiency stays roughly constant when the 
diaphragm size is increased. That way, a small error on the diaphragm diameter has a negligible 
consequence on the PMT efficiency (it has however on the solid angle, but this is easy to control). 
Figure 5. Fluorescence spectrum (vertical lines) with relative intensities and absolute response of the photon 
detector (PMT + filter + diaphragm, dashed curve) (source of the fluorescence spectrum : [14]). The integral-
PMT efficiency for this spectrum is 17.8%. 
The absolute spectral efficiency of the detector {PMT + filter + diaphragm} is the dashed line 
superimposed on the fluorescence spectrum in fig. 5. Its value for photons at 377 nm is (18.9 ± 0.3)%, 
and, when convoluted with the fluorescence bands [14] and the relative variations given by Photonis 
[22], is (17.8± 0.4)%. The spectral-PMT is illuminated on a 10 x 18 mm area (smaller area than the 20 
mm circle for the integral PMT, hence all photons at the exit slit of the spectrometer reaching different 
parts of this area would here also have roughly the same probability to produce photoelectrons).  
On their way from the fluorescence chamber to any of the photon-PMTs, integral or spectral-PMT, 
the 20 cm long tubes are baffled to prevent reflected photons to reach the photocathode. 
1.3. Gas 
The gas used is either nitrogen for the adjustments or Messer dry air for the measurements. Fig. 6 
shows the gas setup. It is possible to mix gases and to introduce controlled quantities of different 
impurities and water vapour. Those measurements including pressure variations are planned for the 
future. 
The gas circulates at a rate of 1 L.h-1 through the chamber to avoid impurities build-up and 
degassing of the walls. This circulation is controlled by a precise flow meter [27], followed by a 
pressure controller [28] and an ultra-clean primary pump with an ultimate vacuum of 50 mbar [29]. 
Internal and external pressures and temperatures are regularly monitored during data taking. 
Figure 6. The gas circulation scheme. 
1.4. Data acquisition 
Hardware data acquisition is basically the same that for other authors, but had to be adapted to 
high counting rates. Fig. 7 shows its principle. 
 The lifetimes of excited levels of nitrogen molecules at atmospheric pressure are of the order 
of a few nanoseconds [8, 14, 15, 18, 21]. A measurement based on the time coincidence between an 
electron and a photon is made to discriminate fluorescence from background photons.  
Figure 7. The data acquisition principle 
Basically, an electron in the scintillator is the trigger for the photon measurements. An 
electron produces about 0.16 photon in the 4 cm long fluorescence volume. Geometrical efficiencies 
toward each photon-PMT are very small: 3.69·10-4 for the integral-PMT and 7.48·10-6 for the spectral-
PMT. As a consequence, only 5.9·10-5 and 1.2·10-6 photon respectively reach the PMTs. So, both 
photon-PMTs work in single photoelectron mode. Their spectra are very “pure” in “1 photo-electron”, 
with a negligible amount of “2”. So a discriminator is enough to select the “1 photoelectron” peak. 
This can be seen in fig. 8. 
 ADCs (LRS 2249A, 0.25 pC per channel) record the electron and photon spectra. They are 
used only to check the gain stability of all PMTs during data taking. The “detection inefficiency”, D, 
defined as the proportion of lost fluorescence counts due to the mandatory discriminator threshold on 
the single photoelectron spectrum (see fig. 8), has also been measured and been found to be 3.76 % of 
the measured single photoelectron peak. 
Figure 8. Single photoelectron spectrum, with and without the pedestal. 
Time to Digital Converters (TDCs) (LRS 2228A, 0.3 ps per channel, monohit) are used to 
record the time difference spectra between electrons and photons.  
 Both ADCs and TDCs could be triggered by the electron signal, but this would produce a very 
high random rate. We cleaned up the trigger by replacing it by an electron-photon coincidence. 
 This coincidence is performed by a fast NIM coincidence unit. The photon pulse is 10 ns 
wide. The electron pulse is 100 ns wide to take into account the delay in photon emission (lifetimes of 
the levels). This was set to prepare acquisitions at low pressure, where the lifetimes are longer than at 
atmospheric pressure. Even at very low pressure, 100 ns ensures the loss due to that effect will be 
negligible. In other terms, a coincidence occurs when the photon arrives with less than 100 ns delay 
after the electron. 
 The TDC is stopped by the same electron (see fig. 7), this time as a 10 ns wide pulse and 
delayed by 150 ns. Therefore, the start has a rate much lower than the stop and this inverts the time 
axis. Results can be seen in fig. 9. The useful signal is the peak in the spectrum. It can be easily 
separated from the flat background. The effect on the peak left slope due to the lifetimes of the 
nitrogen levels cannot be seen on this figure because it has been measured in air at atmospheric 
pressure. The narrow peak on the far right-hand side is due to random photons arriving some 
nanoseconds before electrons. These spectra suffer from an important dead time. But the ratio of the 
peak to total spectrum is not affected. The real number of counts is extracted from scalers measuring 
the total spectrum with a small and well corrected dead time. These fast scalers (CAMAC 
CERNSPEC NE003, 25 MHz, and VME V560E, 100 MHz) count all electron, photon and 
coincidence pulses.  
Two thresholds, creating two triggers, are set on the 90Sr spectrum to study the possible 
dependence of the fluorescence yield with the electron energy even if it is difficult to imagine an 
influence other than energy deposit. One is set at ~ 600 keV and another at ~ 1.2 MeV. The 
corresponding average energies are 1.1 and 1.5 MeV. There are around 1 000 photon pulses per 
second counted by the integral-PMT (with a background of 300 Hz) and 40 by the spectral-PMT on at 
the top of the 337 nm line (with a background of 30 Hz). Moreover, the dead times, TM, of both 
electron scalers have been specifically measured and found to be 1.2 % (scaler rate 2·106 Hz) and 
0.7 % (scaler rate 6·105 Hz). 
2. Results 
2.1. Integral measurement 
Figure 9. Example of TDC spectrum for the integral measurement 
The photon yield per unit length, Y, is derived from the signal portion of the TDC spectrum 
through the following formula:  
where: 
• Π is the number of signal counts in the TDC spectrum (see fig. 9) ; 
• H is the integral of this spectrum ; 
• C is the number of coincidences sent to the TDC measured by a scaler. Only H coincidences have 
effectively started the TDC due to its dead time ; 
• 1 + D is the correction to the detection inefficiency ; 
• Ne is the number of electrons according to the scaler ; 
• 1 + TM  is the correction to the dead time of the scaler itself ; 
• Lmoy is the mean length of the electrons path in the fluorescence volume ; 
• εPMT is the efficiency of the integral-PMT ; 
• Tw is  the transmission of the fused silica window closing the fluorescence chamber ; 
• εgeo is the geometrical efficiency. 
 Systematic errors are presented in table 1. The main uncertainty of this experiment is due to 
the high counting rate of the electrons, leading to a non-linear dead time dependence in the TDC 
module. This effect, which varies from channel to channel, depends on the internal TDC time 
constants and is not fully understood. It has been evaluated by using all the module’s channels, and 
another TDC module (CAEN V1290N, multihit) to compare their results. All values are found equal 
within 4% (at 1σ) and this uncertainty has been chosen in a conservative way. In the future, to further 
reduce this uncertainty, fast flash ADCs will be used, allowing to discriminate pulses with and without 
pile-up on an event per event basis. 
On the contrary, the uncertainty on the efficiency of the integral-PMT is very low. This is due 
to the photomultiplier efficiency measurement made especially for the fluorescence measurement by 
the patented method.  
Table 1. Systematic uncertainties of the experiment. 
An example of typical data sample is presented in tab. 2. The low (1.1 MeV) and high (1.5 MeV) 
energy measurements give respectively 3.95 and 4.34 photons per meter. Statistical uncertainties are 
0.2 % and 0.8 %.  
 The energy normalization is made at 0.85 MeV using the dE/dX ratios with values 
interpolated from NIST data [30] and yields respectively 4.05 and 4.41 photons per meter.  
Table 2. Data sample for the low energy measurement. 
The pressure and temperature normalizations are then applied. Each excited level has its own lifetime, 
and the yield can be written with respect to pressure and temperature using the kinetic theory [6]. Thus 
this normalization has been made for each band using previous parameterizations (which give the 
same variations for the first kilometers above the ground [20]). Here, Nagano's model [21], who uses 
the different bands yields is used. The normalized pressure and temperature are those of the US-
Standard 1976 model [19] at sea level: 760 mmHg and 15°C. In this model, for an electron energy of 
0.85 MeV, one finds that the ratio of the yield at 753.8 mmHg and 295.95° K (the 1.1 MeV 
conditions) to the yield at 760.0 mmHg and 288.15° K (the US Standard conditions), is 0.9863, and 
the similar ratio for the 1.5 MeV conditions which are 751.8 mmHg and 296.05° K is 0.9860. These 
ratios are then used to normalize the measured values.  
 Finally, the two normalized values are 4.05 and 4.42 ph/m and have, due to this normalization, 
an added uncertainty of 0.6 %, setting the total relative uncertainty to 5.0 %. They are separated by 
8.5%, inside an error bar (± 1σ). Hence, these are averaged to get the fluorescence yield, at 
760 mmHg, 15°C and for 0.85 MeV electrons:  
4.23 ± 0.21 photons / m. 
This yield per meter is that of the primary particle, therefore it takes into account its 
production of δ rays and their fluorescence. This number can also be written in units of photons per 
deposited energy. For a given energy, these two quantities are strictly proportional, since: 
where Φν is the fluorescence efficiency at the wavelength corresponding to the frequency ν, with the 
yield per deposited energy being [31]: 
The energy of the δ rays is naturally included in the dE/dX of the initial electron. 
Nevertheless, in the context of this experiment, a special care must be taken for the δ rays. A Monte-
Carlo simulation has been performed and shows that here, with the geometry described earlier and at 
atmospheric pressure, only 1 % of the δ rays have more than 5 keV and some of these could be lost in 
the lead before having produced any fluorescence. The effective dE/dX should thus be reduced. This 
simulation shows then that almost 67 % of these δ rays with 5keV or more will produce detectable 
fluorescence. Therefore only 33 % of them are effectively lost and contribute to the reduction of the 
dE/dX. Finally, this reduction, hence the reduction in yield, is 0.4 %. The central value is shifted from 
0.4 % (we measured 4.21 photons/m before applying this correction). The uncertainty stays the same 
at 5 %. This would be very different at lower pressures, where a more extensive Monte-Carlo 
simulation would be required and the correction would be increased. 
The energy deposited by a 0.85 MeV electron in a meter of the US Standard air is 0.2059 MeV  
[30]. The fluorescence yield per deposited energy is thus 20.38 ± 0.98 photons per MeV. 
 The nitrogen yield to air yield ratio has also been measured, (at one electron energy only: 
1.1 MeV), and found to be 4.90 ± 0.01, where the low uncertainty is only statistical: all systematic 
errors compensate, the gas being the only element changed from one measurement to the other. This 
ratio is compatible with what has been measured at different energies : 6 ± 2 at 28.5 GeV [13], 
5.5 ± 0.3 at 1 MeV [21] 
2.2. Spectral measurement 
Spectral measurements are interesting for many purposes. The gas kinetic theory is valid for 
individual bands. Is the sum of the different bands yield equal to the integrated yield used by the 
majority of cosmic ray experiments using fluorescence? How do the different bands change yield 
when temperature and pressure are modified? Up to now, the different bands have been observed 
either with a grating spectrometer [6, 7, 14] in a first method, the electrons being produced by an 
electron gun. Their energy (around 10 keV) is so small that the electron scattering in the gas prevents 
any measurement of path length, hence cannot give a yield in photons per meter. The second method 
[8,15, 18, 21] uses narrow interference filters to analyze the bands. Here, the electrons, as in this work, 
come from a 90Sr source. Fig. 1 of [21] illustrates the method complexity. It is difficult to separate 
overlapping bands in some filters. The only solution to have a good resolution on the bands is to use a 
grating spectrometer, and the easiest way to have electrons with an energy large enough to know their 
path is to use a 90Sr source. The acceptance of a spectrometer is roughly an order of magnitude smaller 
than that of a filter. So the very first step is to prove the feasibility of such a method. This is what is 
done here. 
Hence, in this experiment, a 90Sr source 10 times stronger than in [8,15, 18, 21] was used, The 
counterpart of the high number of incident electrons is that a very special attention has to be given to 
pile-up effects and to the lead shield geometry to avoid the introduction of a large X-ray background. 
Results of the spectral measurements are represented in fig. 10. The whole fluorescence spectrum has 
been measured, from 300 to 436 nm, in dry air at room temperature and normal pressure, with 
electrons of average energy of 1.1 MeV. The time allowed to measure this spectrum was short and the 
spectrometer equipped with an output slit can measure only one wavelength at a time. So it was 
decided to open the slits at their maximum, setting the 1σ resolution to 3 nm. Thus measurements 
were made with steps of 3 nm. But even with 2·106 electrons detected every second, only 
0.16 fluorescence photons per second are recorded in the signal part of the TDC spectrum for the most 
intense line (337 nm). This is the reason why this spectrum has only been made for the “low” energy 
threshold, as defined above. 
 Fluorescence lines are much narrower than the resolution set for the spectrometer as is seen in 
[14]. The absolute yield is thus given by the height of the curve at a given wavelength, and not by the 
area integrated over a bandwidth dλ. The sum of the yields of all lines indicated in fig. 10 is 
3.9 ± 0.8 photons per meter. This value is in close agreement with the result of the integral 
measurement. The 20% uncertainty is due most entirely to the bad knowledge of the spectrometer 
absolute efficiency, especially in the UV.  
 Superimposed on this spectrum is Ulrich’s spectrum [14], convoluted with a 3 nm 
resolution. As it is a relative yield spectrum, it is shown here normalized to the 337 nm line. Our 
spectrum is well compatible with what would measure [14] with such a resolution. 
Figure 10. Spectrum of the absolute fluorescence yield of nitrogen in air between 300 and 436 nm. The bold line 
is the result of the present experiment, and the dashed line is Ulrich's spectrum [14] as if analyzed by our 
spectrometer. Discrepancies could be explained by the ageing of our spectrometer. 
The first observation is the confirmation of the feasibility of this measurement: all the main 
lines are indeed observed. Evidence is given that an absolute spectrum can be measured with a basic 
apparatus, and taking care of reducing the PMT background as explained earlier. The sum of the lines 
yield is consistent with the previous integral measurement. Moreover, its uncertainty is 20 %, when 
previous experiments do not give better than 15 %.  
 The second observation concerns the discrepancies, around 316 nm and beyond 375 nm. The 
extraction of the absolute yield involves the efficiency of the spectrometer. Its spectral efficiency 
curve is provided by the manufacturer with a low accuracy in the UV (which is true also for Ulrich's 
results). Furthermore two effects induce a very important loss in our spectrometer:  
• the ageing of each optical element (mirrors and grating). The spectrometer efficiency can be 
reduced to a value around 15 % after ten years of use ; 
• the extensive use with intense UV light before this experiment. 
At 400 nm, the absolute efficiency of the spectrometer was measured with an accuracy of 
about 2% to be only 15 %, instead of the 61 % given by the manufacturer (who confirms in a private 
communication such a low value compatible with ageing). The method used is very similar to that 
taken to determine the absolute efficiency of the photon-PMTs (comparison to a NIST photodiode). 
This value of 15 % has been used to calculate the absolute yields in the entire spectral range. But there 
is no reason that this loss is constant with respect to wavelength. The 20% uncertainty on the yield 
arises from this unknown but limited variation. The question of getting the absolute efficiency of 
spectrometers in the UV is quite challenging and is the object of specific attentions by the community 
of atomic / spectral physics.  
It is unfortunate that this spectrometer method does not yield yet an accuracy better than the 
"integrated yield" method. It will if the spectrometer resolution can be made high enough to totally 
separate the bands, which is possible if it is equipped with a CCD readout to minimize the experiment 
duration. Then, the absolute efficiency of the spectrometer will have to be determined with a high 
accuracy in the UV, not an easy task according to Ulrich, but possible through our patented method. 
In the future, two measurements will be done: 
• calibrate in an absolute way the old Jobin-Yvon; 
• use the new spectrometer able to measure the full spectrum at once with a 0.1 nm resolution and 
equipped with a light intensifier to measure the fluorescence yield. 
3. Conclusion 
The absolute fluorescence yield of nitrogen in dry air at atmospheric pressure has been 
measured. The precision of the measurement is improved by a factor of three, which has an immediate 
impact on the cosmic ray energies found by HiRes which uses Bunner's [6] yield. Their energies are 
increased by 22%, hence their spectrum is much closer to AGASA’s (which incidentally have been 
recently lowered the energy of their points by 10% [33]).  
The first continuous fluorescence spectrum of nitrogen excited by electrons from a 90Sr source 
was also measured. 
 Next steps are to introduce impurities in the gas, such as argon, water vapour and pollutants. A 
pressure study of the total yield will be made. On another hand, the spectral measurement will be 
improved thanks to a new spectrometer. Papers will follow to account for these measurements, which 
will provide an overall and realistic view of the fluorescence phenomenon. 
Acknowledgements 
 We would like to thank Bernard LEFIEVRE for his help with GEANT simulation of the setup, 
and François LELONG and Jean-Paul RENY for their help in building the bench. 
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